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Tornado Hazard to Class 1 Electrical Conduits at Pilgrim Nuclear Generating Station
	ML20117K905
Person / Time
Site:	Pilgrim
Issue date:	12/31/1987
From:	Abbott G, Johnson B; SCIENCE APPLICATIONS INTERNATIONAL CORP. (FORMERLY
To:	;
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ML20117K845	List: ML20117K844; ML20117K851; ML20117K860; ML20117K895; ML20117K905;
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i 4 TORNADO HAZARD TO CLASS 1 ELECTRICAL CONDUITS AT PILGRIM NUCLEAR GENERATING STATION T)e.c. 19 B'7 B a Ro *(0M 8i saDDs0 87 to2.3 5.E. # E309 hred 8 n 61 Prepared for Boston Edison Company 25 Braintree Hill Park Braintree, Massachusetts 02184 Prepared by: Bryce Johnson, Principal Investigator Gaynor Abbott, Consultant [ Science Applications International Corporation 5150 El Camino Real Los Altos, California 94022 -(415)960-M2.L Approvals: f -_=- s Dr'. Bry6e W. Johnson Principal Investigator 3b Dr. Thomas E. Albert Quality Assurance Reviewer

TABLE OF CONTENTS SECTION DESCRIPTION PAGE

1.0 INTRODUCTION

1-1

1.1 Background

1-1 1.2 Summary 1-4 1.2.1 Rate of Damage to Electrical Conduits 1-4 1.2.2 Significance of Results 1-5 2.0 METHODOLOGY 2-1 2.1 Direct Wind Failure Rate 2-1 2.1.1 Rate of Wind Impingement Determination) 2-1 2.1.2 Probability of Full-Force Win s (P Determination) 2-4 2.1.3 Prohbility of Damaging Conduits Given External Tornado Damage (C Determination) 2-8 f 2.2 Failure Rate Caused by Tornado Generated Missiles 2-8 2.2.1 Previous Tornado Missile Study 2-8 2.2.2 Application of Previous Study 2-9 3.0 UNCERTAINTY / ERROR ANALYSIS 3-1 3.1 Error Sources 3-1 3.2 Modeling Accuracy 3-2 3.2.1 Direct Wind Damage 3-2 3.2.2 Missile Damage 3-3 3.3 Uncertainty Parameters 3-4 3.3.1 Random Event Uncertainties (Variance) 3-4 3.3.2 Error Factor 3-6 3.4 Errorin Simulation Analysis 3-8 4.0 SIGNIFICANCE OF RESULTS 4-1 4.1 Conservatism 4-1 4.2 Acceptability for Licensing Considerations 4-2 4.3 Conclusion 4-3

5.0 REFERENCES

5-1 APPENDIX A Details of Tornado Data A-1 APPENDIX B Details of Calculations B-1 B.1 Damage Rate from High Winds B-5 B.2 Damage Rate from Missiles B-10 APPENDIX C Computer Code Listings C-1 APPENDIX D Methodology Comparison D-1 i

1

SUMMARY

OF TABLES AND FIGURES i SECTION DESCRIPTION PAGE 1 Table 1-1 Damage Rate Summary 1-4 i Table 2-1 Conditional Probabilities of Tornado 2-5 Intensity Variation Table 2-2 Suinmary of Missile Strikeg on Auxiliary Bay 2-14 Table 2-3 Summary of Strikes on Water Intake Structure 2-16 Table A-1 Tornado Data Comparis6n A-5 1 Table A-2 NSSFC Tornado Data on Pilgrim 1 Site A-6 l Table B.1-1 Probability of Exceeding 217 mph Normal Velocity Winds from Specific Tornadoes on Walls of Specific j Structures B-8 j Table B.2-1 Location of Candidate Missiles for PILGRIM 1 l Analysis B-12 Table B.2-2 Missile Penetration Parameters B-42 Table B.2-3 Summary of Strikes on Auxiliary Bay B-44 Table B.2-4 Summary of Strikes on Water Intake Structure B-51 i i l l Figure 1-1 General Location of Unprotected Class 1 Conduits 1-2 Figure 1-2 Detailed Location of Unprotected Class 1 Conduits 1-3 j Figure 2-1 Large Scale Regionalization for Tornado 2-3 1 Risk Analysis l Figure 2-2 Illustration of Impact Wind Direction 2-7 i Figure 2-3 Strike Locations on Auxiliary Bay 2-11 Fj ure 2-4 Elevation View of Missile Strike Locations 2-12 i g on Auxiliary Bay and Above Figure 2-5 Tornado Missile Strikes on Water Intake Structure 2-17 1 Figure 2-6 Tornado Missile Strikes on South Face of Water 2-18 d Intake Structure Figure A 1 Excerpt from Reference 1 on 10j Wind Probability A-3 Figure A-2 Excerpt from Reference 1 on 10 Wind Probability A-4 Figure B.1-1 Two Locations of Maximum Wind Impact from Same Tornado B-7 Figure B.1-2 Corridors Capable of Producing Perpendicular Winds B-9 Figure B.21 Change of Distribution in Candidate Missiles B-11 Figure B.2-2 Standard PILGRIMI Output B-25 Figure B.2-3 Output for Hits on Auxiliary Bay B 27 Figure B.2-4 Missile Interaction with Steel Walls B-30 i Figure B.2-5 Compressive Energy in Wall B-33 Figure B.2-6 Shear Energy Associated with Missile Impact B-34 Figure B.2-7 Steel Wall Thickness Parameters B-39 Figure B.2-8 Parameters for Calculating Penetration Probability B-41 Figure C-1 PILGRIM 1 Code Listing C-2 ii

l Y i l l

SUMMARY

OF TABLES AND FIGURES (condnued) SECTION DESCRIPTION PAGE Figure C-2 HITWAT Code Lisdng C-33 Figure C-3 STEEL Code Lisdng C-34 Figure C-4 CONPEN Code Listing C-35 Figure C-5 BASIC Program for Calculadng Normal Windspeeds on any Given Wall C-36 l l l l iii

i I

1.0 INTRODUCTION

l l l

1.1 BACKGROUND

In 1987, Class 1 electrical conduits were identified in the Class II portions of the reactor building auxiliary bay and water intake structure of the Pilgrimi Nuclear Generating Station. Original design basis calculations could not be found that i defended the acceptability of this condition. Science Applications International Corporation was commissioned to recreate a design basis, site-specific Tornado Hazard Analysis. Figure 1-1 shows the location of the lines on an overall plan view i l of the plant and details are shown on Figure 1-2. The study reported herein has determined the risk of tornado-induced compromise of 6ese lines in the as-built configuration. j Two hazards are presented by tornadoes. The first is the direct wind damage to - the exterior walls of structure with possible resultant conduit damage accompanying i the collapse of the walls. The. second is tornado missile damage to the lines following penetration of the protective walls (and roofs). A third effect, which can damage structures but is not considered hazardous to the electrical conduits housed therein, is the pressure drop as the center of the tornado passes directly over structures of concern. Although this effect can cause walls and ceilings to rupture outward, it is not a direct hazard to the conduits housed therein. Synergism with the other damage mechanisms (for example, the possible removal of a protective I wall by the pressure drop prior to missile impingement) has been considered, but has been dismissed because the " blow-out" of small doors and ventilation ports would prevent any wall or roof compromise. Tornado data was updated for the plant from the records kept by the National Severe Storms Forecast Center (NSSFC) in Kansas City. A summary of the data and the complete data set has been included in Appendix A. Also contained in Appendix l A is a comparison of the data with that of the recently published book on tornado i l statistics by T.T. Fujita of the University of Chicago (1). E k i 1-1 4 l r

? e 1 j Watpr intake y Structure 5 72 I I l l i I e i Auxiliary Bay \\ I 1, d ] k I Figure 1-1. General Location of Class 1 Conduits 1-2

i l Water intake Structure a D L Auxiliary Bay l c 1 Figure 1-2. Detailed Location of Class 1 Electrical Conduits I-3 i

The direct wind hazard is determined by bounding the rate at which tornado winds in excess of the wall resistance capability impact the regions of concern. This bounding estimate is described in Section 2.1 and the details are provided in Appendix B-1. An analysis of the missile hazard is based on a detailed study performed for the Unit 2 design in 1978 (2). Al preliminary hand-calculation result based on extrapolating the earlier Unit 2 results indicated that the missile risk was acceptable. This motivated the reactivation of the computer code written for the 1 Unit 2 study to provide a detailed assessment of the hazard to the two referenced conduit locations. 1.2

SUMMARY

1.2.1 Rate of Damare to Electrical Conduits An upper limit estimate of the rate at which tornado damage is imparted to electrical conduits in the intake structure and to the auxiliary bay is summarized in Table 1-1. Table 1-1 DAMAGE RATE

SUMMARY

Predicted Fraction From Conduit Location Failure Rate (yr.~l) Missiles Auxiliary Bay 3.2E-07 N,.~5.fD 0 D <0.1

2. A E ~)

u5 I k6 4 6.7E-07j6.2E-7 v Water Intake <0.1 The risk due to missiles is only 10 percent of the total, which is consistent with other studies (3.4). The auxiliary bay sustained a great many more missile strikes in the simulation study simply because its area (which includes that of the reactor above it from which missiles fall down onto the auxiliary bay roof) provides a much 90 percent confidence limits discussed in Section 3. 1-4

larger " target" than does the water intake structure. However, the missile damage rate is dominated by hits from a very few heavy, penetrating missiles and the water intake structure sustained more hits of this type. The reason for the numerical difference in the risk to the two structures is that the water intake structure has a conduit mounted directly to the outside wall

and, hence, this conduit fails each time the wall fails.

Class I conduits inside the auxiliary bay are well removed from the exterior walls and separated from them by intervening equipment. 1.2.2 Sienificance of Results Many of the parameters required for this analysis cannot be determined with great precision. Therefore, the estimates for these parameters have been made to assure conservatism (overestimation of the failure rate). These numbers, therefore, are considered to represent an upper limit to the probability estimate. Elements of conservatism used in this study include: o Conservative tornado impingment rate (using high end of range of estimates) Use of high conditional probability of conduit failure, given extemal wall o compromise by direct wind, or by missiles o Use of conservative number of available missiles Use of conservative missile flight parameters o Use of conservative missile penetration parameters. o Details of these conservative elements are described throughout the report, and are summarized in greater detail in Section 4. - Even with the built-in conservatism, the numbers are very low. They are also consistent with those of similar studies (M) where both direct wind damage and missile damage were considered. Furthermore, use of simulation studies and associated risk determination has been established (see Section 4) as a valid means of assessing safety for nuclear plant licensing purposes. 1-5

T The results of this analysis clearly demonstrate that the as-built design provides more than adequate tornado protection. 1 l 1 1-6

2.0 METHODOLOGY 2.1 DIRECT WIND FAILURE RATE The failure rate (R ) for direct wind impingement on the conduits of interest is f determined as the calculated rate at which damaging winds impact the point of interest times a conditional probability that the walls in question are exposed to full force winds (near perpendicular) times a conditional probability, given a wall collapse, that a failed conduit results. Mathematically, R = R,P,Cf (2-1) f where R, = rate at which wind velocities in excess of that required to fail the wallimpinge on the site, P, conditional probability, given a wall failing tornadic wind, that = the wall orientation allows it to be exposed to the full (wall-failure) force of the wind, Cf conditional probability, given wall failure, that the conduit also = fails. 2.1.1 Rate of Wind Impingement GL.. Determination) The annual probability (rate), R,, at which damaging tornadic winds impact any given point is determined by the ratio of the total tornado damage area created annually within a given area of observation to that area of observation. This is written as ' R, = NA /(YA ) (2-2) d t where N is the total number of tornadoes observed over a given number of years Y, and Ad and A are, respectively, the average damage area per tornado and the total t 2-1 \\.

area of observation. For determining the rate of tornado impact on regions whose size is significant in comparison to the average damage area of the tornado, it is necessary to use the union of the area of the target region and A. For the d auxiliary bay and the intake structure, a point approximation is adequate so that Ad is merely the damage area of the tornado. There is no direct measure of damage area associated with tornado winds exceeding j a given specific velocity. This factor has to be calculated from other available data. The usable data are 1) the average damage area associated with any given I tornado (which is available on an "F" number basis-see References 1, 2, d, 5 and Appendix A), 2) the fraction of the total path length (length over which any damage is observed) over which plant-damaging winds are actually observed for those tornadoes rated as having damaging and higher wind velocities, and, 3) the fraction of the total damage width over which damaging winds are manifest for tornadoes rated as having such winds. The threshold of damaging winds for these structures has been determined to be 217 mph. Tomadoes that have wind speeds in excess of 207 mph, but less than 260 mph, are classified as F4. These F4 tornadoes provide the statistical basis for both N and A i d n Eq. 2-2. Use of F4 and above tornadoes is conservative since these include those whose maximum wind are below the damage threshold. The j conservatism is further augmented by the fact that tornado wind speeds within the higher F-number (such as F4) tornadoes cluster near the lower limit of the range within each category, so that proponionately more tornadoes exhibit wind speeds of lower than 217 mph. In the 37-year tornado data base of the Pilgrim region (Appendix A) only two tornadoes of category F4 and above were observed. Reference 6 (Table I 6) gives an F4 tornado rate of 2.49 E-06 per square mile per year for United States region C (the region of Pilgrim 1, see Figure 21). This is the rate per square mile at which F4 tornadoes originate (i.e., have their initial touch-down points). This rate is N/(YA ) of Eq. 2-2. This data is based on a 31-year record over approximately t 800,000 square miles. The data base of Appendix A is for 65,000 square miles (only about half of which is over land where tornado parameters are measurable). If the land portion of the area of observation of Appendix A is considered the true area 2-2

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of observation, then the F4 tornado rate determined therefrom closely matches that of Region C. In Eq. 2-2, A i d s an average of the F4 tornadoes reported in Appendix A and those reported for the Savannah River Region (a total of 9 tornadoes). These form the total SAIC data base of F4 tornadoes. Their average area is 7.8 sq. miles (Appendix B-1). Table 2-1 is from Reference fi and shows that the F4 wind classification is manifest for only 21.2 percent of the total damage path length of F4 tornadoes. For the width over which F4 and greater (>207-mph) winds are manifest, reliance has been placed on the theoretical wind field model of the tornado (Appendix A of Reference 2), which predicts a wind-speed variation according to the negative 1.6 power of radius outside the region of maximum wind and a positive linear variation within the region of maximum wind. In Appendix B it is shown that the average ratio of the widths of >207 mph winds to total width based on the wind field model is 0.472 (based on an assumed average observable damage width corresponding to a 60 mph wind); the DAPPL* formula predicts the ratio to be 0.505. Therefore, on the average, within damage areas reported for tornadoes rated as having >207 mph winds (F4 and above tornadoes), only 10 percent (0.212 x 0.472 = 0.1) of the damage area reported is actually exposed to winds exceeding 207 mph. In Appendix B, an Ad or F4 tornadoes of 0.78 sq. miles is dedved. Therefore, R,, f of the above equations is 2E-06 per year. Attention is called to the extreme conservatism of this estimate compared to the value of IE-7 per year indicated in the recent Fujita publication (see Figure A-2). 2.1.2 Probability of Full-force Winds (P. Determination) Tornadoes typically are not significantly impacted in the macroscopic sense by hilly terrain (observations indicate that they follow the ground surface fairly well). l

DAPPL is an acronym for " Damage Area Per Path Length". See Eq. 3 of Reference 1 I

2-4 l

j I Table 2-la CONDITIONAL PROBABILITIES OF TORNADO INTENSITY VARIATIONb i Local Maximum Tornado Intensity i Path Length <I O I I I I I I l 2 3 4 S 6 Intensity i i I 0 0 0 0 0 0 0.120 6 a From Ref. 6 b The fraction listed is that associated with the local intensity (left column) for a tornado classified according to the maximum intensity of the top row. l t l e 2-5

However, local effects on low or ground-level wind velocities have to be manifest by such terrain features because the full-circle characteristic of high velocity winds (see Figure 2-2) is broken up by the presence of close-by hills, particularly those as steep as the one at Pilgrim. Only tornadoes approaching from the water side would be expected to have leading-edge tangential velocities comparable to those of flat terrain or even comparable to those at higher elevations in the tomado. Even these tornadoes would be expected to have their trailing edge wind velocities diminished by the presence of the hill and the effective area of the damaging wind would be diminished. Only a small percentage of the tomadoes approach from the ocean side at the Pilgrim site (see the tornado rose of Figure 2-2).

Although, i
unfortunately, there exist neither definitive data nor theoretical models for this effect, we call attention to the phenomenon since it adds additional evidence to the conservatism of the analysis. 1 There are some factors affecting the availability of full-force winds, however, which can be undeniably demonstrated (although not easily quantified). An example is that west-facing walls of sturdy buildings (such as a reactor building) cannot be impacted by an east wind. The effects of these phenomena are estimated below on a heuristic basis by estimating the fraction of given specific damage " corridors" over which given walls being analyzed cannot be impacted by the full wind. For j conservatism,200 mph, rather than 217 mph, winds have been utilized. From the average damage path and fraction exposed to 200 mph winds (using the theoretical wind field model), the annulus of winds shown in Figure 2-2 was constructed. This annulus is the locus of all winds in excess of 200 mph for the "mean" tornado of all F4 tornadoes, and observation of its location relative to the wall being analyzed provides the basis for P,. The damage corridor through which the center point of the average-sized F4 tornado can pass and still impact the poiht in question by >200 mph winds is indicated on Figure 2-2 and is equal to the total path width " swept out" by >200 mph winds. Note that the annulus of counter clockwise wind shown on the figure cannot impact the auxiliary bay wall with winds within the corridor at less than 45 degrees off the surface normal (70 percent of the wind velocity. and only 50 percent of the wind force for a normal-- perpendicular--impact). For the full traversal of this average tornado over corridors parallel to all the tornado octants of the tornado rose (Figure 2-2), only 2-6
/ Range of 200 mph wind Tome i Translation f Intake Structure 2 Auxiliary ~l Bay tial Wind Northeast Tornado Conidor N E Graphical Tornado Direction Probability [ W SE SW S Figure 2-2. Illustration of impact Wind Direction 2-7
k i 33 percent of the cm.,es produce winds impacting either the auxiliary bay or the j water intake structure at impact angles less than 45 degrees with the normal. This { fraction was deliberately overestimated to maintain conservatism. I An analytical evaluation for this effect is derived in Section B.1.2 of Appendix B j and it 'is applied therein to specific tornadoes simulated in Appendix B.2. These l results verify that the 0.33 value for this factor is, indeed, conservative. 2.1.3 Probability of Damaring Conduits Given External Tornado Damage (C Detsmination) f j This parameter is difficult to estimate exactly for a large category of wall failure i 3 modes when the equipment of interest is well removed from the wall which fails (as in the auxiliary bay as shown in Figure 1-2). A conduit is actually attached to the Cutside wall in the water intake structure, hence the probability, C, is 1 for that f j wall. In the auxiliary bay, the conduit is well anchored, and is separated from the j outside wall both by significant space and by considerable steel-constructed j mechanical equipment. Further, these steel conduits are not inherently frangible. It is assumed that only a direct impact by a portion of the failed wall or some secondary missile created locally by the failure could break these conduits. Therefore, based on these admittedly qualitative considerations, a conditional damage probability of 0.5 given either wind damage or missile penetration has been assumed for all walls except the sout wall of the intake structure for which the probability is 1. These C values form the basis for the results listed in Table 1-1. f 2.2 FAILURE RATE CAUSED BY TORNADO GENERATED MISSILES 'I 2.2.1 Previous Tornado Missile Study Reference 2 is a repon of a detailed simulation analysis completed in 1978 of the tornado missile hazard to the proposed Pilgrim Unit 2. This study has been compared in detail with the results of the EPRI-sponsored work (1) in Reference d and the results are very comparable. The Reference 2 study included a detailed modeling of the wind missile interactions as well as the interaction of the missile with the walls of the plant. It also included a detailed inventory of candidate missiles which was based on an exhaustive survey of the plant and surroundings. 2-8
Most of the missile inventory derived for Reference 2 is valid for this investigation. The methodology of Reference 2 is summarized in Appendix B.2 and the associated computer code, as updated for this study, is included in Appendix C. The use of the previous analysis and required modifications made thereto for this study are summarized below with details available in Appendix B.2. 2.2.2 Application of Previous Study Missile Inventory The inventory of candidate missiles used for the Reference 2 study was updated for this study based on aerial photographs provided as well as an actual site visit. The most significant change was the elimination of parking lots for construction workers (automobiles are primary tornado missiles). Some of the missiles associated with plant I were eliminated and, of course, all of the missile associated with plant 2 were eliminated. The large " construction laydown" area of the first study was included in this study and its location relative to plant I was kept the same as the previous location relative to plant 2. This area contained the greatest number and the most damaging of the missiles for the previous study. Its location for this study matches that of the new administration building to the east of the plant. These missiles approximate the missiles which would be generated from tornado destruction of those current office facilities. Such a replacement is conservative because many more missiles are involved in the construction laydown area and they are damaging missiles. Missiles generated by destruction of residences or typical frame office buildings are highly aerodynamic in general, but they do relatively little damage upon impact since they are frangible and of relatively low density. Missile Impact Rate on Auxiliary Bay and Water Intake Structure As with the previous analysis, the missile strikes on the structures were recorded from the operation of the simulation code WIZ (renamed PILGRIM 1) as described in Appendix B-2. An imaginary set of contiguous rectangular parallelepipeds is used to enclose the plant itself (including the auxiliary bay) and a single, separate one encloses the water intake structure. Missile impingement on these parallelepipeds is recorded in the code and an output of missile strike location by coordinates and missile velocity by components parallel to the plant coordinates are provided for 2-9
1 subsequent analysis of missile-plant interaction. Missile-Plant Interaction 4 In the previous study a separate code, MISBECO, calculated missile-plant interaction based on a detailed plant model and on equations of free-flight ballistics for missile transport and predetermined tabular dhta on missile-wall interactions. For this i study, since only one wall interactio'n per missile is appropriate, it was determined to be more efficient to calculate the probability of wall penetration by hand once missile impingement on the region ofinterest is determined. The precise location of missi*e strike is determined from the missile location and velocity components on the envelope (imaginary rectangular parallelepiped) surrounding the volume of interest. Figures 2-3 and 2-4 show the location of strikes on the auxiliary bay for the first 1.9 million years simulated. In same time period, only three strikes on the intake structure occurred, and these were on the opposite corner of the intake structure from the point of location of the critical conduits. i i Wall penetration algorithms used were the CEA-EDF formula for concrete (2) and the Hagg-Sankey method for steel (8) (for the roof of the auxiliary building). These have been recommended in EPRI-sponsored studies (2. 9)_ and they are an improvement over what was available for the previous study (2). Wall penetration is the only mechanism of wall failure which is damaging to the conduits. Concrete spallation fragments' are not considered sufficiently hazardous to damage the conduits, and conduit integrity does not really depend on wall structure. No missile strike is considered sufficiently hazardous to collapse the building. Probability of penetration is determined as follows:
1. The capability to penetrate the wall at the velocity of impact in its most penetrating orientation (that one presenting the minimum impact area) is determined--if penetration cannot occur in this orientation, then penetration probability is 0.
2-10
lll' \\lllIl l l l:l I t) l A 9 1 4 YAB YRA ll IXU p 2 A N 1 O S N 3 R 1 A R E w O Y 5 N e M
9. W)
T x. N 1E 1 I A RV L 6 ON P F A SL NP 1 / O( u ITACO 0\\ L 1 E 8 1 8 K IR T 3 S 8 / 7 3 1 1 A 2 1 7 e 1 rug iF 6 1 4 1 m .= lll l l
4 i j "AE O 'T c.g 1' e\\ -\\ ff. O M 1 ' .l: ~ y ( e i w c ,g 7 t I 2\\ E ,5 8 sN g b. d 2-12
2. If penetration is predicted at the most damaging orientation, the orientation (effective impact area) is changed until penetration is no longer predicted.

3. Penetration probability is calculated as the ratio of the solid angle representing the total range of penetration orientations to the solid angle representing the total range of wall impact orientations (orientation angles are all assumed to be equally probable).
Details of the above determination are in Appendix B.2. Small computer codes were written for both concrete and steel penetration to facilitate determination of the point of penetration (in orientation of the missile) and to enhance QA checks on these calculations. These codes are included in Appendix C. Missile impact velocities on the roof of the auxiliary bay from richochets off the reactor building were determined by free fall of the missile from the strike location. Most vertical velocities at impact are small and the collision of the missile with the reactor wall is considered sufficiently inelastic that no " memory" of the vertical velocity prior to collision is possible. Futhermore, the wind which propelled it into the wall in the first place will likely keep it pinned against the wall for some finite time--probably of sufficient duration to actually impede free fall. Therefore, the free-fall assumption is considered conservative. The roof of the auxiliary bay is built on I-beams on an 11.5 x 19-ft grid and the I-beams on the side are 8 ft apart. No missile which collides with an I-beam can penetrate the enclosure. No credit has been taken for this probability of strike despite the fact that some missiles (i.e., trees and cars) have some dimensions larger than the openings in the grid. Table 2-2 is an example of missile strikes on the auxiliary bay (occurring over about 2 million years). The summary for the data base used to calculate the value of Table 1-1 is in Appendix B.2-1. The reference coordinate system is centered at E5000 and N10000, as indicated on the plot plan of BECO drawing C2. Zero clevation in the coordinate system is the 23-ft ground level at the auxiliary bay. Positive "x" is plant east and positive "y" is plant north. The designation of the l missiles is that of Table B.2-1. Strike designations are as follows: B is on the bay concrete sidewall, and R-B is on the reactor above the roof of the auxiliary bay. 2-13
Table 2-2 EXAMPLE OF MISSILE STRIKES ON AUXILIARY BAY NO.OF VELOCITY MISSIL~c MISSILE IMPACT COMPONENTS PENETRATION HIT DESIG. TYPE POINT (x.v.z) (x.v.z) fos PROBABILITY 1 RB 28 -70,-17,105 145,-6,21 0 2 RB 40 -71,-13,66 127,76,9 0 3 RB 16 -71,-27,86 47,23,-1 0.00005 4 RB 40 -71,+40,12 161,82,7 0 5 RB 23 -71,12,57 42,8,-16 0.06 6 RB 15 71,1,50 76,-50,9 0 7 RB 39 71,-16,122 96,101,-3 0 8 RB 15 -71,-26,76 95,-82,25 0 9 B 15 -122,-12,22 49,-21 -10 0 10 B 16 -122,-17,18 136,24,9 0.00005 11 B 26 -122,-29,+1 146,-18,-9 0.09 12 RB 15 -71,20,84 102,-58,39 0 13 RB 15 -71,14,63 -87,-14,13 0 14 RB 28 -83,-46,31 151,17,26 0 15 RB 26 -122,13,34 102,131,4 0 16 RB 15 -83,-42,61 58,-25,-15 0 17A* RB 21 -83,-38,63 130,-27,29 0 17BI RB 1 -71,-33,58 127,-9,-10 0 18 RB 28 -71,-33,29 141,-7,8 0 19A** RB 40 -71,46,84 140,12,-8 0 19B2 B 40 -122,22,20 143,8,-13 0 19C2 B 40 -122,22,20 21,-17,-1 0
Two missile strikes from same tornado
Three missile strikes from same tomado 2-14
Attention is called to the extremely small likelihood of penetration following a missile strike. Table 2-3 is a summary of the complete number of strikes on the water intake structure. This data base included strikes over 8.5 million years of simulation, and formed the basis for the results listed in Table 1-1 (SE-08 compromises per year). In Figure 2-3, x, y, and z are the coordinates of the strike, x', y', and z' are the velocity components in fps, P is the probability of penetration for that specific I strike and the missiles associated with the missile numbers are those of Table B.2-1. Figure 2-5 is a plan view and Figure 2-6 is a south elevation indicating these strike locations. The number of years of simulation is significant only in that it is adequate to give reasonable statistics. The number of years simulated for the water intake structure differs from that simulated for the auxiliary bay (6.2 million years). This difference is due to times during the simulation process when efficient output algorithms were implemented for obtaining msults. 2-15
Table 2-3 Summary of Strikes on Water Intake Structure Random Number Missile I Y Z X' Y' Z' P Numbers of Years Number -180 148 1.49 101.5 -41.8 -10.5 0 297297 1924701 40 -192 94 5.5 -29.5 61.5 5.1 0 372698 2462280 2 -209 94 2.9 -36 37 2.9 0 537193 3499149 2 -239 94 15.4 74.5 33.2 -4.6 0 583873 3781347 40 -212 94 2.8 -45 54 3.6 0 622760 4045926 2 -228 148 7.7 66 -78 -7.7 0.0105 642264 4194813 26 -247 115.9 12.45 145.6 14.5 -1.6 0.0025 663494 4100924 26 -197 194 5.9 -33 60.9 0.5 0 667454 4370532 2 -247 100 6.8 9.87 6.4 1.3 0 668664 4392598 40 162.7 94 6.3 14.9 83.9 6.6 0 679124 4478316 2 164.3 94 10.1 12.9 89.5 14.1 0 773385 5059593 2 -160 94 5.8 15.52 54.1 0.3 0 804561 5255766 2 196.9 94 11.7 -36.4 73.8 9.1 0 852381 6070159 3 -192 148 0.363 -18.7 84.55 -5.8 0.00213 860907 5589744 2 -229 148 0.236 -1.6 87.88 -5.8 0 902689 5919594 21 -201 94 9.6 72.15 58.71 1.9 0.0004 916027 5984330 26 k43.8 94 10.8 32.1 152.3 -18.4 0.0265 924015 6680949 26 -172 94 2.4 68.8 160.5 -0.8 0.161 1022909 6644733 26 -247 129 14.5 95.9 27.3 -18.6 0 1071503 6810029 1 -247 145.3 11.2 82.4 -19.3 0.7 0 1137733 7234323 40 -147 126.6 16 -47 -34.4 -22 0 1186754 7638991 2 -145 104.3 13.5 -123.9 -22 -23.4 0.38 1199915 7757238 10 =247 125.5 8.9 153.8 -33.8 -14.1 0 1345764 8792199 40 -145 113.9 12.9 -163.9 17.6 -19.3 0.019 1365956 8874723 5 72.9 94 4.2 13.3 25.5 4.2 0 1372242 8901455 21 2-16
l l Table 2-3 (cont'd) Random Ntamber Missile I Y Z X' Y' 2' P Ntaber* of Years Ntamber 179.3 94 11.5 -14 85.6 14.8 0.0025 1456165 9435092 2 -176 94 6.07 -6.3 64.98 0.5 0 1465290 9465131 2 -145 105.75 15.69 -41.3 57.7 -1.2 0 1500515 9669490 2 -206 94 7.5 -38.4 36.16 -2 0 1512212 9974933 2 175.4 148 14.4 78.6 -45.3 7.6 0 1512610 9871649 3 152.6 148 13.13 22.9 -61.9 11.9 0 1525594 9855347 11 41.25 100.9 16 -16.7 186.2 -10.4 0 1532330 9904124 1 Total Prob. =.60453 Randon Number identifies the particular trial in the simulation. 2-17
l l l y = +148 ft. i M / x = -247 ft. x = -145 ft. N h \\ \\ ([ i Scale: 1/15" = 1 ft. y = +94 ft. Figure 2.5 Tomado Missile Strikes on Water intake Structure (Plan View) for 8.5 Million Years of Simulated Tomado impacts
i l t l i L 1 m N 7 / n + /M, x m u: 1 e Scale: 1/12"=1 ft. s Figure 2.6 Tomado Missile Strikes in South Face of Water intake Structure (For 8.5 Million Years of Simulated Tomado impacts)
3.0 UNCERTAINTY / ERROR ANALYSIS 3.1 ERROR SOURCES The purpose of an error analysis is two-fold: 1) to estimate the uncertainty of the analysis, and 2) to ensure that the analysis provides results which are conservative. The main sources of uncertainty in the estimate of tornado-induced failure rates are: Statistical uncertainty - that which stems from the stochastic nature of e random events Lack of knowledge of the physical processes which contribute to the e failure of components e Modeling and measurement uncertainties which limit the accuracy with which the processes can be represented mathematically. Sources of statistical error for this study include the occurrence rate of damaging tornadoes, the dimensions of their associated damage paths, and the breaking strength of plant components and the walls which protect them. The degree of uncertainty with these parameters is estimated by classical statistical means. An additional problem with the statistical data base for tornado frequency is that it is impossible to determine whether local variations in historical frequency are real or merely due to statistical fluctuations. There is evidence that the specific plant site is in an area of lower frequency than the average of the 125 nautical mile data base provided by the NSSFC (Appendix A). Imprecise knowledge, both of the types of damage that can be produced by tornadoes and of what damage state actually causes failure of the component or system function, is another source of error. For example, a conduit could be significantly damaged without destroying the integrity of the wires contained therein. It is shown in Section 3.3 that these error sources are not important contributors to overall uncertainty in estimating tornado risk. 3-1 }
4 i 1 i The measure of the area of the damage path dominates the measurement j uncertainties associated with. tornado risk. Damage path area is measured by l indicators (damage to growing plants and structures) following tornado passage. If good indicators are absent, the measurement will be degraded. Damage path } measurement usually underestimates the area, because if adequate indicators are { l absent at the full damage width, width measurement will be based on indicators j lying inside the full width. There can' never be any compensating indicators lying outside the full width. 4 For the same reason that damage width is likely to be underestimated, there is likely to be a consistent underclassification of tornado intensity. Lack of indicators at the point experiencing maximum wind speed along the path length could cause the tornado to be underclassified. Overclassification is very unlikely because there is no credible overestimation scenario. These measurement uncertainties impact prediction'of wind speed within the tornado, as well as the predicted frequency. Measurement and classification errors are generally not a problem in regions of relatively _ high population density and in forested areas (typical of New England) because good measurement indicators (e.g., trees and man-made structures) _are abundant. Since Pilgrim 1 meets these criteria, corrections are assumed to be unwarranted for this study. Corrections for misclassification (10) increased the variance for damage to this type of structure by about 5% when the measurement / classification error was treated as a random error in the Savannah River analysis (1). It is not considered significant for this analysis and it would be compensated by the fact that the Pilgrim site appears to be in an area of local low tornado frequency. 3.2 MODELING ACCURACY 3.2.1 Direct Wind Damane Direct wind damage to the unprotected areas of the plant has been determined by a separate study to be incurred at a threshold value of 217 mph. Uncertainty stems mainly from measurement of the tornado damage area and the resultant 4-3-2
1 i j determination of a wind velocity profile across the tornado. Hence, although the f wind speed at which a structure fails can be accurately predicted, it is difficult to ] predict the rate at which structures are exposed to such winds. Even a good j knowledge of the overall damage areas associated with tornadoes tells little of the i d tailed wind velocity distribution within such a damage area. Motion picture ) photography has shown that the velocity structure can be very complicated. For j such an analysis as this one, the recourse is to model the winds conservatively-- I thIt is, make certain that the area over which damaging winds are manifest is not { underestimated. There are enough data on tomadoes and tornadic winds that a { reasonable error analysis can be performed for it, and this has been done in Section 3.3. ) 3.2.2 Missile Damane t Missile damage uncertainties include those invoMng: Prediction of those objects in the tornado path which are injected into o the windfield as missiles Prediction of the transport of missiles in the tornado windfield e Prediction of missile interaction with plant structures and equipment. e Because of the difficulty in assessing the magnitude of these uncenainties (i.e., providing a meaningful error analysis), the missile simulation was modelled conservatively to compensate for these factors. Conservative elements are as follows: 1. The algorithm of Reference 2, which selects missiles for flight, overestimates the number that can really be flown according to actual observations. Missiles in a direct centerline path of any tornado have an integrated probability of one (as the total width of the tornado passes over them) of being initiated in flight. Of course, the windfield subsequently -drops those missiles not really sustainable in flight. However, since the windfield model and the flight parameters are also conservative (see element 2, below), both the initiated missile flights and the sustained missile flights are overestimated. 3-3
Furthermore, for many of the panicular missiles which are utilized (parts of structures: roof panels, doors, etc.), the restraint of their attachments are ignored and they are allowed to be injected into the windfield (i.e., initiated in flight) as though they were unrestrained. Most of the missile strikes on the auxiliary bay came from these kinds of missiles (steel roof panels); hence this is a major factor of conservatism. 2. The windfield model has an u at all radii at all elevations (even at 0 elevation); pward component this artifice keeps more missiles aloft than would be expected in an actual situation, and it allows for them to achieve greater elevation. Also, the maximum area, rather than a "mean-projected or random tumbling" area, of the missile is used in the flight parameter C A/W, and this overestimates missile velocity. In summary, D more missiles are flown and they are flown higher and faster than is possible in a real situation. 3. The number of striking missiles penetrating the walls is overestimated because
1) the estimation is not diminished by those structural members (such as I-beams) which prevent penetration and 2) the true projected im-pact area of the missile is deliberately underestimated (see Appendix B.2) which overestimates penetration rate.
3.3 UNCERTAINTY PARAMETERS 3.3.1 Random Event Uncertainties (Variance) for Direct Wind Damnpe The rate at which F4 winds impact the site is R4-AA where i the mean damage area associated with F4 winds a4 = A4 the mean return interval of F4 winds = A the total area of observation (that for which 4 is the = return interval). The rate at which winds exceeding the breaking strength, o, of the walls impact the site is p, N Us Be Jo NA (3-1) 3-4
where c4 threshold stress induced by minimum F4 winds = threshold breaking stress for structure (s) under a = invesdgation This relation comes from the fact that, within limits appropriate for this analysis, the area
==M = *A with winds exceeding a given value, V, is approximately pivyvidonal to V-I (the wind speed var;iation formula of Appendix A of Reference 4 2, uses a pavyvidonality of V.625)land the induced stress, o, is pivyvidonal to 2 V, The randomly distributed parameters which govern R are a4, 4, and a. The variance, S, of R is related to the variance of the component factors according to: R 2 2 2 S*= f6Ri S2 f% g2 f6,, R g (3-2) g (6aj (6Aj (6cj Obtaining the indicated derivatives: 6R 40, (3-3) 6 a, " 8AA (3-4) ~ 4 ' a, = 6 2 Jo A A 4 ,14 c, a, (3-5) 6R 6c, 2 o,3/2 AA 4 fd 84[ (Ja,a,Sy*l+k4AAg r o, a,2 3r\\ Factors of 3-2 become o j I 2 2 2 3 do AAj (gx, A j 4 4 2 f Jo, a, 3 f,S [ (Sx3 2 2 g I. + (3-6) 3 or S A Aj ( a, j ( 4g2 (40 4 l 3-5
where partial derivatives are evaluated at the mean values of their associated 2 2 parameter. Sx and S a were derived for F4 tomadoes from NSSFC data of 2 'S a was derived from Reference H using a coefficient of variation Appendix A. (ratio of standard deviation to mean value) of 0.14, which is twice the Reference H value given for typical reactor containment structures. The following variances apply: S, a,2 1.104 Sx,2 7 1.63 A4 2 So .0 5 = 4o 2 Substituting in Eq. 3-6 and evaluating the associated constants gives: i 2 40, a, 3 2 S ( la A, A [(1.104 + 1.63 +.005) 2.739R g [ l3.3.2 Error Factor and Confidence Limits The overall error in the calculations for direct wind damage (except for that due to
consistent error, or bias) is estimated using an assumed lognormal disnibution for the risk estimate (expected rate of compromises per year of the proteciv

walls i surrounding the conduit).
As an application of the modified central limit theorem l (see, for example, any good text on statistics), it can be asserted that the risk is lognormally distributed. The theorem states that products or quotients of factors which have reasonably well-behaved distributions are lognormally distributed. The ! failure parameters of this study which are factors of the risk equations can be cssumed to have reasonably well. behaved distributions. Besides being the !appropnate distribution for the overall risk, the lognormal has properties that make it useful for error prediction. These are embodied in the relation 3-6
~ X X, X I# .95 ( y.95 ) (3-7) EF = = = .50 .05 .05 where EF Error Factor = 95th,50th, And 5th percentile values, respectively. X.95,X.50,X.5 = To determine an error factor from the variances derived in the previous section, the following relations are also required. 2 p+ a /2 In EF 1.645 2pd{,o2-1) 2 (,o2, l} 2 3 .e X 2 where S variance of the lognormal distribution, = Xm= mean value of the lognormal distribution, p =. mean value of the associated normal distribution, standard deviation of the associated nonnal distribution. o = i With these definitions, the following expressions are derived: 2 [I n (1 + } _. In ~ o= m 2 -o n X .50 " m The resulting error factor for tornado-wind-induced wall failure rates is 6 for impact by tornadic winds, The confidence limits listed in Table 1-1 were evolved using the above relations and the mean values listed in that table. 3-7
As indicated in Section 3.2, we have built significant conservatism into the missile analysis. Therefore, we can assume the uncertainty in the missile analysis does not signficantly affect uncertainty in the overall risk assessment, since the overall risk from missiles, even with the added conservatisms is less than that due to direct wind. Section 3.4 addresses the uncertainty due to the calculation procedure by itself, which is less than that of the direct wind hazard. 3.4 ERROR IN SIMULATION ANALYSIS If all the physical parameters in a' simulation analysis are strictly accurate, it is still necessary to ensure statistical accuracy, which means that a sufficient number cf events must be simulated. For this type of (binary) simulation (either the missile . penetrates or it doesn't), the accuracy (90 percent confidence) is determined by confidence limits given by the + or - range (13): - ta {iz 2/n (1 - { ) P = where: n = number of trials (or years) x = number of times the event studies occurred in n trials i p = the true probability of the event simulated z = value (+ and -) of the abscissa of the normal probability curve between which lies the area corresponding to the defined confidence. The 90 percent confidence point on the normal probability distribution is at an abscissa of 1.65. The above relation shows that, if we are simulating an event that occurs twice in ten million years and we simulate 5 million years of events, the confidence limits are + or -115 percent of the value simulated. The limits are a larger percent of the value for fewer years simulated and smaller for more years. In other words, if we wish to have an accuracy (as measured by 90 percent confidence limits) which is comparable in magnitude to the number itself, it is necessary to simulate the number of years which is approximately equal to the recurrence interval of the 3-8
i l l l event. l In this analysis, we are not actually simulating penetrations, but missile strikes; we l are then calculating penetration probability for each simulated strike.
However, since the probability is dominated by a few strikes with very large penetration probabilities, it is still necessary to simulate a large number of years.
i I 1 l [ l I o l l 3-9 ?
4.0 SIGNIFICANCE OF RESULTS 4.1 CONSERVATISM The ultimate goal of the analysis is to determine whether the Class I conduits are housed.in structures that afford a demonstrable level of safety that _is adequate for plant licensing. Therefore, the conservatism of the analysis takes precedence over accuracy. However, there is no point in conservatism merely for conservatism's sake. Conservative approximations are used herein only where they are needed to give assurance that the choices of parameters or calculation procedures do not underestimate the severity of the tornado / tornado missile hazard. The points of conservatism utilized are summarized below. For the direct wind damage, the frequency data base is based on winds above 207 mph (all F4 and above tornadoes) rather than the 217 mph value calculated to be' the damage threshold. This factor increases both the tornado frequency and the tornado damage area. Furthermore, the tornado frequency of 200+ mph winds in the area is higher by more than an order of magnitude than that listed in the recent Fujita document, and no credit has been claimed for the sharp hill adjacent to the plant which would diminish the velocity of low-elevation winds in a tornado. The latter factor influences both the missile and the wind analysis. Specific points of conservatism for the missile analysis are: 1. The choice of missile types includes much more damaging ones than those recommended by the NRC G2). Large trees and large structural members, which actually dominate calculated risk, are included. 2. The wind field model is conservative relative to missile flight--including an upward velocity component at all elevations which keeps missiles aloft longer and augments missile flight initiation. 3. The flight parameters chosen for the missiles, mainly C W, are d conservative (high), and the projected flight area is the maximum missile area, not the " random tumbling" or mean area. This approximation, along with that of 2, above, causes the missiles to fly higher and faster than true observations would indicate (heavy missiles falling from high levels of the reactor onto the roof of the auxiliary bay dominate the risk to that structure). 4-1
4. Conservative distributions in the area of missile impact (smaller areas than actual) and conservative penetration algorithms are used. 5. A very large inventory of candidate missiles is used (approximately 75,000, out to a radius of one mile), in addition to local houses which are allowed to contribute missiles as a result of tornado impact (the EPRI-s%nsored TORMIS tornado missile analysis - Reference 5 - uses only amut ten percent of this number out to 2000 feet). A total of forty-three different types of missiles are utilized. 6. The restraints on missiles from plant structures (such as roof panels) are ignored; the missiles are allowed to be flown as if unrestrained (roof panels from other parts of the reactor cause the greatest number of missile strikes). 7. No credit has been claimed for those structural members, such as I-beams, which would prevent missile penetration. These multiple conservatisms undoubtedly add at least an order of magnitude to the calculated risk number. 4.2 ACCEPTABILITY FOR LICENSINO CONSIDERATIONS Probabilistic risk assessment has long been recognized and utilized in NRC regulation and licensing. The NRC and its predecessors were the major sponsors of its development in the nuclear industry. This analysis involves simulation as part of the risk assessment. Simulation, too, has been accepted by the NRC as a valid mechanism for safety assessment. Simulation of turbine missile hazards was utilized and accepted in the license application of the Floating Nuclear Plant (FNP) by Offshore Power Systems (Docket STN 50-437), is currently being utilized by New York Power Authority, and has been pan of the application for other plants (plants which were subsequently cancelled, but not before the simulation roethodology was given NRC review and acceptance). Tomado/ tornado missile simulation has also been used in NRC-approved licensmg actions (see, for example, the Limerick FSAR) which utilized the EPRI-sponsored TORMIS code developed by Twisdale (5). Results of TORMIS and the method 4-2
described herein are relatively close, particularly in view of the complete independence of their development. Appendix D contains a point by-point comparison of the two analyses (as reported in Reference 4). In summary, despite their relative rarity, simulation analyses are not new and not without acceptance in the licensing / safety assessment community. Furthermore, they are certainly the best mechanism available to model as complex a problem as tornado missile hazards.
4.3 CONCLUSION
The analysis herein is based on accepted techniques with conservative assumptions and predicts a very small probability (3.2E-7 for the auxiliary bay and 6.7E-7 for the water intake structure) of a tornado-induced compromise of the Class 1 electrical conduits in these buildings. It provides a very reasonable basis for determining acceptability of the as-built design for the auxiliary bay and the water intake structure. 4-3
l
5.0 REFERENCES
1. Fujita, T. Theodore, U.S. Tornadoes. Part 1. 70-Year Statistics. University of Chicago,1987. 2. " Simulation of Tornado Missile Hazards to the Pilgrim 2 Nuclear Thermal Generating Station", Science Applications, Inc., Sunnyvale, CA, November 1978. 3. " Tornado Hazard to Production Reactors at Savannah River", DPST 86-579, E.1. du Pont de Nemours & Co., Aiken, South Carolina, May 1986. 4. Oconee PRA. A Probabilistic Risk Assessment of Oconee Unit 3, Appendix K, NSAC 60, June 1984. 5. " Tornado Missile Risk Analysis", EPRI NP-768, Palo Alto, CA, May 1978. 6. " Tornado Missile Simulation and Design Methodology", EPRI NP-2005, Palo Alto, CA, August 1981. 7. Sliter, G.E., " Assessment of Empirical Concrete Impact Formulae", Journal of the Structural Division. ASCE. Vol.106, No. ST, May 1980. 8. Hagg, A.C. and G.O. Sankey, "The Containment of Disc Burst Fragments by Cylindrical Shells", Journal of Engineering for Power. TRANS ASME. p. 114-123, April 1974. 9. Patton, E., et al, "Probabilistic Analysis of Low Pressure Steam Turbine Generator Events", Draft EPRI report RP 1549-1 Battelle Nonhwest Laboratories, Richland, WA,1981.
10. Twirdale, L.A., et al, " Tornado Windspeed Frequency Analysis of Savannah River Plant", Report C5949, Applied Research Associates, Inc. Raleigh, NC, December 1984.

11. Fordis, M.N.,
A. Nacar and M.A. Delichatsios, Reinforced Concrete { Containment Safety Under Hydrogen Imading. M.I.T., Dept. of Civil Engineering, NUREG/CR-2898,1982.
12. Standard Review Plan, Section 3.5.1.4, " Missiles Generated by Natural Phenomena", USNRC, November 1975.

13. Miller, I.
and J.E. Freund, Probability and Statistics for Engineers. Prentice Hall, New York, NY,1965.
14. Private Communication, Professor James R. Mcdonald, November 1987.
1
( l l APPENDIX A l DETAILS OF TORNADO DATA l l t 1 J i l l l 2 A-1
M APPENDIX A DETAILS OF TORNADO DATA i i The tornado parameters upon which the missile code are based were derived by Professor James Mcdonald of Texas Tech University from the NSSFC and from the so called " tornado data tapes" from the University of Chicago (Professor T. T. Fujita). These are summarized in Appendix A of Reference 1 Also ] meluded in the Appendix is a statistical analysis and a summary of the parameters used in the code. 1 i i An updated record from the NSSFC was obtained for this study to include the 1 ) years since 1977. No significant changes in the parameters of this study were revealed by the updated data set. Table A-1 is a summary of the NSSFC data as of 1986 with a comparison of the significant parameters between the latest data and that of 1977. The 1977 data showed two F5 tornadoes and no F4s, but both of these were considered F4s in the latest data set. This difference l does not impact the results of this analysis. A minor difference exists in the i direction distribution as indicated, but
again, this difference is not consequential.
The updated NSSFC data corroborated the validity of that used for the original code development. It should be noted that the total number of tornadoes listed in the column i above for 1978 is the number used by Mcdonald in obtaining the F-number distribution, only. He used another data base which included 130 tornadoes in 16 years for the tornado frequency. Of considerable interest is the recent publication by T. T. Fujita (1) which lists Tornado statistics for the past 70 years in the United States. Fujita used his DAPPL formulation (discussed in Section 2 and Appendix B.1) to evolve probabilities of achieving specific wind speeds throughout the United States. The results for the 1 E-06 and 1 E-07 probabilities are shown in Figures A-1 and B-1. A-1
From Figure A.1 it is obvious that the use of the 125 nautical mile data base for tornado frequency at the Pilgrim Site penalizes the risk results because within that radius is a large section whose frequency for winds in excess of 200 mph is the same as that for 100 mph winds at the Pilgrim site. Figure A-2 shows that the Pilgrim site is exposed to 200+ mph winds with a probability only 1 E-07 per year, which is significantly less than that which would be predicted either with the NSSFC data of Table A-2 or using the entire " Region C" area of the United States (Figure 2-1). This difference is discussed further in Appendix B.1. l i l l 1 l l l l l A-2 i l
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Table A-1 TORNADO DATA COMPARISON j F Number Tornadoes Av Area Direction 1986 1978 1986 1978 Fraction 1987 1978 4 0 42 42 0.112 na* N 0.033 0.09 1 124 126 0.152 NE 0.40 0.39 2 62 60 0.193 E 0.37 0.32 3 11 8 1.709 SE 0.17 0.14 4 2 0 13.57 S 0.17 0 5 2 0 SW 0 0 W 0.17 0 Not directly available l 1 i A-5 l l l l
I m _De eastemad_ternede_ listing movidee.safeeention en cla reecetse trenedsen in 44e croe andtect:d stace 3950. Ths vectows entetes. and testas eco esotained ost If os. hews ocettaenst gvestisna. please wette se eats the eletteest severe .39erec Ferocaat teater, nees.123Ei_ARLA_24th st. abeam Cite Jto.rAleA shins _tatu 27.4-3427-I he nese-6 -stem t antane ehema use _ gear. eenth._d;:.te.and. 48ee et.actatr:r.ence.ef sect. ternade. in Centret Stenderd Tlee m. .ht seleses_1 stated REe an4Ee tedicata.the_meteeste. num6st. and.seement messer et each toenede. Betwence avetees are.aeetened chronologically within each state. The fleet tornede ese 1971 in Ohte le given segwence number i fee the state of Ohle that meer. Mene termedeem have tenethe oathe that.creen sments_pr ?t. ate lists,.Ade with 3 segmente heeece..chenst_d trat ion _avitAlem _In auch_tetes_t t tracts are treten inte segmente that are denoted hg seement neeh ne. A teen the esoe eequence nester. tot a different sessent neater. Per each senerete seament. The stettatice in_tett 106.133 see tened_ ente en tLe intteet tesechdown pointe. 2 The t.attlede and Longttede of the beginning and ending pointe er each l fett :f he S_ f::ede are shown fattooed by the everett length and a meldth. Beans and animenes fee each seeeemt are tieted, p_ e Clees. Benene Clpes nuebert renes free i to 9 and l ,e..t.. .n estte.te., th. 4.m.go. .e. tag t. o e t.hio ie1,.e he columene teheted PPP provide Me FwJite-(*eseeen state eetteetes e#Teece. Path Length and Path 48tdth. All three scales are l Eseerithmetic with vetees renetne fees -1 fee the emettest catesere te +5 fee the lacettt. I The fallausime table feel "___ the eases in emeh scale. The Path a - th and the Path Midth welees eserement estimetas as te the acteet _____t of ground contact fee each t ornede. Fee instance. if a teenade had en everstl length of 4S estes but made i actest eressed contact estle 40 eercent of the time the Path a_e-eth scale value smessid be a 2. The A2RMS teleen ledicates the matempth and 72::: free the teater saint. 199/93 Andteates the t:rrrfr tengAdeue esse 129 desteen. teoetheastl at S3 smetical ettee from the canter point. i A carcetoe plot of toenede teachdenen pointe se enciesed. h e ettg of interest to et the conter of He ytet. neeth to at the top. _ east at h e rieht hand side. . hat eight.e. etc..ete.... diait emeresents the,mueber of teochdemme Emet in a ame11 messee area. eteet I sites en a y et.o. we. -e lg ee,resente to.chde.no in.sie e,were.n. i towchde.n in the.4,.c.at ege.ee. Os The h ; fregwence tattee provide detetted in h u tten a6eet he time of deg. Stee of geme and length and esteth theracteristice of termodeos in the area of interest. he Pan W8dth we Path Leneth tatte to coneeted free %e Pt and Po date. At ee.. He seen meth _ lenen and seen eeth etees see competed free the Pt and Pm date. Whose the length and erldth state welwee are converted bact to tength and width figweee the etsigene welwee in oech eense see esed. Fee esseele, a Pt watee of 3 to c; ;eted to e teneth of to alles in the calculottose. he eenple and bevele dietettetten tattee indicate Me fevered 4 tees of dee'end meer fee teemedeee in each sees. Monthle and howrig percentages are ei:= en He howelg dis te sbut ten table. Mean timee are shouse for each month and fee the entire gear. These times shoold be inteeseeted esed weed in conjonction oath the hovete mercentenes in essetnine the divenet trend of t o rned eos. Att 4 tees in these tettes are Central Standard flee. The lettlede end longitude of Me center point of Me search progeme to Itated at the opper right hand elde of he Howetg ~~ 9tetelbotten Tatte. M ese floween are in destees and hundredtbe. The ese scale ::;d in the circular stet _le comestible esith he SMR 57 veder esp. 125 newettet ette renge. Totte 94 (B MetGE PL C D I tette e2 (FPP SCAL.El I medla F tephi 2 ^ ^ ^Z Pt smiteel Pm fuldths t 1 i Lees Man #55 8 Lees tien de ilittle se Less then.3 Lees then & E e50 te esOS i ne dameeal 3 esos to GS.coe O 40-72 Light 0.3-10 6-t? goede 4 95.900 to 930.600 t 1 73-112 Moderate
1. 0-2. I 19-55 marde 5 e50.000 to 6500 000 4
2 113-157 Cenenderable 3.2-9.9 56-175 goede & $300.000 te 45 milliam I 2 158-206 2:v;ee 10-31 17&-S56 maede 7 95 MttIten to GSO Mt11 ten 4 4 207-240 Deventeting 32-g9 0,3-0.9 etles e ese Meint.n t. esoO Mtliten e w mat-3:e ince.dtti. too-sis i.o-3.I ettee Table A-2 NSSFC Tornado Data on PILGRIM Site
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1 1 1 l i l ) i I F l l l mae 1 e o me N O Cf en W 3Ou Rw i .d a= es 4S > & es O suf - >ee 1 M i Em @S Se es sie W T.A l i g i &w i D em l l Em n i l Og e i 8 O &M Om l EE en en m i &D D l & ne e 8's P p l e.a ne ) me i EG US> m i Wf3 T i ee W f MW 3 \\ en o m mp3 E s e ar=
=
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m U
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l APPENDIX B DETAILS OF CALCULATIONS
l l APPENDIX B DETAILS OF CALCULATIONS i B.1 DAMAGE RATE FROM HIGH WINDS i B.I.1 Data Sources i e A separate analysis has concluded that the walls of the auxiliary building and the l water mtake structure are capable of withstanding winds of 217 mph. These winds l occur in F4 tornadoes (which include the wind speed range from 207 to 260 mph). A conservative approach to establishing the rate at which 217 mph winds impact the site is to consider all F4 and higher tornadoes to be capable of damaging the walls. l Another, less conservative, approach is to attempt to divide the F4 tornadoes at 'the 217 mph value and include only those above this wind speed in the wind damage data base. l In either case it is necessary to determine the damage area generated per unit time by winds in excess of the threshold damage value. This number is used to define the wind damage probability (which, by custom, is used interchangeably with l " expected frequency"). Such a determination is, indeed, the usual definition of tornado frequency / probability, which (Reference 1, for example) is specified as the probability, or rate, per year that any point within the area will exposed to the conditions for which the rate (" probability") is given. Specific data on tornadoes of this magnitude are sparse, simply because they are such rare events and the determination of statistically adequate tornado data suffers from the paradox that any region large enough to produce adequate statistics is probably too large to be representative of the locale under investigation. This paradox is certainly true of the Pilgrim site. A appropriate tornado data base was determined for the missile study as described in Appendix A of Reference 2. Direct wind damage, however, requires a different data base (winds in excess of 217 mph), and it is discussed below. i l B-1 4 n
Data are available on the existence of winds in excess of 217 mph and on the path lengths over which they are manifest; however, data on the path widths associated with such wind speeds are very sparse. For determining path width, a calculation based on the theoretical wind speed variation over the tornado radius may be the most reliable. However, despite the lack of data, there are sufficient methods available to allow the probability numbers to be bounded. These are described below. The DAPPL Formula and the Fuiita Data Base The Fujita group at the University of Chicago (1) has developed a correlation based on the "Superoutbreak" tomadoes of April 3-4, 1974. This correlation is known as DAPPL(y) for " Damage Area Per Path Length" (DAPPL) for a given velocity (V). The formula is Y DAPPL(y)= 10-xV (B.1-1) where x and y for F4 tornadoes are, respectively,1.05E-04, and 1.477. Inserting these in Eq. B.1-1 predicts a 0.505-mile-wide path having winds in excess of 217 mph, averaged over that length of tornado where F4 winds exist. The Fujita data also states that the average F4 tornado path length (based on 70 years of data within the United States) is 27.2 miles. However, this value is for total damage length associated with any tornado having F4 magnitude winds anywhere along its path, and the path for any tomado of magnitude greater than F0 does not have the maximum winds upon which its categorization was based for its total path length (see Table 2-1). Fujita does not address the problem of determining the fraction of tornado path length that actually is exposed to wind speeds as high as the level which formed the basis for its classification, but he had to have considered it in order to produce the statistics described below. The Fujita tornado statistics also include windspeed probabilities for so-called "subboxes" (areas bounded on each side by either 15 minutes of latitude or 15 minutes of longitude) in the contir,uous United States. The subbox containing the Pilgrim site has a probability of exceeding 200 mph of only lE-07 per year (Figure 8.5 of Reference 1, which has been reproduced as Figure A-2 of this report). B-2 f
l i However, Fujita's description u) lacks sufficient detail to verify its validity, and the use of NSSFC data with alternative length and path-width information (2,5) does not produce so low a number. Derivation of this rate with altemative data sources i a is described below, i The NSSFC Data i The NSSFC provides tornado data fb any locale in the United States (specified by the latitude / longitude coordinates). Table A-2 is such a data base provided for the + Pilgrim site. From this source (and similar sources for other locations), average ~ damage areas for F4 tornadoes can be determined. However, damage areas as specified by the NSSFC are total damage areas (areas subject to observable damage). Therefore, it is necessary to account for that fraction due to wind speeds significantly higher than the damage-threshold value. The threshold of observable damage occurs between 40 and 75 mph. Data on a total of nine F4 tornadoes are 3 available from the two data sources available at SAIC (that for Pilgrim 1 and that for the Savannah River DOE site). giving an average damage area of 7.83 sq. miles and an average length of 21.56 miles. The two F4 tornadoes in the Pilgrim 1 data . base average 13.3 square miles in area and 23 miles in length. The area shown as " Region C" in Figure 2-1 and the associated F4 occurrence rate are also NSSFC data. Path Lengths and Path Widths of F4 Tornadogs A determination of path length associated with F number speed winds per unit path length of tornado has been provided by Twisdale (f) and is shown in Table 2-1 of this document. This analysis, like the Fujita DAPPL, was based on a single occurrence of multiple tornadoes (an outbreak). This value (0.212) is used with the specific Pilgrim 1 NSSFC data, Region C data, and the theoretical wind speed variation (2) to evolve a comparison with the Fujita lE-07 data for 200+ mph wind probabilities at Pilgrim. B-3
c i The negative one-sixth power variation of wind speeds (Appendix A of Reference 2) 1 outside the radius of maximum wind predicts a ratio of 200 mph wind-speeds path J width to total path width of 0.472. The average 200 mph wind value (based on only two events) at Pilgrim is 1.33 square miles. l Mcdonald reports in Appendix A of Reference 2 that the 120 mile radius data base area contains 16,500 square miles of land. If the ratio of land area to sea area remains relatively constant between 120 statute miles and 125 nautical miles (the region of the most recent NSSFC data base), then the land area associated with the latest NSSFC Pilgrim data base is 23,678 square miles and the predicted F4 tornado rate is (1.33)(2)/(23,678)(37) = 3.04 E-06 per year. Combining the Pilgrim and Savannah River (3) data on size of F4 tornadoes with i the Region C F4 tornado rate (2.49 E-M per square-mile-yr) predicts a rate of 1.94 E-06 per year for use at the Pilgrim site. The latter value is considered more vdid than that based on the NSSFC Pilgrim data alone because the Pilgrim F4 data are too sparse for reliable statistics; it was shown in Appendix A that the 125 nm data on tornadoes very likely exceeded that which is valid for the Pilgrim site. Unfortunately, there is no guarantee that Region C frequency data are more valid. Both predict a frequency that is more than an order of magnitude greater than that Fujita predicted by. The 0.33 reduction factor for direct wind impingement on these structures predicts 6.4E-7 for the water intake structure (Section 2). Using the additional conditional probability of 0.5 for conduit damage following auxiliary bay wall failure, the predicted conduit compromise rate is 3.4 E-07 for the auxiliary bay and 6.8 E-7 for the water intake structure. The 0.5 conditional probability is applied to the water intake structure only for those outside walls which do not have a conduit attached directly thereto. Confidence limits on this prediction are derived in Section 3. B.I.2 Effect of Local Wind Direction l As discussed in Section 2.1.2, the fact that a given wall lies within the envelope of } winds exceeding the wall breaking strength does not mean that the wall will fail. I B-4 i w -m.-
In order to fail, the velocity component perpendicular to the wall must exceed the breaking strength.and this condition occurs far less than 100 percent of the time that given walls lie within the " envelope" of wind speeds capable of breaking the wall. In this section an analytical expression is developed for the normal wall velocity component and it is applied for a number of specific tornadoes from those simulated in Appendix B.2 to determine the fraction of damage path width over shich the normal velocity component can exceed the 217 mph value and thus, verify i the heuristically developed 0.33 average of Section 2.1.2. The Equation of the path centerline of a given tornado is 1 I 1 = m xc + yi B.1-2 ye where m = slope of the pathline (ratio of y-direction travel to corresponding x-direction travel; xe,yc= coordinates of path line; l yi intercept value of ye (yc value when xc = 0). = The equation of the circle corresponding to the maximum tangential wind of a tomado is ] (x - xc)2 + (y,ye)2 Rm = 0 B.1-3 2 where x,y = coordinates of the circle where the maximum winds corresponding to radius Rm occur; 1 xc,yc= coordinates of the center of the above circle; Rm = radius of maximum tangential wind for a given tornado (determined j by the relations of Appendix A of Reference 2). B5 4 i ,.n.- n
l I I 1 Simultaneous solution of the above two equations for xe,yc with the x,y values corresponding to the coordinates of one of the walls being analyzed locates path l centerline points for tornadoes corresponding to the exact maximum wind on the ~ structure (wall) of interest. There are two such solutions for each tornado (for the leading edge and trailing edge winds of a tornado-Fig B.1-1). For all the tornadoes analyzed the range of radial distance over which 217+ mph winds occur is very narrow and the maximum velocity wind radius inside this band l is a good approximation to the location of all winds over 217 mph. i Following determination of the path centerline points corresponding to the two l points of maximum wind incidence on the structure of interest, the velocity normal to that wall from each point is determined by adding 90 degrees to the radial j direction from the tornado center to the wall (to determine actual tangential wind direction). The normal component of this tangential velocity on the wall is added j vectorially to the tornado translation component to determine the total normal l component on the wall. The BASIC computer program which solves the above equations and determines the total normal velocity component is listed as Figure C-5 ef Appendix C. Table B.1-1 shows the results of applying this procedure for a representative set of tornadoes selected from the simulated set of Appendix B.2. l l Specific path-width fractions which can impact the auxiliary bay and the water j intake structure for a specific. tornado are illustrated in Figure B.1-2. The average i value from Table B.1-1 is 0.24 for the auxiliary bay and 0.28 for the water intake structure. Only the south and east walls of the intake structure are considered. Collapse of the west and north walls, because of the significant intervening internal structure is not considered a credible failure mechanism for the conduits housed therein. The average values listed in Table B.1-1 verify the consesvatism of the 0.33 used in section 2 to determine overall probability of conduit failure. 1 4 B-6
Tornado Travel Direction Circles of maximum windspeeds / Target N O Winds / from leading 3 a edge i Winds from trailing edge Figure B.1-1 Two Locations of Maximum Windimpact from Same Tomado B-7
l l l l t Table B.1-1 Probability of Exceeding 217 aph Normal Velocity Winds from Specific Tornadoes on Walls of Specific Structures Tornndo Max. Wind Transl. Tornado Path Radius of 217 mph Wind Prob Id:ntity Speed Speed Direction Width Max Wind (normal to wall) l R nd. No. sph sph radians feet feet Aux. Intake Bay Structure 3 15787) 231 33 0.471 2800 693 0.27 0.41 584631 251 34 1.257 2800 568 0.52 0.47 169697 235 28 0.471 6500 1600 0.29 0.43 596440 220 45 1.257 2800 710 0.36 0.19 764614 220 43 0.471 870 222 0.11 0.25 i 827863 217 27 1.257 870 223 0 0 857288 241 33 5.969 870 209 0.19 0.27 857710 241 55 0.471 870 209 0.22 0.66 i I 945881 234 33 5.1 84 870 213 0.39 0 cce note 234 33 2.042 870 213 0.09 0.12 t Average 0.244 0.28 Note: there was no tornado in the data base which had winds in excess of ths damage threshold (217 mph) and also traveled in this octant direction. Therefore, the tornado of RN 945881 was used with this octant direction casumed. { l B-8
1 Tornado Direction ) Corridor for Rormal (perpendicular) j winds exceeding 217 mph on auxiliary bay / Target l Location I i I l i Corridor for i normal winds i exceeding 217 i mph on water intake structures i ) J path width for any wind > 217 mph Figure B.1-2 Corridors Capable of Producing Perpendicular Winds Exceeding 217 mph on Auxiliary Bay and intake Structure Walls (for Tornado 857288). B-9
l B.2 DAMAGE RATE FROM MISSILES 1 B.2.1 Calculation of Missile Strikes on the Plant This section summarizes the operation of the tornado missile code PILGRIM 1 which is an adaptation of the code WIZ (2). The reader is directed to Reference 2 for a complete description of the method. i a Site Delineation and Missile Placement l l A site one-mile in radius surrounding the actual plant was chosen, the plant t external boundaries were precisely modelled, and the potential missiles were laid down (pre-placed within the site) for tornado simulation. The size of the site is l chosen to: 1) be large enough to include the approximate maximum distance a tornado-borne missile would be carried, and 2) still keep tractable the number of missiles maintained in the computer inventory. 'Ihe number and general location of the missiles were determined by actual site survey. Random (Monte Carlo) l placement of missiles within known areas and elevation ranges was employed except for a few significant missiles which could be precisely located (e.g., weather towers, manhole covers, etc.). Figure B.2-1 shows the missile placement for the PILGRIM 1 analysis relative to that of the Reference 2 analysis. Table B.2-1 indicates the number and location of all eligible missiles for the PILGRIM 1 code. Tornado Selection By random (Monte Carlo) sampling from given distributions, the following tornado l parameters are selected: l Maximum horizontal wind speed e l e Width of damage path (width of region of winds greater than 75 mph.) e Translation rate of tomado center e Direction of travel l l e Path line across site, t i B-10
7 True 7 Plant i Shoreline North N rth j ^ l Containment i F1 Center For Plant 2 i F1 d C3 N O' Plant fast h B' W A 'El E1 F1 l-4 g F2 ~ 1 m[kt Water Intake i structure Auxf11ary Bay Y= i i R Areas: D3. E2. E3, E4 Eliminated 3 "~ Area: El Translated l 309 ft. to West and 15 ft. North g n i \\ i F4 l a 9P Figure B.2-1 Change in Distribution of Candidate Missiles from Plant 2 Study for PILGRIM 1 Assessment i t
Table B.2-1 Location of Candidate Missiles for PILGRIM 1 Analysis B C D E A B C D E A B C D E
g. 0. -240.100.00 16 800 180. -180. 28.00 17 8
120. -180. 28.00 18 1
0. -240.
1.00 20 1 0. -240. 4.00 21 4 -120. -240. 7.50 22 1 e0. -240. 50.00 285649 -180.
60. 14.00 12 6 -180.
-60. 14.00 13 32 'O. O. 28.00 16 330 -120. -60. 4.00 21 2 -180. O. 7.50 22 3
0.
360. 8.75 12 59 -180. 300.,19.50 16 165 -120. 300. 19.50 19 14 00. -80. 46.00 16 50 -360. 60.107.50 13 16 -240. 0.107.50 13 16
0. -180.107.50 13 16 -540.
]#0.107.50 13 16 -300. 120.107.50 13 16 00. 0.107.50 13 16 -420. 120.107.50 13 16 -540. -180.107.50 13 16 80. 120.107.50 13 12 -300. -120. 42.50 13 23 -240.
60. 42.50 13 23

0.

60. 42.50 13 23 -360. -240. 42.50 13 23 -240.
-60. 42.50 13 23
40. -120. 42.50 13 J3 -420.
O. 42.50 13 23 -420. -240. 42.50 13 23
60. -180. 42.50 13 16 -420.
-60. 50.00 13 28 -360. -120. 50.00 13 28
20. -120. 50.00 13 28 -480. -120. 50.00 13 28 -300.

60. 50.00 13 28

80. -300. 50.00 13 28 -480.
240. 50.00 13 28 -480. -60. 50.00 13 28 '80. O. 50.00 13 25 -420. -300. 12.00 14 2 -540.
60. 12.00 14 2
60. O. 12.00 14 2 -360. -60. 12.00 14 2 -420.
60. 12.00 14 2

80. -240. 12.00 14 2 -540.
120.100.00 15 189 -360. 120.100.00 15 189 60. 180.100.00 15 189 -540. 0.100.00 15 189 -420. -180.100.00 15 189 00 -60.100.00 15 189 -300. -180.100.00 15 189 -420. 180.100.00 15 189 .4 0. -120.100.00 15 188 120.-1200. 60.50 12 4 60.-1080. 60.50 12 4 60.-1200. 60.50 12 4 60.-1140. 60.50 12 1-1020.
60. 18.00 16 11 10.
70. 7.00 28 26 -540. -420. 13.00 12 31 -530. -410. 26.25 15 105
20. -400.
4.00 21 8 -480. -360. 8.00 12 24 180. -480. 20.00 16 361
40. -600. 20.00 16 361 360. -360. 20.00 16 361 480. -480. 20.00 16 357

00. -480.
4.00 21 5 300. -420. 4.00 21 5 360. -420. 4.00 21 5
40. -420.
4.00 21 1 360. -540. 7.00 23 1 420. -480. 7.00 23 1 i80. -540. 10.00 28 237 420. -420, 10.00 28 237 240. -480. 10.00 28 237
00. ~540. 10.00 28 235

60. -540. 20.00 15 270

60. -420.
4.00 21 4
60. -600. 10.00 28 620 -960. -420.
1.00 24 7 -780. -720. 1.00 24 7 080. -600. 1.00 24 7 -960. -780. 1.00 24 7-1080. -540. J.00 24 7 080. -420. 1.00 24 7 -780. -600. 1.00 24 7 -840. -720. 1.00 24 7
40. -840.
1.00 24 7-1020. -660, 1.00 24 7 -900. -720. 1.00 24 7 020. -420. 1.00 24 7 -660. -780. 1.00 24 7 -840. -420. 1.00 24 7
60. -720.
1.00 24 7 -660. -660. 1.00 24 7 -840. -480. 1.00 24 7 840. -780. 1.00 24 7 -900. -840. 1.00 24 7 -960. -600. 1.00 24 7 140. -540. 1.00 24 7 -780. -960. 1.00 24 7 -900. -540. 1.00 24 7 900. -420. 1.00 24 7 -780. -840. 1.00 24 7 -960. -540. 1.00 24 7 720. -660. 1.00 24 7-1020. -540. 1.00 24 7 -960. -360. 1.00 24 7 L 900. -660. 1.00 24 7 -720. -780. 1.00 24 7 -600. -780. 1.00 24 7 140. -480. 1.00 24 7 -960. -720. 1.00 24 7 -780. -540. 1.00 24 7 080. -480. 1.00 24 7 -720. -900. 1.00 24 7 -900. -600. 1.00 24 7 5900. -480. 1.00 24 7-1020. -600. 1.00 24 7 -840. -660. 1.00 24 7 7 780. -900. 1.00 24 7 -780. -660. 1.00 24 7 -900. -780. 1.00 24 7 ,600. -720. 1.00 24 7 -960. -480. 1.00 24 7 -780. -780. 1.00 24 7 1020. -480. 1.00 24 7-1140. -420. 1.00 24 7 -720. -840. 1.00 24 7 B-12 ~
Table B.2-1, continued B C D E A B C D E A B C D E 0. -840. 1.00 24 7 -720. -960. 1.00 24 7 -840. -600. 1.00 24 6 00. 480. 1.00 24 14-1080. 480. 1.00 24 14-1080. 540. 1.00 24 14 0. 480. 1.00 24 14 -960. 420. 1.00 24 14-1020. 420. 1.00 24 10 0. 480. 1.00 25 1-1140. 540. 1.00 25 1-1320.-1140. 1.00 24 9 00.-1140. 1.00 24 9-1260.-1080. 1.00 24 9-1140. -960. 1.00 24 9 0. -840. 1.00 24 9-1320. -900. 1.00 24 9-1200.-1200. 1.00 24 9 1.00 24 9-1080.-1020. 1.00 24 9-1260. -840. 1.00 24 9 0.-1020. 1.00 24 9-1260.~1140. 1.00 24 9-1320.-1020. 1.00 24 9 h0.-1200. @0. -960. 1.00 24 9-1260. -960. 1.00 24 9-1020.-1020. 1.00 24 9
40. -960.
1.00 24 9-1260.-1020. 1.00 24 9-1140.-1080. 1.00 24 9
40. -900.
1.00 24 9-1380. -960. 1.00 24 9-1260. -900. 1.00 24 9
40. -900.
1.00 24 '9-1200. ~780, 1.00 24 9-1080.-1080. 1.00 24 9 40.-1140. 1.00 24 9-1200. -900. 1.00 24 9-1380. -900. 1.00 24 9
80. -960.
1.00 24 9-1380.-1020. 1.00 24 9-1200. -840. 1.00 24 9 40.-1020. 1.00 24 9-1200. -960. 1.00 24 9-1200.-1080. 1.00 24 3 20.-1140. 1.00 24 5 ~780.-1320. 1.00 24 5 -900.-1320. 1.00 24 5 00.-1260. 1.00 24 5 -720.-1140. 1.00 24 5 -780.-1260. 1.00 24 5 20.-1200. 1.00 24 5 -420.-1320. 1.00 24 5 -660.-1440. 1.00 24 5 20.-1440. 1.00 24 5 -900.-1260. 1.00 24 5 -780.-1080. 1.00 24 5
60.-1260.
1.00 24 5 -480.-1440. 1.00 24 5 -540.-1380. 1.00 24 5
60.-1320.
1.00 24 5 -600.-1380. 1.00 24 5 -540.-1200. 1.00 24 5 20.-1320. 1.00 24 5 -420.-1440. 1.00 24 5 -420.-1500. 1.00 24 5 20.-1260. 1.00 24 5-1020.-1200. 1.00 24 5 -840.-1320. 1.00 24 5 -00.-1080. 1.00 24 5 -660.-1140, 1.00 24 5-1020.-1080. 1.00 24 5 080.-1140. 1.00 24 5 -660.-1320. 1.00 24 5 -960 -1020. 1.00 24 5 e40.-1440. 1.00 24 5 -840.-1380. 1.00 24 5 -900. -960. 1.00 24 5 400.-1200. 1.00 24 5 -420.-1380. 1.00 24 5 -780.-1200. 1.00 24 5 840.-1200. 1.00 24 5 -480.-1380. 1.00 24 5 -840.-1080. 1.00 24 5
40.-1260.
1.00 24 5 -720.-1260. 1.00 24 5 -900.-1020. 1.00 24 5 360.-1260. 1.00 24 5 -960.-1200. 1.00 24 5 -840.-1020. 1.00 24 5 600.-1320. 1.00 24 5 -600.-1200. 1.00 24 5 -660.-1200. 1.00 24 5 780.-1380. 1.00 24 5-1080.-1200. 1.00 24 5 -720.-1380. 1.00 24 5 900.-1140. 1.00 24 5 -540.-1500. 1.00 24 5 -660.-1260. 1.00 24 5 420.-1560. 1.00 24 5 -960.-1080. 1.00 24 5 -780.-1140. 1.00 24 5 j600.-1500. 1.00 24 5 -480.-1500. 1.00 24 5 -480.-1260. 1.00 24 5 480.-1320. 1.00 24 4 420.-1440. 1.00 24 4 120.-1260. 1.00 24 4 300.-1380. 1.00 24 4 180.-1440. 1.00 24 4 420.-1260. 1.00 24 4 f300.-1380. 1.00 24 4 420.-1200. 1.00 24 4 -240.-1320. 1.00 24 4 4180.-1260. 1.00 24 4 240.-1320. 1.00 24 4 480.-1260. 1.00 24 4 1320. 1.00 24 4 -180.-1380. 1.00 24 4 0.-1260. 1.00 24 4 120.-1320. 1.00 24 4 360.-1200. 1.00 24 4 -240.-1260. 1.00 24 4 =120.-1260. 1.00 24 4 180.-1500. 1.00 24 4 -120.-1320. 1.00 24 4 1260. 1.00 24 4 60.-1260. 1.00 24 4 120.-1380. 1.00 24 4 660.-1200. 1.00 24 4 -60.-1380. 1.00 24 4 360.-1440. 1.00 24 4 240.-1380. 1.00 24 4 720.-1320. 1.00 24 4 540.-1200. 1.00 24 4 300.-1260. 1.00 24 4 -300.-1500. 1.00 24 4 -120.-1440. 1.00 24 4 600.-1260. 1.00 24 4 0.-1440. 1.00 24 4 60.-1320. 1.00 24 4 B.13
Table B.2-1, continued A B C D E A B C D E A B C D E 180.-1320. 1.00 24 4 240.-1260. 1.00 24 4 -180.-1500. 1.00 24 4 0.-1500. 1.00 24 4 300.-1320. 1.00 24 4 480.-1380. 1.00 24 4 600.-1320. 1.00 24 4 540.-1140. 1.00 24 4 -60.-1500. 1.00 24 4 60.-1440. 1.00 24 4 300.-1500. 1.00 24 4 540.-1380. 1.00 24 4 540.-1440. 1.00 24 4 360.-1320, 1.00 24 4 -120.-1500. 1.00 24 4 180.-1380. 1.00 24 4 120.-1500. 1.00 24 4 360.-1380. 1.00 24 4 360.-1380. 1.00 24 4 -360.-1440. 1.00 24 4 0.-1380. 1.00 24 4 300.-1260. 1.00 24 4 60.-1380. 1.00 24 4 660.-1260. 1.00 24 4 300.-1440. 1.00 24 4 600.-1380, 1.00 24 4 480.-1440. 1.00 24 4 660.-1320. 1.00 24 4 480.-1200. 1.00 24 4 -180.-1440. 1.00 24 4 540.-1320. 1.00 24 4 420.-1380. 1.00 24 4 600.-1140. 1.00 24 4 0.-1320. 1.00 24 4 120.-1440, 1.00 24 4 720.-1260. 1.00 24 4 240.-1500, 1.00 24 4 -120.-1380. 1.00 24 4 -240.-1500. 1.00 24 4 360.
60. 50.00 1
7 360. 240. 50.00 1 5 360. 300. 1.00 1 19 180. 240. 1.00 1 18 240. 180. 50.00 2 1 360. O. 1.00 2 3 420. -60. 1.00 2 1 300. -120. 50.00 3 6 420.
60. 50.00 3
4 420. O. 1.00 3 16 300. 240. 1.00 3 14 360. -60. 50.00 4 6 240. 240. 50.00 4 4 420. -240. 1.00 4 26 480. -120. 1.00 4 24 480. O. 50.00 5 151 360. -240. 50.00 5 149 360. -120. 1.00 5 526 180. 180. 1.00 5 524 300. -60. 1.00 6 6 240. -180. 1.00 6 4 300. 360. 50.00 7 126 300. 180. 50.00 7 124 420. -120. 1.00 7 501 360. -180. 1.00 7 499 240. 360. 1.00 8 7 420. 180. 1.00 8 6 420. -180. 1.00 9 7 300. -180. 1.00 9 5 240. -120. 50.00 10 7 300.
60. 50.00 10 6
480. 120. 1.00 10 20 480. -60. 1.00 10 18 420. 120. 50.00 11 3 360. 120. 50.00 11 2 480. 60. 1.00 11 11 300. 300. 1.00 11 9 300. 120. 1.00 24 3 360. 180. 1.00 24 2 420. 240. 1.00 38 3 300. O. 1.00 38 2 540. -60. 50.00 1 7 660. -180. 50.00 1 6 780. -120. 1.00 1 20 660. 300. 1.00 1 18 600. O. 50.00 2 1 780. 180. 1.00 2 3 720. -120. 1.00 2 1 780. 240. 50.00 3 6 540. 300. 50.00 3 4 480. 300. 1.00 3 16 600. 180. 1.00 3 14 540. -120. 50.00 4 6 600. -180. 50.00 4 4 540. 60. 1.00 4 26 660. O. 1.00 4 24 720. -300. 50.00 5 151 480. 180. 50.00 5 149 600. 60. 1.00 5 526 780. O. 1.00 5 524 600. 360. 1.00 6 6 600. 240. 1.00 6 4 720. 360. 50.00 7 126 600. 420. 50.00 7 124 720. -240. 1.00 7 501 540. 360. 1.00 7 499 660. -240. 1.00 8 7 720. 60. 1.00 8 5 660. 120. 1.00 9 7 780. -60. 1.00 9 6 660. 240. 50.00 10 7 540. 120. 50.00 10 5 780. 120. 1.00 10 19 780. -240. 1.00 10 18 420. 300. 50.00 11 3 660.
60. 50.00 11 2
660. -60. 1.00 11 11 720. -60. 1.00 11 9 780. -180. 1.00 24 3 600. -240. 1.00 24 2 480. -180. 1.00 38 3 720. 240. 1.00 38 2 2940.-3960. 1.00 1 2 2580.-3360. 1.00 1 2 700.-3180. 1.00 1 2 2160.-2760. 1.00 1 2 2820.-3360. 1.00 1 2 460.-3360. 1.00 1 2 2400.-3120. 1.00 1 2 2520.-3000. 1.00 1 2 040.-2760. 1.00 1 2 2220.-2940. 1.00 1 2 2880.-3960. 1.00 1 2 700.-3600. 1.00 1 2 2820.-3600. 1.00 1 2 3180.-3660. 1.00 1 2 340.-3180. 1.00 1 2 1920.-2520. 1.00 1 2 2880.-3600. 1.00 1 1 460.-3120, 1.00 2 2 3000.-4020. 1.00 2 2 2940.-3480. 1.00 2 2 B-14
Table B.2-1, continued A B C D E A B C D E A B C D E 2460.-3000. 1.00 2 2 2340.-2760. 1.00 2 2 2640.-3480, 1.00 2 2 3060.-3420. 1.00 2 2 2520.-3240. 1.00 2 2 2760.-3240. 1.00 2 2 2880.-3720. 1.00 2 2 2520.-3060. 1.00 2 2 2700,-3240. 1.00 2 2 2460.-3240. 1.00 2 2 3180.-3840. 1.00 2 2 2760.-3600. 1.00 2 2 .3120.-3480. 1.00 2 2 3240.-3720. 1.00 2 1 3000 -3420, 1.00 3 13 2400.-3060. 1.00 3 13 2700.-3Dd0. 1.00 3 13 2940.-4020. 1.00 3 13 2340.-2880. 1.00 3 13 3300.-3780. 1.00 3 13 2160.-2820. 1.00 3 13 2460.-2820. 1.00 3 13 2160.-2700. 1.00 3 13 2940.-3720. 1.00 3 13 2760.-3660. 1.00 3 13 2580.-3060. 1.00 3 13 2100.-2880. 1.00 3 13 3000.-3960. 1.00 3 13 2520.-3180. 1.00 3 13 2520.-3120. 1.00 3 13 2880.-3480. 1.00 3 13 2940.-3900. 1.00 3 13 2460.-3300. 1.00 3' 13 2100.-2520. 1.00 3 10 2280.-2580. 1.00 4 18 2220.-2820. 1.00 4 18 2400.-2940. 1.00 4 18 2580.-2880. 1.00 4 18 2220.-2580. 1.00 4 18 2460.-2760. 1.00 4 18 2880.-3420. 1.00 4 18 3240.-3660. 1.00 4 18 2220.-2700. 1.00 4 18 2940.-3540. 1.00 4 18 2040.-2580. 1.00 4 18 3060.-3480. 1.00 4 18 2220.-3000. 1.00 4 18 2820.-3840. 1.00 4 18 2160.-2460. 1.00 4 18 2640.-3360. 1.00 4 18 1920.-2640. 1.00 4 18 2940.-3660. 1.00 4 18 3120.-3720. 1.00 4 18 2340.-3060. 1.00 4 12 3060.-3900. 1.00 5 51 2520.-3300. 1.00 5 51 2640.-3420. 1.00 5 51 3240.-3600. 1.00 5 51 2880.-3540. 1.00 5 51 2160.-2400, 1.00 5 51 3000.-3360. 1.00 5 51 2460.-2940. 1.00 5 51 2820.-3540. 1.00 5 51 3000.-3720. 1.00 5 51 2700.-3480. 1.00 5 51 2340.-2700. 1.00 5 51 e000.-3780. 1.00 5 51 2700,-3420. 1.00 5 51 2640.-3060. 1.00 5 51 1920.-2580. 1.00 5 51 2700,-3120. 1.00 5 51 2880.-3360. 1.00 5 51 e100.-2580. 1.00 5 51 2280.-3120. 1.00 5 31 2400.-2820. 1.00 8 1 2640.-3240. 1.00 8 1 3120.-3600. 1.00 9 1 2520.-2820. 1.00 10 2 4180.-3540. 1.00 10 2 3060.-3780. 1.00 10 2 3120.-3900. 1.00 10 2 3060.-3660. 1.00 10 2 2700.-3360. 1.00 10 2 2400.-2760. 1.00 10 2 280.-2700. 1.00 10 2 2280.-2880. 1.00 10 2 2040.-2520. 1.00 10 2 460.-3180. 1.00 10 2 3000.-3660. 1.00 10 2 2700.-3000. 1.00 10 2 580.-2940. 1.00 10 2 2100.-2700. 1.00 10 2 2400.-3180. 1.00 10 2 460.-2880. 1.00 10 1 2580.-3180. 1.00 11 2 3180.-3780. 1.00 11 2 '520.-2940. 1.00 11 2 2820.-3660. 1.00 11 2 2580.-3300. 1.00 11 2 v880.-3660. 1.00 11 2 2220.-2640. 1.00 11 2 1980.-2700. 1.00 11 2 '580.-3120. 1.00 11 2 2040.-2460. 1.00 11 2 2820.-3180. 1.00 11 2 v760.-3360. 1.00 11 2 2160.-2580. 1.00 11 2 2280.-2760. 1.00 11 2 '880.-3240. 1.00 11 2 2580.-3480. 1.00 11 2 2400.-3300. 1.00 11 2 e820.-3420. 1.00 24 1 2280.-3060. 1.00 24 1 2940.-3420. 1.00 24 1 '820.-3240. 1.00 24 1 2220.-2880. 1.00 24 1 2760.-3720. 1.00 24 1 '160.-2880. 1.00 24 1 2040.-2700. 1.00 38 1 2640.-3000. 1.00 38 1 280.-2940, 1.00 38 1 2340.-2940. 1.00 38 1 2760.-3000. 1.00 1 4 f460.-2220. 1.00 1 4 2820.-3120. 1.00 1 4 2760.-2700. 1.00 1 4 400.-2340. 1.00 1 4 2760.-2640. 1.00 1 4 2400.-2400, 1.00 1 4 '460.-2400. 1.00 1 4 2280.-2280. 1.00 1 1 2220.-2400. 1.00 2 4 '880.-2700. 1.00 2 4 2760.-2940. 1.00 2 4 2760.-2580. 1.00 2 4 '760.-3060. 1.00 2 4 2340.-2400. 1.00 2 4 2460.-2520. 1.00 2 4 820.-2640. 1.00 2 4 2160.-2340. 1.00 2 2 2820.-2580. 1.00 3 26 B-15
Tablo B.2-1, continued A B C D E A B C D E A B C D E 2280.-2400. 1.00 3 26 2640.-2400. 1.00 3 26 2580.-2340, 1.00 3 26 2520.-2580. 1.00 3 26 3000.-2940. 1.00 3 26 2640.-2880. 1.00 3 26 2520.-2700. 1.00 3 26 2580.-2580. 1.00 3 26 2220.-2340. 1.00 3 23 2460.-2460. 1.00 4 36 2940.-2700. 1.00 4 36 2700.-2460. 1.00 4 36 2340.-2160. 1.00 4 36 2700.-2700. 1.00 4 36 2580.-2700. 1.00 4 36 2820.-2880. 1.00 4 36 2880.-2940. 1.00 4 36 2700.-2640. 1.00 4 36 2580.-2460. 1.00 4 29 2520.-2400. 1.00 5 101 2340.-2580. 1.00 5 101 3120.-2820. 1.00 5 101 3060.-2820. 1.00 5 101 2880 -2760. 1.00 5 101 2340.-2340. 1.00 5 101 3000.-2880. 1.00 5 101 2940.-3000. 1.00 5 101 2580.-2760. 1.00 5 101 2880.-3000. 1.00 5 91 2340.-2520. 1.00 8 1 2880.-2880. 1.00 8 1 2520.-2340. 1.00 9 1 2400.-2520. 1.00 9 1 2340.-2220. 1.00 10 4 3000.-2760. 1.00 10 4 2580.-2520. 1.00 10 4 2340.-2280. 1.00 10 4 2640.-2760. 1.00 10 4 2460.-2580. 1.00 10 4 2220.-2280. 1.00 10 4 2640.-2460. 1.00 10 4 2280.-2220. 1.00 10 1 2700.-2580. 1.00 11 4 2880.-3060. 1.00 11 4 2700.-2940. 1.00 11 4 2820.-2940. 1.00 11 4 2880.-2640. 1.00 11 4 3060.-2760. 1.00 11 4 2280.-2340. 1.00 11 4 2700.-2820. 1.00 11 4 2820.-2700. 1.00 11 1 2460.-2280. 1.00 24 1 2400.-228C. 1.00 24 1 2820.-2820. 1.00 24 1 2460.-2640. 1.00 24 1 2400.-2220. 1.00 24 1 2280.-2520. 1.00 24 1 2520.-2520. 1.00 24 1 2520.-2460. 1.00 38 1 2760.-2820. 1.00 38 1 2400.-2640. 1.00 38 1 3000.-20Co. 1.00 1 3 3300.-2400. 1.00 1 3 3000,-1980. 1.00 1 3 3120.-2460. 1.00 1 3 3180.-2700. 1.00 1 3 2820.-2040. 1.00 1 3 276L -2460. 1.00 1 3 3180.-2220. 1.00 1 3 3120.-2760. 1.00 1 3 2940.-2220. 1.00 1 3 3300.-2160. 1.00 1 3 2700.-2040. 1.00 1 1 3300.-2460. 1.00 2 3 3000.-2400. 1.00 2 3 2940.-2340. 1.00 2 3 3420.-2460. '1.00 2 3 3'90.-2700. 1.00 2 3 2760.-2040. 1.00 2 3 3000.-2580. 1.00 2 3 2840.-2160. 1.00 2 3 3240.-2460. 1.00 2 3 3000.-2640. 1.00 2 3 2940.-1920. 1.00 2 3 2760.-2160. 1.00 3 19 3060.-2400. 1.00 3 19 3060.-2100. 1.00 3 19 3120.-2640. 1.00 3 19 3240.-2400. 1.00 3 19 3060.-2160. 1.00 3 19 3480.-2340. 1.00 3 19 2760.-1980. 1.00 3 19 3120.-1980. 1.00 3 19 3480.-2280. 1.00 3 19 3000.-2700. 1.00 3 19 2940.-2520. 1.00 3 19 1000.-2280. 1.00 3 19 3360.-2520. 1.00 3 9 3000.-2160. 1.00 4 26 3180 -2160. 1.00 4 26 3120.-2280. 1.00 4 26 2820.-2460. 1.00 4 S 1120.-2220. 1.00 4 26 3000.-1920, 1.00 4 26 3300.-2580. 1.00 4 26 2700.-2280. 1.00 4 26 2820.-2160. 1.00 4 26 2820.-2220. 1.00 4 26 !820.-2520. 1.00 4 26 3120.-2040. 1.00 4 26 3060.-1920. 1.00 4 26 2880.-2340. 1.00 4 15 3000.-2100. 1.00 5 72 3240.-2280. 1.00 5 72 !640.-2280. 1.00 5 72 3180.-2460. 1.00 5 72 3180.-2520. 1.00 5 72 B820.-2100. 1.00 5 72 3120.-2160. 1.00 5 72 2700.-2100. 1.00 5 72 $240.-2220. 1.00 5 72 2700.-2400. 1.00 5 72 3540.-2280. 1.00 5 72 $880.-2220. 1.00 5 72 2940.-2280. 1.00 3 72 2940.-2160. 1.00 5 64 )240.-2640. 1.00 8 1 2640.-2100. 1.00 9 1 2940.-1860. 1.00 9 1 B760.-2280. 1.00 10 3 3060.-2460. 1.00 10 3 2880.-2040. 1.00 10 3 !880.-1800. 1.00 10 3 3000.-2460. 1.00 10 3 3120.-2400. 1.00 10 3 1120.-2520. 1.00 10 3 3300.-2220. 1.00 10 3 3360.-2400. 1.00 10 3 l000.-2520. 1.00 10 3 3060.-2040. 1.00 10 3 3180.-2760. 1.00 10 1 B-16 J
Table B.2-1, continued A B C D E A B C D E A B C D E 3060.-2700, 1.00 11 3 2580.-2160. 1.00 11 3 3420.-2160. 1.00 11 3 2820.-1920. 1.00 11 3 3000.-P140. 1.00 11 3 2640.-2220. 1.00 11 3 2820.-1980. 1.00 11 3 3060.-2520. 1.00 11 3 3540.-2220. 1.00 11 3 1 2760.-1920. 1.00 11 3 3060.-2340. 1.00 11 3 2640.-2160. 1.00 24 1 2700.-2340. 1.00 24 1 2580.-2220. 1.00 24 1 3300.-2100. 1.00 24 1 3300.-2640. 1.00 24 1 3060.-1980. 1.00 24 1 2940.-2100. 1.00 24 1 3120.-2580. 1.00 24 1 3240.-2040. 1.00 38 1 3360.-2280. 1.00 38 1 3420.-2400. 1.00 38 1-2100. 600. 1.00 24 2-2460. 660. 1.00 24 2 =2040. 780. 1.00 24 2-2220. 540. 1.00 24 2-2520. 600. 1.00 24 2 { c2160. 660. 1.00 24 2-2160. 600. 1.00 24 2-2400.
720, 1.00 24 2
m2700. 720. 1.00 24, 2-2280. 540. 1.00 24 2-2040. 660. 1.00 24 2 =2280. 720. 1.00 24 2-2460. 780. 1.00 24 2-2640. 720. 1.00 24 2 >2160. 540. 1.00 24 2-2700. 780. 1.00 24 2-2640. 660. 1.00 24 2 =2340. 660. 1.00 24 2-2580. 660. 1.00 24 1-2340. 720. 1.00 27 1 2400. 660. 1.00 27 1-2340. 600. 1.00 27 1-2220. 660. 1.00 27 1 2040. 540. 1.00 27 1-2220. 720. 1.00 27 1-2400. 600. 1.00 27 1 2100. 660. 1.40 27 1-1980. 660. 1.00 27 1-1980. 720. 1.00 27 1 2280. 660. 1;ne 27 1-2520. 660. 1.00 27 1-2160. 720. 1.00 27 1 2340. 780. 1.00 27 1-2220. 600. 1.00 27 1-2400. 780. 1.00 27 1 2100. 780. 1.00 27 1-2580. 720. 1.00 27 1-2100. 720. 1.00 27 1 2700. 660. 1.00 27 1-2640. 780. 1.00 27 1-2220, 780. 1.00 27 1 .1980. 780. 1.00 27 1-2580. 780. 1.00 27 1-2460. 720. 1.00 27 1 2940. 180. 1.00 24 1-2820. 120. 1.00 24 1-3600. 540. 1.00 24 1 2880. 360. 1.00 24 1-3360. 540. 1.00 24 1-2820. 60. 1.00 24 1 2520. 60. 1.00 24 1-2760. 480. 1.00 24 1-2400. 480. 1.00 24 1 .2220. 360. 1.00 24 1-3060. 540. 1.00 24 1-3600. 180. 1.00 24 1 2700. 540. 1.00 24 1-3540. 420. 1.00 24 1-2280. 300. 1.00 24 1 3500. 420. 1.00 24 1-2520. 54&r 1.00 24 1-2160. 120. 1.00 24 1 h3360. 480. 1.00 24 1-2760. 360. 1.00 24 1-3540. 600. 1.00 24 1 3120. 240. 1.00 24 1-2220. 480. 1.00 24 1-2820. 360. 1.00 24 1 2940. 480. 1.00 24 1-3240. 120. 1.00 24 1-2340. 240. 1.00 24 1 .2580. 60. 1.00 24 1-2880. 540. 1.00 24 1-3060. 120. 1.00 24 1 3300. 300. 1.00 24 1-2160. 60. 1.00 24 1-3480. 360. 1.00 24 1 2580. 480. 1.00 24 1-3300. 180. 1.00 24 1-3120. 180. 1.00 24 1 l 3300. 480. 1.00 24 1-3420. 540. 1.00 24 1-3180. 600. 1.00 27 1 3240. 420. 1.00 27 1-3000, 660. 1.00 27 1-2100. 480. 1.00 27 1 3240. 720. 1.00 27 1-2460. 120. 1.00 27 1-2700. 120. 1.00 27 1 3120. 360. 1.00 27 1-3420. 420. 1.00 27 1-2460. 300. 1.00 27 1 2820. 600. 1.00 27 1-3600 720. 1.00 27 1-2700. 480. 1.00 27 1 3360. 180. 1.00 27 1-294u. 420. 1.00 27 1-2760. 420. 1.00 27 1 2580. 420. 1.00 27 1-3360. 360. 1.00 27 1-3600. 360. 1.00 27 1 2220. 120. 1.00 27 1-2100. 300. 1.00 27 1-2520. 240. 1.00 27 1
3000, 600.
1.00 27 1-2280. 180. 1.00 27 1-3240. 600. 1.00 27 1 3600. -240. 1.00 24 1-2460. -180. 1.00 24 1-3600. -480. 1.00 24 1 2280. -300. 1.00 24 1-4500. -360. 1.00 24 1-2640. -60, 1.00 24 1 3420. -360. 1.00 24 1-3300. -420. 1.00 24 1-4620. -480. 1.00 24 1 l 2340. -180. 1.00 24 1-2460. -240. 1.00 24 1-3180. -180. 1.00 24 1 i B-17 l
Table B.2-1, Continued A B C D E A B C D E A B C D E 2400. -240, 1.00 24 1-4620. -60. 1.00 24 1-3900. -420. 1.00 24 1 4380. -180. 1.00 24 1-3780. -540. 1.00 24 1-4440. -660. 1.00 24 1 3240. -180. 1.00 24 1-4500. -300. 1.00 24 1-2700. -60. 1.00 24 1 4200. -540. 1.00 24 1-4200. -300. 1.00 24 1-4020. -300. 1.00 24 1 4620. -360. 1.00 24 1-4080. -240. 1.00 24 1-2520. -240. 1.00 24 1 3900. -480. 1.00 24 1-2760. -240. 1.00 24 1-2100. -60. 1.00 24 1 4200. -120. 1.00 24 1-2460. -300. 1.00 24 1-3720. -540. 1.00 24 1 2160. O. 1.00 24 1-3600. -540. 1.00 24 1-2700. -180. 1.00 24 1 4260. -360. 1.00 24 1-2820. -240. 1.00 27 1-3480. O. 1.00 27 1 4320. O. 1.00 27 1-3540. -540. 1.00 27 1-3000. -360. 1.00 27 1 2760. -120. 1.00 27 1-4380. -540. 1.00 27 1-4080. -120. 1.00 27 1 2880. -60. 1.00 27' 1-2880. -360. 1.00 27 1-4080. -660. 1.00 27 1 3540. -360. 1.00 27 1-2400. -120. 1.00 27 1-2100. -240. 1.00 27 1 3480. -300. 1.00 27 1-2460. -420, 1.00 27 1-4440. O. 1.00 27 1 4200. -480. 1.00 27 1-4020. -420. 1.00 27 1-3180. -120. 1.00 27 1 2340. -360. 1.00 27 1-4560. -60. 1.00 27 1-3420. -120. 1.00 27 1 4380. -360. 1.00 27 1-4260. -120. 1.00 27 1-4560.-1920. 1.00 24 1 4560.-1800. 1.00 24 1-4140.-1500. 1.00 24 1-4260. -780. 1.00 24 1 4920.-1030. 1.00 24 1-4440.-1020, 1.00 24 1-4800.-1860. 1.00 24 1 4200.-1620. 1.00 24 1-4500.-1860. 1.00 24 1-5160. -960. 1.00 24 1 4680.-1800. 1.00 24 1-4500.-2400. 1.00 24 1-4200.-1200. 1.00 24 1 -4740.-1980. 1.00 24 1-4440.-1860. 1.00 24 1-4920.-1320. 1.00 24 1 4620.-1320. 1.00 24 1-4680.-1260. 1.00 24 1-4320.-1260. 1.00 24 1 4440.-1620. 1.00 24 1-4920.-1740. 1.00 24 1-3900.-1920. 1.00 24 1 4380. -960. 1.00 24 1-4560.-1080. 1.00 24 1-4380.-1140. 1.00 24 1 4980.-1620. 1.00 24 1-4140.-1620. 1.00 24 1-4140.-2100. 1.00 24 1 4500. -900. 1.00 24 1-4020.-1920. 1.00 24 1-4500.-1560. 1.00 24 1 5160.-1020. 1.00 24 1-4620.-1620. 1.00 24 1-4380.-2340. 1.00 24 1 4440.-2400. 1.00 24 1-4200.-2040. 1.00 24 1-4500.-1980. 1.00 24 1 4860.-1440. 1.00 24 1-4260.-20407 1.00 27 1-4560.-1260. 1.00 27 1 4800.-1740. 1.00 27 1-4260.-1980. 1.00 27 1-4680.-2160. 1.00 27 1 4080.-1560. 1.00 27 1-4860.-1500. 1.00 27 1-4320.-1740. 1.00 27 1 4620.-2220. 1.00 27 1-4380.-1980. 1.00 27 1-4320.-1860. 1.00 27 .1 4560. -960. 1.00 27 1-4680.-1620. 1.00 27 1-4200.-2220. 1.00 27 1 4440.-2280. 1.00 27 1-4320.-1200. 1.00 27 1-4500.-1440, 1.00 27 1 4260.-2220. 1.00 27 1-4500.-1260. 1.00 27 1-4860.-1080. 1.00 27 1 4500. -840. 1.00 27 1-4200.-1380. 1.00 27 1-4920.-1200. 1.00 27 1 .4440.-1920. 1.00 27 1-4500.-1140. 1.00 27 1 3720.-2880. 1.00 24 1 3660.-2580. 1.00 24 1 3960.-2880. 1.00 24 1 4260.-2460. 1.00 24 1 4320.-2640. 1.00 24 1 4200.-2880. 1.00 24 1 3900.-2340. 1.00 24 1 4080.-2220. 1.00 24 1 4380.-2400. 1.00 24 1 4200.-3000. 1.00 24 1 4620.-2460. 1.00 24 1 3720.-2580. 1.00 24 1 3780.-2640. 1.00 24 1 0080.-3000. 1.00 24 1 3960.-2700. 1.00 24 1 4080.-2760. 1.00 24 1 4380.-2520. 1.00 24 1 3960.-2940. 1.00 24 1 4020.-3060. 1.00 24 1 0440.-2520. 1.00 24 1 4620.-2520. 1.00 24 1 4080.-2580. 1.00 24 1 4320.-2580. 1.00 24 1 3780.-2400. 1.00 24 1 4380.-2340. 1.00 24 1 G260.-2340. 1.00 24 1 4200.-3120. 1.00 24 1 4320.-2460. 1.00 24 1 l l B-18
l l Table B.2-1, continued A B C D E A B C D E A B C D E l4440.-2700. 1.00 24 1 4560.-2640. 1.00 24 1 3960.-3060. 1.00 24 1 3840.-2940, 1.00 24 1 3660.-2640. 1.00 24 1 3900.-2940. 1.00 24 1
3660.-2760.
1.00 24 1 4140.-3000. 1.00 24 1 4140.-2220. 1.00 24 1
3960.-2340.
1.00 24 1 3660.-2700. 1.00 24 1 4440.-2760. 1.00 24 1 l4020.-2160. 1.00 24 1 4140 -2160. 1.00 24 1 4260.-2700. 1.00 24 1 !4080.-2940. 1.00 24 1 4200.-2700. 1.00 24 1 4440.-2640. 1.00 24 1 l3660.-2820. 1.00 24 1 4560.-2520. 1.00 24 1 4200.-2760. 1.00 24 1 l4440.-2280. 1.00 24 1 4080.-2700. 1.00 27 1 3840.-3000. 1.00 27 1 l3780.-2820. 1.00 27 1 3900.-2220. 1.00 27 1 3960.-2820, 1.00 27 1
4440.-2460.
1.00 27 1 4560.-2580. 1.00 27 1 3780.-2700. 1.00 27 1
3840.-2640, 1.00 27, 1 3780.-2940, 1.00 27 1 4020.-2400.
1.00 27 1 !4500.-2340. 1.00 27 1 4020.-2100. 1.00 27 1 3840.-2460. 1.00 27 1 4320.-2940. 1.00 27 1 4140.-2820. 1.00 27 1 4080.-2340. 1.00 27 1 l3960.-2640. 1.00 27 1 4380.-2640. 1.00 27 1 4080.-2400. 1.00 27 1 4200.-2820. 1.00 27 1 3960.-2520. 1.00 27 1 4440.-2400. 1.00 27 1 13600.-2760. 1.00 27 1 4080.-2100. 1.00 27 1 4140.-2460. 1.00 27 1 4080.-3060. 1.00 27 1 3600.-2700. 1.00 27 1 3840.-2400. 1.00 27 1 4020.-3000. 1.00 27 1 4440.-2340. 1.00 27 1 4680.-2400. 1.00 27 1 3840.-2820. 1.00 27 1 4320.-2520. 1.00 27 1 3240.-1560. 1.00 24 1
3240.-1080.
1.00 24 1 3540.-1440. 1.00 24 1 2940.-1320. 1.00 24 1 3480.-1380. 1.00 24 1 4140.-1320. 1.00 24 1 3060.-1380. 1.00 24 1 3840.-1380. 1.00 24 1 3540. -840. 1.00 24 1 3480.-1020. 1.00 24 1 '@000.-1320. 1.00 24 1 3480.-1680. 1.00 24 1 3480.-1200. 1.00 24 1 3240.-1260. 1.00 24 1 4080.-1380. 1.00 24 1 4200.-1020. 1.00 24 1 @l80.-1020. 1.00 24 1 3420.-1260. 1.00 24 1 3300. -960. 1.00 24 1 3360.-1140. 1.00 24 1 3840.-1740. 1.00 24 1 3540.-1800. 1.00 24 1- @780.-1200. 1.00 24 1 3960.-1800. 1.00 24 1 3480.-1080. 1.00 24 1 3000.-1380. 1.00 24 1 3960.-1380. 1.00 24 1 3420.-1020. 1.00 24 1 @240.-1020. 1.00 24 1 3420.-1080. 1.00 24 1 3660.-1440, 1.00 24 1 '3540.-1380. 1.00 24 1 3960.-1740. 1.00 24 1 3720.-1860. 1.00 24 1 8360.-1620. 1.00 24 1 3960.-1000. 1.00 24 1 3960.-1440. 1.00 24 1 3300.-1320. 1.00 24 1 3780.-1920. 1.00 24 1 4260.-1200. 1.00 24 1 @360. -960. 1.00 24 1 3840.-1500. 1540 24 1 3600.-1320. 1.00 24 1 '3660.-1560. 1.00 24 1 3420. -840. 1.00 24 1 3060.-1140, 1.00 24 1 8000.-1200. 1.00 24 1 3720.-1680. 1.00 24 1 3840.-1620. 1.00 24 1 3720.-1320. 1.00 24 1 3540.-1500. 1.00 27 1 4020.-1860. 1.00 27 1 8360.-1080. 1.00 27 1 4020.-1740. 1.00 27 1 3840.-1860. 1.00 27 1 3900.-1980, 1.00 2'/ 1 2880.-1200. 1.00 27 1 3060. -840, 1.00 27 1 G320.-1020. 1.00 27 1 3000.-1140. 1.00 27 1 3900.-1680. 1.00 27 1 3840.-1440, 1.00 27 1 3180.-1500. 1.00 27 1 3840.-1560. 1.00 27 1 !G140.-1200. 1.00 27 1 3540.-1020. 1.00 27 1 3120.-1080. 1.00 27 1 l0080.-1620. 1.00 27 1 3480.-1260. 1.00 27 1 3900.-1560. 1.00 27 1 @600.-1740. 1.00 27 1 3300.-1260. 1.00 27 1 3960.-1980. 1.00 27 1 LO320.-1080. 1.00 27 1 3360. -840. 1.00 27 1 3900.-1860. 1.00 27 1 $200.-1500. 1.00 27 1 3900.-1620. 1.00 27 1 3240.-1380. 1.00 27 1 @300.-1140. 1.00 27 1 4020.-1440. 1.00 27 1 4080. -960, 1.00 27 1 3180.-1440. 1.00 27 1 3000. -540. 1.00 24 1 2640. -480. 1.00 24 1 l B-19
i Table B.2-1, continued .A B C D E A B C D E A B C D E 2760. -180. 1.00 24 1 2520. -120. 1.00 24 1 2340. -300. 1.00 24 1 2820. -300. 1.On 24 1 2880. -600. 1.00 24 1 2940. -240. 1.00 24 1 2640. -420.
1. Je 44 1 2880. -660.
1.00 24 1 2700. -600. 1.00 24 1 2880. -60. 1.os 24 1 2280. -420. 1.00 24 1 2700. -420. 1.00 24 1 2400. -120. 1.00 24 1 2640. -360. 1.00 24 1 3060. -360. 1.00 24 1 ,2040. -60. 1.00 24 1 2280. -480. 1.00 24 1 2100. -60. 1.00 24 1 12220. -480. 1.00 24 1 2700. -300. 1.00 24 1 2520. -360. 1.00 24 1 '2940. -480. 1.00 24 1 2940. -360. 1.00 24 1 2760. -60, 1.00 24 1 2940. -180. 1.00 24 1 2280. -120. 1.00 24 1 2160. -60. 1.00 24 1-2400. -300. 1.00 24 1 2340. -420. 1.00 24 1 2820. -240. 1.00 24 1 2100. -480. 1.00 24. 1 2700. -540. 1.00 24 1 2100. -420. 1.00 24 1 2940. -540. 1.00 24 1 2400. -540. 1.00 24 1 2640. -300. 1.00 24 1 ,3000. -300. 1.00 24 1 2220. -60. 1.00 24 1 2280. -300. 1.00 24 1 2040. -180. 1.00 24 1 3060. -420. 1.00 24 1 2340. -60. 1.00 24 1 ,2820. -540. 1.00 24 1 3000. -480. 1.00 24 1 2640. -180. 1.00 24 1 l3000. -60. 1.00 24 1 2400. -60. 1.00 24 1 2460. -540. 1.00 24 1 l2220. -300. 1.00 27 1 2700. -60. 1.00 27 1 2S80. -120. 1.00 27 1 I2280. -60. 1.00 27 1 2820. -120. 1.00 27 1 2100. -120. 1.00 27 1 l2340. -360. 1.00 27 1 2040. -420. 1.00 27 1 2820. -420. 1.00 27 1 !2880. -360. 1.00 27 1 2580. -360. 1.00 27 1 2940. -120. 1.00 27 1 $520. -480. 1.00 27 1 3060. -60. 1.00 27 1 3000. -360. 1.00 27 1 !2460. -360. 1.00 27 1 2880. -420. 1.00 27 1 2160. -360. 1.00 27 1 $640. -120. 1.00 27 1 2400. -480. 1.00 27 1 2940. -60. 1.00 27 1 l2880. -120. 1.00 27 1 2580. -180. 1.00 27 1 2460. -240. 1.00 27 1 8160. -300. 1.00 27 1 2520. -300. 1.00 27 1 2940. -300. 1.00 27 1 l3060. -540. 1.00 27 1 2640. -60. 1.00 27 1 2220. -240. 1.00 27 1 8760. -420. 1.00 27 1 3000. -660. 1.00 27 1 3000. -600. 1.00 27 1 )-480.-2940. 1.00 24 1-1320.-3120. 1.00 24 1-1380.-3660. 1.00 24 1 H540.-3660. 1.00 24 1 -900 -3120. 1.00 24 1 -480.-4140. 1.00 24 1 H720.-4080. 1.00 24 1-1200 -3120. 1.00 24 1-1680.-3780. 1.00 24 I s480.-4020. 1.00 24 1 -420.-3360. 1.00 24 1 -780.-3960. 1.00 24 1 H360.-4020. 1.00 24 1-1620.-3660. 1.00 24 1 -360.-3360. 1.00 24 1 L360.-4140. 1.00 24 1 -780.-3540. 1.00 24 1 -480.-3600. 1.00 24 1 o480.-4200. 1.00 24 1 -600.-2580. 1.00 24 1 -540.-2820. 1.00 24 1 P600 -3000. 1.00 24 1-1080.-3000.) 1.00 24 1-1320.-3540. 1.00 24 1 l1380.-3960. 1.00 24 1-1140.-3480. 1.00 24 1 -960.-2700. 1.00 24 1 '420.-3240. 1.00 24 1-1200.-3840. 1.00 24 1-1620.-3780. 1.00 24 1 P 9600.-2640. 1.00 24 1 -780.-2820. 1.00 24 1 -660.-2700. 1.00 24 1 F300.-3780. 1.00 24 1 -780.-3060.. 1.00 24 1 -480.-3660. 1.00 24 1 l3 620. -3 90 0. 1.00 24 1 -360.-3780, 1.00 24 1-1260.-3600. 1.00 24 1 >540.-3060. 1.00 24 1-1380.-3780. 1.00 24 1 -420.-3000. 1.00 24 1 '240.-3360. 1.00 24 1 -900.-3840. 1.00 24 1 -480.-2820. 1.00 24 1 P>960.-3720. 1.00 27 1 -420.-3120. 1.00 27 1 -660.-3180. 1.00 27 1 ) '300.-3360. 1.00 27 1 -780.-4020. 1.00 27 1 -600.-3660. 1.00 27 1 '080.-3060. 1.00 27 1-1260.-3960. 1.00 27 1 -720.-4020. 1.00 27 1 840.-3300. 1.00 27 1 -720.-3900. 1.00 27 1-1020.-3420. 1.00 27 1 540.-3960. 1.00 27 1-1020.-3240, 1.00 27 1 -600.-3420. 1.00 27 1 B-20 i
Table B.2-1, continued A B C D E A B C D E A B C D E -780.-3240. 1.00 27 1 -720.-4140. 1.00 27 1 -780.-3480. 1.00 27 1 1140.-2760. 1.00 27 1 -840.-2880. 1.00 27 1 -660.-2580, 1.00 27 1 1020.-2880. 1.00 27 1 -960.-3960. 1.00 27 1 -300.-4200.- 1.00 27 1 -840.-2820. 1.00 27 1 -240.-3180. 1.00 37 1 -720.-2880. 1.00 27 1 -480.-3540. 1.00 27 1 -300.-2820. 1.00 27 1 -720.-3660. 1.00 27 1 -960.-3300. 1.00 27 1 -660.-3300. 1.00 27 1-1140.-3360. 1.00 27 1 -120.-3360. 1.00 24 1 120.-3720. 1.00 24 1 180.-3300. 1.00 24 1 60.-3360. 1.00 24 1 420.-3360. 1.00 24 1 720.-3840. 1.00 24 1 720.-3300. 1.00 24 1 420.-3720. 1.00 24 1 -60.-3480. 1.00 24 1 180.-3720. 1.00 24 1 360.-3600. 1.00 24 1 600.-3420. 1.00 24 1 -180.-3660. 1.00 24-1 240.-3720. 1.00 24 1 120.-3840, 1.00 24 1 660.-3420. 1.00 24 1 360.-3540. 1.00 24 1 480.-3720. 1.00 24 1 480.-3480. 1.00 24 1 480.-3420. 1.00 24 1 300.-3780. 1.00 24 1 !-120.-3660. 1.00 24 1 480.-3660. 1.00 24 1 0.-3540. 1.00 24 1 180.-3480. 1.00 24 1 720.-3540. 1.00 24 1 300.-3420. 1.00 24 1 -120.-3240. 1.00 24 1 120.-3240. 1.00 24 1 -180.-3300. 1.00 24 1 0.-3660. 1.00 24 1 180.-3180. 1.00 24 1 840.-3600. 1.00 24 1 360.-3840. 1.00 24 1 720.-3780. 1.00 24 1 -240.-3720. 1.00 24 1 720.-3720. 1.00 24 1 540.-3300. 1.00 24 1 240.-3780. 1.00 24 1 0.-3360. 1.00 24 1 360.-3660. 1.00 24 1 240.-3180. 1.00 24 1 540.-3540. 1.00 24 1 240.-3900. 1.00 24 1 420.-3540. 1.00 24 1 -120.-3420. 1.00 27 1 420.-3600. 1.00 27 1 -60.-3540. 1.00 27 1 540.-3720. 1.00 27 1 720.-3180. 1.00 27 1 -60.-3900. 1.00 27 1 600.-3780. 1.00 27 1 0.-3240. 1.00 27 1 540.-3780. 1.00 27 1 -120.-3840. 1.00 27 1 240.-3360. 1.00 27 1 900.-3780. 1.00 27 1 240.-324&. 1.00 27 1 720.-3240, 1.00 27 1 780.-3430. 1.00 27 1 180.-3660. 1.00 27 1 840.-3660. 1.00 27 1 720.-3360. 1.00 27 1 -240.-3840. 1.00 27 1 420.-3480. 1.00 27 1 780.-3420. 1.00 27 1 -60.-3600. 1.00 27 1 660.-3600. 1.00 27 1 -60.-3300. 1.00 27 1 720.-3420. 1.00 27 1 660.-3480. 1.00 27 1 120.-3420. 1.00 27 1 -60.-3660. 1.00 27 1 -240.-3780. 1.00 27 1 420.-3420. 1.00 27 1 720.-3120. 1.00 27 1 -60.-3180. 1.00 27 1 -120.-3960. 1.00 24 1 480.-4260. 1.00 24 1 -120.-4260. 1.00 24 1 -120.-4020. 1.00 24 1 -120.-4200. 1.00 24 1 -300.-3960, 1.00 24 1 0.-4200. 1.00 24 1 120.-4200. 1.00 24 1 120.-3960. 1.00 24 1 -60.-4200. 1.00 24 1 180.-4080. 1.00 27 1 240.-4140. 1.00 27 1 60.-4140. 1.00 27 1 240.-4200. 1.00 27 1 -300 -4320. 1.00 27 1 360.-4140. 1.00 27 1 240.-3960. 1.00 27 1 420.-4200. 1.00 27 1 420.-4080. 1.00 27 1 300.-4200. 1.00 27 1 -840. -300. 1.00 26 1 120. -840. 1.00 26 840. -240. 1.00 26 1 420. -720. 1.00 26 1 -840. 120. 1.00 26 1 3840. 180. 1.00 26 1 -480. -780, 1.00 26 1 -180. -900. 1.00 26 1 300. -840. 1.00 26 1 -720. -540. 1.00 26 1 -240. -840. 1.00 26 1 420. -780. 1.00 26 1 540. -720. 1.00 26 1 -780. -300. 1.00 26 1 660. -600. 1.00 26 1 780. -480. 1.00 26 1 -900. 180. 1.30 26 1 720. -420. 1.00 26 1 -60. -900. 1.00 26 1 -720. -480. 1.00 26 1 360. -360. 16.00 16 80 -480. -420. 12.00 16 60 -360. -420. 4.00 21 4 420. -480. 8.00 28 305 -490. 60. 1.00 32 1 -500. 60. 1.00 32 1 B-21
Table B.2-1, continued A B C D E A B C D E A B C D E -320. 100. 1.00 32 1 -320. 110. 1.00 32 1 -320. 120. 1.00 32 1 1 -320. 130. 1.00 32 1 180. 80. 6.50 29 1 180. 90. 6.50 29 1 180. 100. 6.50 29 1 180. 110. 6.50 29 1 180. 120. 6.50 29 1 180. 130. 6.50 29 1 180. 140. 6.50 29 1 180. 160. 6.50 30 1 180. 180. 6.50 30 1 180. 200. 6.50 30 1 180. 220. 6.50 30 1 180. 240. 6.50 30 1 180. 255. 6.50 31 1 180. 270. 6.50 31 1 180. 285. 6.50 31 1 180. 300. 6.50 31 1 888. -280. 1.00 33 5 168. -664. 1.00 34 79
84. -404.
1.00 35 1 2120. 400. 1.00 36 1 8170. 400. 1.00 37 1 2220. 400. 1.00 37 1 -480. 60. 1.00 2 1 in Ecot coordinate B is North coordinate C is elevation so Diosile designation according to Table B.2-2 in the number of missiles at that particular site l'01100 are distributed by a random (Monte Carlo) process within the missile p hdown regions shown in Figure B.2-1 \\ ] B-22 i
1 l l Traversal of Tornadoes Across Site l i l When it has been determined that the damage path of a particular tornado includes missiles that could inflict plant damage, the tornado is moved across the entire l plant site in equal-distance increments. The other tornadoes, assumed to be non- ) l damaging, are counted as satisfying the recurrence interval, but are not incremented across the site., Missile Flight l At each translational 'tep of the tornado, each missile within the 75 mph wind field s that satisfies the flight initiation criteria is flown and subjected to potentia! j reflight (if it lands ahead of the tomado) until one of the following fates is encountered: Missile lands outside the path of a tornado e Missile remains in the wind field beyond some time limit (possible with e the lighter missiles) Missile lands in a body of water (Cape Cod Bay, in this case) e l e Missile leaves boundary of site Missile intersects boundary of plant proper. e 1 For the latter fate, the missile velocity vector, the position coordinates at the plant l boundary, and the identification of the tornado are recorded for subsequent utilization in the plant interaction portion of the code. h Missile-Plant Interaction The original missile-plant interaction portion of the analysis (MISBECO) was run as a separate computer program with initial missile data supplied by the tornado-flight portion (WIZ). Missile trajectories are determined by the equations of free-flight ballistics. At the plant wall 3, the appropriate missile interaction was determined by l tabulated values of critical missile velocities versus wall thickness. All thicknesses of walls used in the plant are included in the tables. The missile was allowed to J B-23
i l _ perforate the wall, cause. spallation damage, cause " punching" shear, cause structural damage, or rebound (ricochet) without inflicting damage to the wall. For missile ~ perforation, the post-perforation velocity was determined from tabulated values (as a function of incident velocity). For missile ricochet, the ricochet velocity was calculated. Missile flights within the plant were terminated if the missile exited the plant or if. it degraded in energy to a non-hazardous level. Damage to any critical area or room was recorded according to the damage type for use in the probability calculation. Individual computer traces of the missile flights within the plant are l cvailable from the program if desired. Probabilitv rnicuinnoni For this study, a detailed model of the plant with associated interactions is unnecessary, since only a single (outside) wall penetration is modeled. This penetration by a missile of the outside wall is an upper limit to the rate of imparting unacceptable damage to the conduit. The total probability of penetration of the structure housing the electrical conduits by the ratio: P . total nrobability of nenetration summed over all tornadoes = total number of years of tornadoes simulated If more than one missile per tornado impacts the structure of interest, these penttration probability values are individually snmmed up to a maximum of 1. B.2.2 Calculation of Penetration Probability The PILGRIM 1 code produces the " standard" output shown in Figure B.2-2. The cbbreviations at the top of the columns are, respectively, the missile number and type code (Table B.2-1), missile start location in polar coordinates (radius, r, and polar mph),. initial wind velocity and angle of direction in degrees, tornado center location in r coordinates, integration time in reconds, final missile location in r coordinates, final missile horizontal velocity in the r system, I l B-24 -., ~ -.
DATE':10-20-p7 TEPE:' 2:l'3:36 0 PAfiE 79 MISSILE MISSILE LOC: INIT.NND.YEL TORNADn LOC. MIST.. LOC:END INT. TRM. HIST. VEL EIGHT 2-DOT MISSILE DSPt.. T.DSPt. NM/iYPE F? ART FT/DFG (TT/SI C)/Dr0 - fT/Drn TT/KG TINr'(TT/';rC)/DrG FT FT/SrC-' DIST/DIR - DIST TIE F EtFTDEt-' --c33/41-se7th s/-170:5-199:r/--15.7 i .G/ 176.1 3112:ct-119.4 6.5 42.6/ ii.. ovu.u <u.s a wa.n/ h.s ervs.. i.= a = 1.mu seu 601/26 617.4/-149.3 295.9/ 93.6 2039.0/ 176.1 2354.0/ 141.9 35.0 151.6/ -2.4 .3 -11.7 2707.1/ 126.9 2411.1 6.3 1 9 .20 479 615/?6 709.1/-119.7 246.5/ 96.9 2039.0/ 176.1 1914.1/ 126.2,40.7 P03.4/ 22.3 620.9 2.2 2296.3/ 109.9 2005.7 7.0 1 4 1.10 519 6In/P6 son.s/-t33.4 ?^5.7/ -oO.a 203n.0/ t 76. 10n2.4/ !?2.9 40.2 200.7/" 77.5 391.9 -- 4.1 2106.9/ Irv. 9 2770;it 7.6 1 4 1.10 572-621/21 43n.0/ -96.7 213.9/ 91.6 203H.0/ 176.1 207.1/-107.9 2.0 175.6/ 93.4 64.3 39.1 23H.2/ 93.0 137.9 1.1 1 6 .10 64 63s/ 2 17A.9/ 165.3 233.3/ 102.4 20'te.0/ 176.1 2fEt.4/ 151.7 1.0 97.4/ 103.2 12.9 19.4 55.7/ 103.2 68.9 9 17 .10 54 -e /es-eBa re/---34:e-t5e.e/-sers-1:m.1/ 237.e 3150:e/ 64.s 26.7 222.9/ ic>.6 cor.5 <=.3 3rui.5i muu.s awar.a ..a I = x.au zia 43/24 990.4/-136.5 253.3/ 66.7 1992.1/ 157.6 562.4/-157.5 4.4 103.3/ 60.5 .O -9.3 4*7.9/ 67.4 301.6 '1.0 1 1 .09 62 45/24 933.5/-149.5 207.6/ 70.4 1992.1/ 157.6 1204.9/ 104.9 9.9 ?40.5/ 94.3 .5 -29.1 1649.6/ 75.9 617.0 1.6 1 9 .25 117 54/P4 - 76a: a /-133: 7 F4*.0/---712 5-t*n2rl/- 157.s-4n0.9/4151:9 --3.6 1 ws;3/-72:s .6 -7.T 345:6/ 72.0 244.7 - '.912-.25 53 64/24 967.3/-149.2 294.7/ 66.9 1992.1/ 157.6 1t171.7/ 109.9 9.7 230.P/ 00.3 .4 -29.7 15H4.3/ 72.2 599.9 1.6 1 9 .10 119 71/24 052.9/-133.9 240.6/ 69.6 1992.1/ 157.6 568.5/-147.4 3.5 157.0/ 70.5 .1 -7.4 3?O.4/ 70.0 237.9 .9 1 1 .25 52 -131/94-fe34r9/-136tf-e44:4/--etre--f G2. ;/ 137.e iG13.e/~140.-1 2.6 i38-4/ si.4 .i w.i 2ai.+/ es.i ave.s .2 m a .es
== 107/ 1 432.7/ 33.7 193.3/ 92.6 1902.1/ 157.6 2734.6/ 107.7 40.6 167.7/ 39.4 1677.9 4.9 2649.2/ 116.7 2799.0 7.7 1 4 1.10 549 117/ 4 365.0/ -9.5 199.4/ 97.6 1992.1/ 157.6 369.2/ 9.6 2.7 90.9/ 97.9 .3 -36.2 121.4/ 99.1 196.1 .7 1 1 .50 40 --t i 7/-4 -- 349.7/-9:6 163.n/ --69.5 2s47:D/- !?2.3-411.7/ --1n.2 - 2.3-56.n/ 6n.2 1.5 -42.5 72;te/- 60.3 167.o--.6 2 2 ~;25-36 117/ 4 3e,9.2/ 9.6 145.0/ 63.5 30g3.5/ 112.9 399.9/ 15.1 2.2 42.1/ 63.0 .5 -45.4 40.3/ 63.0 149.2 .532 .05 32 121/ 5 400.0/ .O 100.P/ 98.7 19ft2.1/ 157.6 5?O.4/ 22.t 3.7 104.4/ 99.4 -1.7 -32.0 195.7/ 09.3 220.6 61 1 1.on 44 25/ 300. / -::.: ::::4/ 07.0 : e2.2/ 237.e 324it/-19.o 2.e 117.7/ ee.2 .i -5.. io+.-/ vo.2 moa.r .i a a .a. =a 126/ 6 300.0/ -36.9 195.2/ 95.2 1992.1/ 157.6 253.5/ 2.0 2.5 123.0/ 96.0 .1 -6.0 199.4/ 96.0 174.1 711 43 42 120/ 7 349.9/ 31.0 199.2/ 91.6 1992.1/ 157.6 2606.7/ 111.0 40.3 177.6/ 29.6 1463.6 7.2 2569.5/ 110.7 2779.2 7.4 1 4 1.10 526 US nsa/-4-5% e/--1P:s 174.1/-86:* 1*Re:t/ -tsr.6-544.n/ -3;n-- 2:5 - 6s.7/- 1i7.3 -i.5 -3,.7 ai.2/ 97 s--172.3 .5 i 1. :o 36-tJ 159/ 4 544.9/ -3.0 170.3/ 76.9 2203.4/ 135.9 564.4/ 5.0 2.4 61.4/ 76.9 .9 -41.0 90.5/ 77.0 165.4 .522 .20 34 158/ 4 544.9/ -3.0 113.2/ 60.9 40A4.4/ 100.9 557.0/ .7 2.0 25.0/ 60.1 -2.3 -50.7 75.9/ 60.1 137.9 .5 3 2 90 29 m/
2.:./ =. : :=,5/ 7:.: : _.:/ :07.; ett: / 3;.3 3.3 :se.3/
12.4 .i -su.e <uo.ei +2.5 2,5.e ... a i .u. 163/ 5 611.0/ 39.5 154.1/ 65.5 3053.6/ 112.3 697.9/ 42.9 2.5 67.5/ 65.1 -1.4 -39.9 95.1/ 65.2 172.3 .621 .30 36 101/11 662.7/ 5.2 169.6/ 99.6 1992.1/ 157.6 779.2/ 25.5 3.6 116.9/ 90.6 .5 -29.9 254.3/ 90.4 244.7 .911 .25 49 - eas/P4-3796.3/ 17e:9 1e7.9/ ;-a t : t --1*aert /- 157.6 3?23.3/ -173.1 - 1.3 51.0/--3n.1 .6 -2.3 A..n/ sn.1r 91.a .rl tr.20 52-297/39 3070.4/ 173.5 171.4/ -23.8 1992.1/ 157.6 3747.7/ 112.9 40.4 19.6/ -15.6 312.7 -23.6 3496.9/ 62.9 2796.9 7.3 1 4 1.10 552 207/40 3070.4/ 173.5 171.4/ -23.8 1992.1/ 157.6 3000.2/ 113.4 40.4 19.7/ -47.1 236.0 -23.4 3507.1/ 63.9 2707.6 7.3 1 4 1.10 554 --aza/39-e5es:9/-a7*.e-e05:e/ :2.c ; a.;/ 107.o 3e62.6/ 113.7 es.4 5+.7/ i.4 ie7.6 <=.e mu5.2/ Ji.+ < r.. 4. m.au saa 330/40 2523.9/-174.2 205.2/ 12.0 1992.1/ 157.6 3493.2/ 114.9 40.4 59.3/ .9 98.7 -26.0 3502.2/ 73.0 2792.5 7.3 1 4 1.10 $57 330/41 2523.9/-174.2 205.2/ 12.0 1992.1/ 157.6 3435.7/ 111.4 40.3 62.4/ 29.9 372.4 -24.0 3677.2/ 70.0 2791.6 7.5 1 4 1.00 574 - 331/39 3171:O/-179 7 FF1.3/--16.0-1*a2.1/- 157;6 36R2.8/ 114.6 40.5 -40.0/'21 ;6 966-9-*16-3 3742.7/ 64.0 2793.< 7;r 1"4 1.10 544-331/40 3171.0/-179.7 221.3/ -16.0 1992.1/ 157.6 3746.5/ 115.5 40.4 40.3/ -40.5 919.6 -15.1 3739.8/ 65.3 2793.3 7.1 1 4 1.10 537 331/41 3171.0/-179.7 221.3/ -16.0 19n2.1/ 157.6 3501.5/ 112.3 40.5 41.7/ 14.2 996.1 -17.7 3705.1/ 61.6 27R9.4 7.3 1 4 1.10 557 -334/39-e71ae/-47 era-e30s/ e.e 2 6.;/ ;37.6 347e:4/-114.7 es.3 62.4i i.i oui.5 <u.e si.e.si 334/40 2717.0/-172.1 230.2/ 6.6 1992.1/ 157.6 3519.5/ 115.9 40.3 61.0/ -10.9 542.9 -19.2 3722.9/ 72.0 2777.3 7.3 1 4 1.10 553 ru.i < .o i.a a, 1.10 5s7 334/41 2717.0/-172.1 230.2/ 6.6 1992.1/ 157.6 3444.7/ 112.0 40.5 62.7/ 23.7 756.7 -20.0 sn33.9/ 69.6 2791.1 7.4 1 4 1.10 561 -34 r/3* 3?se.7/-173:4 -t =2. 7/ --3. 7 1*a2: t / -t S7: 6 3649.*/ -115.9 - co.s -54.1/--24. s-1352. s 9:3 4nne:6/- ss.v 279tr:tr 7.u r 4 r;ln s23-34t/40 3252.7/-173.4 192.7/ -3.7 1992.1/ 157.6 3716.3/ 116.9 40.5 56.3/ -39.3 1316.9 -7.3 4000.3/ 67.2 2791.9 7.1 1 4 1.10 525 34t/41 3252.7/-173.4 192.7/ -3.7 1992.1/ 157.6 3559.4/ 113.3 40.5 50.4/ 6.1 1444.3 -12.0 4074.3/ 63.4 2791.3 7.5 1 4 1.10 561 O Mgure B.2-2 " Standard" PILGRIM 1 Output l_ g R N A L hLouT1 (.4 comJ WA d D
1 1 a final missile height, final missile vertical velocity, total missile displacement in r coordinates, distance of tornado displacement, the time of flight, the number of missiles flown, and a code for the end condition (final two numbers are no longer used). The end condition codes 5, 6, and 7, are those that terminate on the plant cnvelope with a position and velocity such that strikes are possible on the containment above the auxiliary bay, op the auxiliary bay, itself, and on the water intake structure, respectively. The code was modified for actual use to print out only 5, 6, and 7 end condition locations for this study. A post processor code was added to calculate actual building strike conditions for hits on the auxiliary bay and the containment wall above it. There were few enough hits on the water intake structure that these parameters were calculated outside the main system with the BASIC code HITWAT listed in Appendix C. Typical results of the post processor code, BAYHITS, for hits on or above the tuxilirry bay are shown in Figure B.2-3, which lists location and velocity components of strikes on regions which could impact the auxiliary bay. Walls of the auxiliary bay subject to missile penetration are designated walls 1, 2, and 3, and 4 for the roof, the west face wall, the side of the reactor building above the bay, and the north wall (which is actually a wall of the reactor entry port), respectively. The south and east walls of the structure abut, respectively, on the office building and the reactor building and are not subject to missile strikes. Wall 1 strikes are all on the metal roof; wall 2 strikes are either concrete panel strikes or strikes on doors, depending on location (as determined by strike coordinates); wall 3 strikes are all non-penetrating for the reactor building, but all missiles striking this wall subsequently fall on the auxiliary bay roof and their v locity is assumed to be determined by free fall from the point of impact as explained in Section 2.2.; and, finally, wall 4 strikes are all strikes on concrete panels. Strikes simulated for the water intake structure were all on the concrete panels. The probability of penetration of each strike ' was determined independently with interactive computer codes, one each for concrete and for reel. Concrete penetrations were governed by the CEA/EDF formula (2) and steel penetrations by the Hagg-Sankey formula (1) as described below. B-26 o
i 2 4 l i j I i Thic is file 10300952. HIT with aux bay hit results from: Filo 10300952.DAT, started: 10-30-87 , 09:52:59 cftcr -530229 random numbers and 3441645 years. l 530259 165 181.22 870.0 1.257 42.54 181.9 242.7 3442923 i 21 4 144.2 -102.0 23.8 -112.4 86.4 26.9 6 W211 3 hit coords: x= -71.00, y= 62.62, z= 75.30 533510 202 121.76 870.0 .471 48.61 96.0 328.4 3460602 536045 34 81.29 300.0 2.042 31.39 65.5 136.0 3491487 i 536176 184 159.65 2000.0 2.042 46.44 148.5 B43.6 3495960 ' 537194 53 193.25 300.0 .471 36.57 205.5 82.4 3499155 537577 21 118.28 300.0 5.184 35.03 109.2 123.9 3503628 l 538163 166 189.37 070 0 1.257 50.40 182.3 216.9 3512148 540175 8 162.06 110..O 1.257 17.11 190.1 35.5 3525354 1 540694 35 90.35 300.0 1.257 42.95 62.2 122.3 3540903 ! 542230 382 138.34 2800.0 1.257 35.23 135.3 1010.0 3543672 i j CD 6 -137.9 49.0 17.2 50.9 -23.2 -22.1 6 Wall 2 hit coords: x= -122.00, y= 41.75, z= 10.30 4' Figure B.2-3 Output for Hits on Auxiliary Bay B-27
Missile Penetration (Perforation) of Concrete This study used a formula for concrete penetration which was derived on the basis of tests performed by the Commissariat a l'Energie Atomique - Electricite de France (CEA-EDF). EPRI recommends this formula as providing the best match to experimental data over a full range of missile velocities. Its form is T = 0.765 c ~38 (h) 10 3M Vi B.2-1 p c where T= thickness of wall that is penetrated 50% of the time for the given missile (in) p o= concrete compression strength (psi) c W= missile weight (Ib) D= effective diameter (in) D = 2i A/x where A represents an effective impact area V= incident velocity (ft/sec) i The combination of impact area and velocity obviously governs barrier penetration for a given missile. Missile State Following Penetration If Tp (as calculated by Eq. B.2-1) exceeds T, the velocity (V ) required to penetrate p the barrier is calculated by a rearrangement of Eq. B.2-1, as follows: 14(h) V =T 40 p p cc 0.765 B.2-2 B 28
The residual velocity (Vs) following penetration (Reference 9) is Vr = kw+w, (Vf - Vj) B.2-3 where W, = weight of wall plug removed (Ib) = x (1.4D)2 pct 4 pc = density of concrete = 0.086lb/m3 l The wall exit velocity following penetration is computed for the study for potential subsequent use in determining Cf of Eq. 2-1 (conditional probability of conduit failure given wall failure, if required. Missile Penetration (nerforation) of Steel Barriers The Hagg Sankey (8) method is utilized for interactions with steel walls on the basis of EPRI recommendations (2). This method predicts steel wall perforation as a "two-phase" process. In the first phase, resistance is affected only by local shear and compression. In the second phase, the wall has had time to " stretch" in the plane of the wall, with tensile resistance also contributing. Perforation can occur in either phase. It is considered the only method available which realistically predicts effects when tensile stress is the most important contributor to perforation resistance. This is, indeed, the situation with a wall as thin as the roof panels of the auxiliary bay. Figure B.2-4 illustrates the process. In the figure, M3 is the missile mass, m21 is the mass of the sheared punching which is ejected along with the missile if stage 1 failure occurs, m22 is the mass between the two plastic hinges, and m3 is the portion (a fraction of m22) which is effectively accelerated along with m21 The fraction is determined as the square of the ratio of the radius of gyration of m22 to length of plastic hinge and is 0.34 for a plastic hinge of length 3T. The equations involved are described below. The Hagg-Sankey formalism requires initially that M, the barrier mass which can be effectively accelerated 2 ] along with the missile, m2i + m3, be calculated. Its value is: B-29
a m22 3T U D1 %2 T e Figure B.2-4. Missile interaction with Steel Walls and Hagg-Sankey Parameters. B-30
M = p[A + 1.36 @ (Vni) T(A ]T (B.2-4) 2 where density of steel (slugs /ft ) 3 p = A effective impact area of missile (ft ) 2 = T barrier thickness (ft) i = Vai impact velocity component normal to barrier (fps) = i @(V ) is a function of impact velocity normal to the barrier which r.ccounts for the ni distance in the wall from point of missile contact that is affected by the impact. From a private communication with Sankey, co-author of the method, we have derived the empiricalrelation: 2 @Wni) = g,,.,ooi3gy i n (B.2-5) which fits the measured results of Westinghouse on their turbine housing (which requires that @=2 at 400d fps,3 at 800 fps, and 10 at 100 fps). I Also needed is the initial missile energy loss, AE, required to accommodate i momentum conservation as M is accelerated. 2 2 AE = 1/2 M Val (1 ) i i (B.2-6) where M is missile mass. i I In order for Phase I failure to occur, AE1 must exceed the effective strength of the barrier in local compression and shear (E + E )- c s i B-31 1
i i (B.2-7) Ee= ARod Es = KtdPT2 (B.2-8) 1 where g an effective compressive strain (0.07) = od compressive yield strength (~50,000 psi) = K constant accounting for the amount of shear energy used (0.45) = d the shear yield strength of the barrier (~30,000 psi)(E) t = P the periphery of the missile impact area. = i Note that 50,000 and 30,000 are the static yield stresses for compression and shear, which is a conservative assumption. Use of the higher dynamic yield stresses would predict a smaller number of penetrations. j Figure B.2-5 shows how Eq. B.2-8 is derived. It is simply the yield stress in compression times area of application times displacement ((TA). The clastic component is small compared to the plastic deformation and is ignored, as is the elastic energy in the missile itself. The strength alloy of the missiles is assumed sufficient to prevent its yielding, and its clastic energy storage is even less than that in the wall. Such an assumption is very conservative for tornado missiles since they typically absorb much of the energy of the interaction. Figure B.2-6 shows how the shear strain energy term (Eq. B.2-8) is derived. The original Hagg-Sankey work listed Eq. B.2-8 without explanation other than that K was determined experimentally to be in the range from 0.3 to 0.5. Shear strain energy (in the plastic flow regime) is 7 A&PT, where A is the length of the plastic hinge, PT is the d area over which the shear stress is manifest, and $ is the angle of deformation B-32
4 i i I 1 l I t t I & 44 A f --+ (T M ch( TA = compressive stored energy I Figure B.2-5. Compressive Energy in Wall B-33 L
t a P = periphery of punched-out (sheared) section. 9 A= length of plastic hinge v g NT(*) 9= angle of deformation caused by plastic shear 1 +x T(x) = ( T-x )Td + T 4-- T where Td= elastic limit in shear (psi) Work of shear deformation (E,) .T = A sp PT Td (T-x) dx B.3 7 T o-2 = K PT Te, where K E 2T Figure B.2-6. Shear Energy Associated with Missile impact. B-34
l I j (i.e., that of permanent set, since it has been assumed that the clastic contribution i is negligible). For a plastic hinge length of between 2T and 3T, and a shear yield stress of 30,000 psi, the deformation angle would be in the range from 0.2 to 0.5 radians. This value is reasonable and is consistent with Hagg Sankey experiments. Inserting appropriate constants and converting to ft-lb units we have: Ec = 292 AT fr-lb (B.2-9) Es = 4500 VA T2 ft-lb If Ei exceeds Ec + E, the barrier fails during the so-called Phase I and the 3 missile has a residual normal velocity, Vne given by MiVni M1Vni 2(Ee + Es) m3 - MiVni (m3 - Mi) "*
M1 + M2 +V M3 + M2}2
~ (M1 + M2) (M1 + m2) where m2 the mass of the barrier having the same cross sectional area as = the missile M - m2 m3 = 2 Eq. B.2-10 has been derived from the equations of energy conservation: hM V 2-f (M +m2)Vne -fm3 2 V 2 - Es - Ee = 0 i1 i 3 l and momentum conservation: i M V - (M + m2) Vne - m3 3 = 0 1 i i V B 35 1
l If Ec + E, exceeds AE, the tensile-strength phase (or Phase II) of the interaction i ensues, and then AE2,. the kinetic energy of the modg wall and missile which must be resisted by tensile strength in the barrier, is determined. 1 l
Ihe relations are l
E = hM Vai 2 M1 2 t ) (B.2-11) l l t l E = 7.1Cd (B.2-12) T I l where Q the effective volume which can be stressed in tension (assumed to = be approximately equal to the volume associated with m21 + m22 of Figure B.2-4) ST the effective tensile strain (0.05) = od the tensile ultimate strength (same as cumpmssion) in steel = l l with appropriate constants, ET = (m22 + m21) = (3Fr2 + AT) x 208 (B.2-13) Psteel If ET exceeds E, the breach of the barrier is prevented. If not, the missile exits 2 with a velocity Vne given by i Vne = (B.2-14) M + ~Mi M2 J s B-36 i 3 I
l l l The missile is assumed to maintain its initial direction after perforation. Table B.2-1 shows the required parameters for the steel or concrete penetration j formula of all the missiles striking the auxiliary bay. The concrete penetration code uses both the secant method (calculating penetration on the basis of the total velocity vector through an effectively elongated thickness path through the concrete) and the cosinc sc' hod (calculating penetration on the basis of the velocity component normal to the wall through the actual thickness). For the CEA-l DEF formula, the cosine method is more conservative and it is used to determine t penetration probability. Both codes calculate both the penetration and residual velocities following penetration, and both can be used to determine the' probability of penetration (as described below) which requires the determination of the exact threshold of penetration, for a given combination of impact velocity and impact This determination can be accomplished in closed form for concrete, but since area. l a quartic equation applies for steel, a " trial and-error" solution was invoked. Repetition and varying impact areas using the STEEL code are used until calculated penetration thickness differs insignificantly from actual wall thickness or, in the j case for steel, when the energy required to rupture the wall (Eq. B-2.7, B-2.8, and B-2.12) exactly matches that available in the missile (Eq. B-2.6 and B-2.11). In all j cases for the steel penetration, the Phase 2 failure described above was the failure i mechanism. In the Phase 2 portion cf steel penetradon described above, the Hagg-Sankey formula has been modifled somewhat to accommodate the relatively thin steel of the auxiliary bay roof. The original Hagg Sankey formulation was based on experiments with models of turbine missiles exiting through turbine casing walls which are relatively thick. The appropriate distance beyond the boundaries of the penetrating missile over which tensile stresses were considered to be effective was empirically determined and was typically a few inches in length (three times the wall thickness). If the same relation were used for the thin wall of the auxiliary bay t i roof, only about 0.2-inch would be effective. Such a short range is unrealistically I low. A much better measure of the effective length.of ten;ile effect is the distance traveled by an acoustic wave during the time of interacdon of the missile with the wall. Acoustic velocity in steel (8pwhere b = bulk modulas in psi and j B-37 3 i N
i t i j p= density in slugs per cubic inch) is roughly 50,000 inches per second, and the velocity of the fastest missile (falling from the top of the reactor building) is 86 l fps or roughly 1000 ips. If it is assumed (conservatively) that only one-half-inch ] deflection of the roof occurs before wall perforation, then the acoustic wave can l travel above 25 inches in the metal during this time. Only 5 inches has been 4 l claimed for this analysis, which seems more than adequately conservative (i.e., does f not overestimate wall strength). If the original prescription by Hagg and Sankey { for this " tensile" length were adopted, a somewhat greater overall penetration probability (by about 50 percent) would be predicted, but the effect would not change the overall conclusions that penetration probability is sufficiently small that 1 this risk is acceptable. Furthermore, the original Hagg-Sankey prescription was 4 compared to other empiricisms for calculating steel wall perforation (the SRI and e l BRL formulas--see Reference 2) and the Hagg Sankey method more conservative. 3 i Even the modification to the Hagg-Sankey formula described above for this analysis is more conservative than the SRI (Stanford Research Institute) formula. Conservative materials pvgees have been used in these formulas. 50,000 psi is I the tensile ultimate umi for steel (which is rather low and augments the l conservatism of the calculated penetrations probability). Conservative assumptions and comparisons with other formulas are used in lieu of experimental data on wall j l perforation for the walls of this type. J Steel wall thickness for the roof and the vehicle door (which sustained some I strikes) was the average thickness perpendicular to the plane of the wall considering the augmented thickness due to the corrugations as shown in Figure B.2-7. Effective thickness for the roof is 0.092 inches and that for the wall is 0.1 f inches. i Parameters used for the concrete penetration calculations were 7-inch slab thickness (based on actual measurement) at 6000 psi. Probability of penetration once the missile has struck is determined by the following sequence: 1. Minimum velocity to penetrate the barrier is calculated for the most penetrating 'brientation (smallest projected im?act area) and any missile striking with a smaller velocity is assignec. a 0 B-38
Roof (18 Gauge) 4--- 8 in. 2-3/8 in. 5-3/8 in. l 4- --> 4- + a i 3 in. t V l + 4- ) 2-1/8 in. Effective Roof Thickness i = ( y ) x Nominal =.092 in. Steel Door Effective Door Thickness - (H ) x Nominal - 0.1 in. l n --+ 4-1/16 in. i 1-1/2 in. i 9 l ->1/2 in.4-f i i Fig. B.2-7 Steel Wall Thickness Parameters B-39 i
probability of penetrating the wall. 2. The velocity required to penetrate the barrier at the orientation of greatest projected missile impact area is determined, and any missile impacting with greater velocity is assigned unit probability of penetrating. 3. For impacts between the two extremes, the impact area is successively altered (along Mth wall missile periphery for steel wall penetrations), and tpal calculations are performed, until penetration capability exactly matches wall thickness. This impact area, A, is used in the probability equation below. j Figure B.2-8 depicts use of the A3 value for calculating probability of penetration as follows: sin-I((A -A x cos4)/(W x L))/90 (B.2-15) P = j m where A, W, and L are the minimum area, the mean width, and the length of the m missile shown in Figure B.2-8; Aj s the total projected impact area shown and 4 is i the argument of the inverse sine function. The equation is generally adequately approximated by assuming cos $ = 1. Otherwise an iteration solution is required since the cosine of the function is part of the function. W, the 'nean width, is the average projected width over 360 degrees perpendicular to the major axis of the missile. For a cylinder this is merely the diameter. For missiles having rectangular sections of dimensions a x b the value is 2(a + b)/x. For penetrations in steel (the roofs) the associated impact periphery must be determined for each in; t area. Missile parameters used in this determinat on are i listed in Table B.2-2. The above methodology calculates penetration probability as the ratio of solid angle of missile orientation capable of penetrating the wall (at that velocity) to the total range of solid angle variation for missile orientation. There are very few missiles that attain velocities that would cause them to be capable of penetrating the walls ct all orientations (i.e., have penetration probabilities equal to 1). B-40
I l l l l 9 Missile V Am cos 9
+
W IS THICKNESS PERPENDICULAR ':4-- Al TO PLANE OF PAPER Figure B.2-8 Parameters for Calculating Penetration Probability B-41
i i i Table B.2-2 Missile Penetration Parameters for Missiles Which Strike Water Intake Structure and Auxiliary Bay i cicoile missile min. area impact mean length missile i number weight of impact periphery width description t l (1bs) (sq in) (inches) (inches) (inches) ) 1 140 48 32 10.2 144 Wood Plank i 2 114 7.1 9.4 3 180 Steel Pipe i 3 285 28.3 19 6 300 Steel Pipe 4 Steel Pipe i 5 136 1.27 4 1.27 480 Steel Rod 6 6600 360 246 78.3 360 Steel Form 7 80 72 60 17.2 48 Steel + Wood Form 8 Truck, 12-Ton 9 Flatbed Truck 10 3000 288 72 23 300 Structural Steel 11 440 144 48 15.2 144 Timber 12 Pre-cast Concrete Panels 13 Pre-Cast Concrete Panels 14 Pre-Cast Concrete Panels 15 110 1.76 70 17.2 288 Metal Decking 16 175 2.8 70 17.2 300 Metal Decking 17 80 72 54 17.2 48 Removable Hatches 18 2000 39.64 193 96 180 Removable Hatches 19 Removable Hatches 20 Removable Hatches 21 200 63 75 24 86 Steel Doors 22 Steel Doors 23 250 147 170 53 84 Steel Doors 24 4000 2880 216 69 180 Automobile 25 Bus 26 416 23.8 17.3 5.5 540 Tree 27 House designation (see 39-43) 28 56 0.88 70 8.9 300 Metal Siding 29 Truck Trailer 30 Office Trailer 31 Office Trailer 32 Concrete Floor Plugs 33 Snow Plow Blades 34 Gas Tanks 35 Boston Whaler 36 Chris Craft 37 Lobster Trawler 38 1490 143 42.5 13.5 420 Telephone Poles 39 446 198 183 57 144 House, Roof Pieces 40 45 24 20 6.4 120 pair 2 in. x 6 in. x 10 41 27 12 12 5.1 144 2 in. x 6 in. x 12 42 2 in. x 4 in. x 6 43 Garage Lintel B-42
j The methodology of determining the penetration probability is conservative -(overestimates probability) because it underestimates the impact area of the missile. When a missile strikes the wall at an angle, the reaction at the first point of j contact and the missile inertia acting at the center of gravity form a couple to rotate the missile to a position more parallel to the. wall (with a resultant larger l impact' area and lesser chance of. penetration). It is not practical to model this l cffect, so the projected area at first contact is used as an additional built-in { conservatism of the analysis. A of Eq. B.2-15 for concrete is. determinable in closed form from Eq. B.2-1 with i l the D (diameter value) replaced by 2iA/x.. A; for steel is determined by iterating on Eq. B.2-12 with varying impact areas until the tensile energy available ir. the l wall equals the missile impact energy available for overcoming tension (i.e., when E2 of Eq. B.2-11 equals ET of Eq. B.2-12, since all roof failures are in the " tensile" failure phase of the Hagg-Sankey failure model described above). The probability of penetration for all missiles striking the auxiliary bay roof, as a function of height (measured from the ground) of strike on the reactor building, was determined using the free-fall velocity in the penetration algorithm. Very few missiles struck - this roof directly (without having first struck the containment structure). In such cases, the vertical impact velocity determined by the tornado missile code PILGRIMI war used in the penetration formula. All missile strikes on the auxiliary bay for 6.2 million years of simulated tornado strikes are listed in Table B.-2-3. Table B.2-4 shows missile strikes for the water intake structure based on 8.6 million years of simulated strikes. In these tables, x, y, and z are strike locations relative to the center of the containment (the x-y origin) and the ground elevation at the auxiliary bay (the z origin) from BECo drawing C the Plot Plan (x =E5000, yo= 5000 and z =23). Probability of o o penetration for most strikes is extremely low, except for a few heavy missiles propelled by F4 (and higher) which dominate the risk number. There is a significant body of informed opinion that holds that automobiles and other similar heavy missiles are not really lofted to significant heights (more than about 20 feet) in tornadoes. After-the-fact examination of reported "high-in-the-B-43
Table B.2-3 Summary of Strikes on Auxiliary Bay Randon Number Missile X Y Z X' Y' Z' P Number of Years Number -71 45.46 39.26 84.8 -31.0 2.8 0 467735 3109365 15 -71 -22.73 107.12 96.7 -70.3 41.9 0 473688 3154521 15 -71 67.92 36.23 98.2 -22.7 0.1 0 476060 3156864 15 -71 15.21 43.78 80.6 130.4 7.9 0 477264 3163254 26 -71 31.38 62.46 171.7 -43.8 11.8 0 481229 3181998 26 i -71 20.69 29.00 161.2 -32.7 -0.9 0 481229 3181998 26 -122 41.39 7.31 72.9 -5.6 9.6 0 481229 3181998 2 3 -71 -2.89 95.12 127.5 -85.1 51.4 0 497101 3266346 15 -71 40.93 49.33 181.5 -0.7 23.9 0 499302 3281256 26 -122 42.34 15.22 88.3 -5 25.1 0 499302 3281256 2 I -71 39.45 29.72 88.3 -5 25.1 0 499302 3281256 2 1 -71 -19.69 57.94 25.8 81.3 0.4 0 511897 3331524 15 -71 -13.26 113.31 22.9 111.4 11.8 0 513094 3337914 15 4
-122 48.78 5.68 62.7 4.9 4.9 0
513900 3339618 2 -71 50.16 87.53 123.3 -33.6 42.5 0 513900 3339618 15 -71 20.89 61.04 149.8 -18.9 22.3 0 514916 3357297 16 -71 63 43.29 9.1 156.4 -4.5 0 519633 3373272 26 -122 41.75 10.3 50.9 -23.2 -22.1 0 542230 3543672 40 -71 52.72 92.45 11.2 96.5 -5.6 0 695470 4557339 15 -122 -34.1 25.61 148.9 -11.6 4.1 0.0244 700873 4586520 26 -122 -29.12 11.16 149.9 -19.8 4.5 0.025 700873 4586520 26 -71 24.98 71.64 90.3 -37.3 19.3 0 713061 4660857 15 -71 -29.73 61.48 59.7 60.4 -8.3 0 713601 4674489 15 -71 9.68 68.29 133.8 -44.4 16 0 716665 4689186 40 -71 69.4 71.48 121.2 -26 27.1 0 716665 4689186 15 B-44
Tcble B.2-3 (cont'd) Random Number Missile X Y Z X' Y' Z' P Number of Years Number i -122 -27.08 3.88 115.8 30.3 -13.5 0.012 721252 4711551 39 -71 65.93 93.15 34.4 -84.9 1.2 0 741022 4831683 15 -71 -21.92 128.89 22.3 101.2 15.1 0 746864 4868532 15 -122 13.87 5.57 52.5 -32.3 3.8 0 749276 4870023 2 -71 7.27 107.14 106 -58.2 47 0 755709 4906872 15 -122 24.12 11.2 62.6 -25.9 11.9 0 755709 4906872 2 -122 24.33 3.8 52.5 -20.6 1.1 0 756770 4908789 2 -71 -2.91 101.83 91.7 -10.4 -9.5 0 755709 4953519 7 -71 46.92 99.65 89.4 -25.7 35.3 0 755709 4953519 15 -71 16.44 107.73 105.2 -17.3 -51.7 0.008 764619 4963956 26 4 a l-122 27.33 15.55 45.9 -15.5 15.1 0 768960 5001444 2 3 -71 44.6 75.31 99.7 27.9 25.8 0 770769 5021253 15 i i j-122 29.85 12.06 73 -21.4 14.4 0 774303 5066622 2 j -71 55.51 79.93 129.7 -40.5 42.4 0 774303 5066622 15 i -122 -1.63 3.72 44.1 -41.8 1.1 0 775582 5068965 2 1;-122 18.06 18.73 65.8 -34.5 22.6 0 779351 5074077 2 i j -71 58.79 40.8 29.7 106.3 -1.1 0 781856 5116890 15 1 -71 -24.2 97.85 80.8 73.6 -12.1 0 804563 5255766 40 -71 65.17 126.53 52.3 -126.7 47.4 0 804563 5255766 15 -71 63 73.85 105.8 -24.2 28.7 0 810386 5277918 15 -122- -14.1 6.82 47.9 -56.6 3.9 0 810386 5277918 2 -122 54.19 16.63 74.1 14.4 23.1 0 810386 5292189 2 -71 63.63 93.97 12.2 100.4 -4.7 0 818983 5321370 15 D8.11 11.39 27 47.4 64 -22.8 0 821069 5359923 15 -122 48.79 4.43 60.4 4.6 3.4 0 825894 5399754 2 -71 -35.04 67.56 97.4 -79.8 18.4 0 827270 5405292 15 -122 22.79 25.17 80.1 -34.1 38.3 0 827804 5410830 2 -71 -27.91 54.49 85.2 -70.4 11 0 831566 5433195 15 B-45
Table B.2-3 (cont d) Randon Number Missile X Y Z X' Y' Z' P Number of Years Number -122 36.85 7.45 67.3 -11.7 8 0 846101 5498373 2 -86.33 -25.06 27 49.3 57.1 -17.2 0 847959 5523507 15 -122 54.13 3.96 52.4 11.7 0.6 0 853204 5559504 2 -122 27.4 1.72 58.5 -21.1' -0.7 0 857289 5576544 2 -71 -35.8 124.4 22.4 104.2 15.6 0 859737 5583147 15 -71 -14.56 47.61 43.7 -30.5 4.9 0 860294 Sgr 7 3 -71 52.57 34.05 38 166.7 -12.4 0 871636 566. .9 24 -71 0.23 102 109.7 -71.7 48.5 0 873273 5663448 15 -122 15.09 15.11 64.8 -39 16.8 0 873273 5663448 2 -71 13.15 139.76 58.6 54.1 -6.2 0 878054 5716272 15 l -71 37.86 98.75 30 20.8 -12.8 0 880558 5733312 23 -122 37.83 7.17 64.4 -9.5 7.1 0 881150 5738424 2 -122 54.56 3.72 64.2 12.6 1.2 0 883271 5742045 2 -71 -27.71 30.98 41.8 111.5 -2.5 0 910264 5948016 15 -71 15.42 79.4 131.3 -71.6 39.3 0 914252 5571233 15 -71 36.85 59.96 111 20.5 -2.1 0 916028 5984439 26 -71 31.86 72.57 93.6 -39.3 22.7 0 916671 5985078 15 l -122 22.9 22.28 124.1 25.8 -5 0.0014 917882 5986143 16 -71 -3.64 58.06 32.8 108.3 8 0 920500 6003183 21 -122 -28.05 20.64 45.8 -62.3 14 0 924092 6041097 2 -71 -13.54 27.92 85.1 141.7 -11.4 0 929016 6078159 26 -71 47.53 51.47 168.7 -33.1 8.6 0 929016 6078159 26 -71 34.31 72.97 -110.9 -155.7 16.6 0.065 938247 6184659 38 -122 11.45 14.53 58.4 -39.7 15 0 950901 6227472 2 L20.02 -34.79 27 34.7 -65.1 -78.4 0 957696 6259422 11 -122 32.79 3.7 60.3 -15.2 2.3 0 957696 6259422 2 -122 64.99 8.51 55.1 22.3 6 0 964749 6274332 2 -71 3.14 72.08 98.6 60.5 -22 0 965969 6289242 21 a na
Table B.2-3 (cont'd) i Randon Number Missile X Y Z X' Y' Z' P Number of Years Number -122 36.55 4.75 64.2 -10.1 4.9 0 968622 6295419 2 i -122 26.32 21.25 69.5 -25.5 27.7 0 969758 6316932 2 -122 9.03 2.9 51.6 47.,4 -29.4 0 971652 6318636 7 a -122 49.76 5.76 46.5 n6.4 3.9 0 971652 6318636 2 -122 0.11 13.96 105.5 106.1 -11.5 0 990637 6491805 39 -71 36.87 72.59 116.2 96.7 18.3 0 990637 6491805 39 -71 66.63 117.43 41.3 -102.2 28.4 0 994108 6494361 15 -71 24.17 133.04 32.5 -74.8 -3.8 0 1006517 6532275 16 -122 -30.73 19.1 51.2 -73.5 15.1 0 1006517 6532275 2 l -71 -0.41 119.61 47.2 -128.5 26.4 0 1010108 6562734 15 -71 -25 86.45 140.1 29.2 14.6 0 1010233 6567420 26 -71 60.7 48.34 55 154.6 9.7 0 1010233 6567420 26 1 -71 -31.3 31.22 142.1 2.8 11.4 0 1036175 6695433 16 -71 40.8 54.76 33.4 -44 -36 0 1036175 6695433 2 -71 -22.21 117.06 226.7 -52.8 99.7 0 1036175 6695433 15 j -71 3 68.03 104.8 -61.4 25 0 1043541 6730152 15 -122 7.15 13.16 70.3 -56.1 15.7 0 1043541 6730152 2 -71 -5.62 41.31 115.7 125.4 12.3 0 1044262 6745062 26 -71 -20.72 35.83 36.2 111.5 -2.6 0 1051564 6748470 15 -71 26.69 39.91 118.7 111 -2.6 0 1056703 6785106 26 -122 47.43 11.44 70.2 3.5 14.1 0 1057643 6786810 2 -122 51.31 10.33 60.6 8 10.5 0 1069451 6798525 2 -71 55.41 107.26 65.4 -71.7 -1.9 0 1074696 6813648 28 -71 -12.99 84.71 135.6 40.9 7.3 0 1077796 6826428 40 -71 -32.06 104.63 97.6 50.3 -17.5 0 1077796 6826428 1 -71 -28.53 57.04 120 39.9 -12 0 1080004 6828984 7 -71 41.57 39.67 83.4 -31.4 2.7 0 1082454 6831966 15 -71 i t 4. 96.55 44.2 14.3 28 0 1084520 6840912 15 riur7
Table B.2-3 (cont'd) Randon Number Missile X Y Z X' Y' Z' P Number of Years Number -71 47.56 53.06 90.3 18.7 -21.7 0 1084804 6849006 40 -122 3.34 17.02 67.1 -56.7 20.6 0 1101160 6907368 2 -71 47.48 61.83 128.1 153.5 13.7 0 1107913 6962748 24 -71 -8.41 78.33 86.4 73.2 18.4 0 1110609 6986178 15 -122 -29.98 8.89 156.5 32.9 -6.2 0 1111380 7000875 26 -122 12.86 7.29 51.7 -32.8 6 0 1127218 7146354 2 -71 -3256 103.91 85.1 92.1 -25.4 0 1129390 7155726 21 -71 22.02 46.27 138.9 13 13.3 0 1134454 7214727 2 -71 52.68 67.72 150.6 -13 8.8 0 1134454 7214727 26 -71 -4.31 113.01 149.1 20.8 34.1 0 1137734 7234323 28 -71 33.86 38.09 100.1 92.8 -2.1 0 1158560 7348917 7 -71 -8.75 75.82 133.2 66.8 8.1 0 1162914 7407492 21 -71 -27.52 78.24 167.5 -6.9 19.9 0 1165808 7421550 26 -122 49.54 4.78 59.6 5.5 3.4 0 1165808 7421550 2 -71 -1.08 52.62 36.4 25.8 -19.1 0 1177025 7550628 15 -122 44.24 7.73 54 0.5 7 0 1180755 7600470 2 -122 48.99 25.94 83.8 -44.4 -2.9 0 1186425 7632846 15 -71 53.38 82.45 110.9 -34.6 36.4 0 1186797 7639236 15 -71 66.57 35.81 94.7 -22.4 -0.5 0 1189929 7657554 15 -71 62.31 37.31 92.2 -24 0.8 0 1198886 7738707 15 -71 37.39 37.4 109.3 51.6 4.4 0 1202063 7763415 39 -122 50.95 12.89 64 8.3 14.7 0 1223399 7883121 2 18.87 10.09 27 42.4 -20.1 -83.9 0 1224984 7902930 6 -122 51.47 18.77 122.6 35 -9.2 0.0014 1233638 7983231 26 -71 -34.91 38.37 58.5 92.7 2.5 0 1234903 7991325 15 -71 -14.83 61.36 96.4 -69.6 16.1 0 1240872 8034777 15 -71 1 113 42.8 -119.4 16.5 0.0185 1245741 8093139 15 -71 27.01 45.9 25 103.7 5.5 0 1250435 8156613 21 B-48
1 i Table B.2-3 (cont'd) Random Number Missile X Y Z X' Y' Z' P Number of Years Number -71 67.66 79.45 132.2 -29 37.3 0 1259316 8260557 15 -122 50.91 5.4 67.9 8.2 4.8 0 1271430 8349165 2 -122 46.82 10.26 60.1 3.1 10 0 1284508 8417538 2 -71 10.97 126.48 66.1 6.8 24.2 0.004 1295293 8472918 2 -122 25.51 26.75 23.7 77.2 -0.7 0 1296013 8475261 15 -122 54.76 2 62.5 12.2 0.7 0 1302680 8501673 2 -71 56.47 128.43 40.1 -64.5 8.5 0 1306927 8528085 15 -122 -28.39 20.68 49.5 -65.3 17.1 0 1306990 8530215 2 -71 66.36 62.01 124.4 -29.1 21.2 0 1317165 8610090 15 i -71 18.55 124.39 74.3 -44 12 0 1320458 8638206 11 -71 -23.71 111.68 104.3 -58 43.5 0 1321727 8646726 15 -122 64.81 3.95 50.2 21.7 0.4 0 1325315 8666961 2 -71 -29.29 87.7 136 -15.6 14.3 0 1328147 8692308 28 -71 -19.04 43.87 60.2 -37.5 0.8 0 1334747 8723832 1 -71 11.63 39.08 81.8 -45.4 3.6 0 1336075 8735973 15 -122 67.73 11.39 69.3 32.4 13.9 0 1336637 8744280 2 -122 50.07 13.87 52.8 -52.9 -11 0 1340837 8750031 28 -122 21.46 1.64 55.6 -26.8 -0.6 0 1343984 8785389 2 >87.63 68.4 27 152.4 -32.7 -14.6 0 1345765 8792205 40 -71 16.45 105.65 123 -67.6 57 0 1351147 8831397 15 -71 54.8 119.22 42.5 -91.3 23.8 0 1374062 8923200 15 -71 18.35 93.19 104.4 -55.9 39.6 0 1377125 8951103 15 -122 37.4 3.48 58.5 -8.4 1.4 0 1381104 8981775 2 -71 57.91 75.75 110.3 -22.2 28.2 0 1389468 9043332 15 -71 -33.6 91.63 74.9 92.6 -9 0.0012 1395613 9072513 26 -122 4.26 26.94 94.6 -67.5 47.5 0 1406932 9132153 2 -71 5.15 63.58 122.8 13.3 3.4 0 1407524 9142164 40 -122 58.53 7.34 57.4 16.1 6.4 0 1407524 9142164 2 B-49
l l Table B.2-3 (cont d) Random Number Missile X Y Z X Y Z P Number of Years Number -71 15.57 30.06 160 -36.7 -1 0 1411028 9150684 26 -122 40.43 8.52 59.3 -3.8 7.1 0 1423095 9220187 2 -71 15.44 63.3 159.9 -4.,6 29 0 1431680 9300275 26 1 -71 14.6 80.69 116.9 -64.7 36.3 0 1432166 9308582 15 -122 40.78 12.87 76.1 -6.2 18.2 0 1434582 9345857 2 -71 63.43 89.46 142 -36.4 50.8 0 1438947 9359489 15 (18.41 50.04 27 -53.1 -34.5 -7.5 0 1448444 9399746 21 -71 23.11 114.97 179.1 29.6 76.9 0 1454468 9418916 15 -71 27.52 64.57 112.5 -43.8 24.1 0 1455240 9427010 15 -122 40.74 7.35 121.9 18.9 -2.6 0 1455428 9430631 26 -71 -33.97 132.25 20.1 120.9 34.9 0 1458110 9439364 15 -71 61 38.35 101.9 -27.7 2.8 0 1472902 9498385 15 i -71 13.64 75.77 109.4 -55.1 33.2 0 1475129 9513701 15 -71 30.27 42.26 125.4 -21.4 7.5 0 1485699 9587825 40 -122 39.47 9.98 67.7 -7.6 11.7 0 1488351 9607208 2 -71 46.8 66.59 42.7 -42.7 -16.5 0 1504983 9713069 15 -122 28.6 1.96 53.9 -16.3 0.2 0 1509240 9746510 2 -71 66.01 92.34 11.7 -26.9 12.9 0 1510405 9760781 15 -71 -21.38 44.77 115 33.5 5.8 0 1516713 9793796 21 -71 -31.65 46.2 88.8 161 13.1 0 1521872 9821486 26 88.42 -35.89 27 67.3 203.5 -5.2 0 1532331 9904130 24 -122 -32.97 0.96 39.7 -58.7 -3.7 0 1535664 9925856 2 -71 26.56 137.04 21.9 130.2 23.9 0 1537328 9954536 15 -71 43.26 92.94 165.8 32 16.5 0 1538315 9954824 16 -71 6.83 66.79 63.2 68.9 -2.8 0 1545743 9999341 15 Total 0.1609 B-50
Table B.2-3 (cont ,____________________________________________'J) Random Number Missile X Y Z X Y Z P Number of Years Number -71 67.66 79.45 132.2 -29 37.3 0 1259316 8260557 15 -122 50.91 5.4 67.9 8.2 4.8 0 1271430 8349165 2 -122 46.82 10.26 60.1 3.1 10 0 1284508 8417538 2 -71 10.97 126.48 66.1 6.8 24.2 0.004 1295293 8472918 2 -122 25.51 26.75 23.7 77.2 -0.7 0 1296013 8475261 15 -122 54.76 2 62.5 12.2 0.7 0 1302680 8501673 2 -71 56.47 128.43 40.1 -64.5 8.5 0 1306927 8528085 15 -122 -28.39 20.68 49.5 -65.3 17.1 0 1306990 8530215 2 -71 66.36 62.01 124.4 -29.1 21.2 0 1317165 8610090 15 -71 18.55 124.39 74.3 -44 12 0 1320458 8638206 11 -71 -23.71 111.68 104.3 -58 43.5 0 1321727 8646726 15 -122 64.81 3.95 50.2 21.7 0.4 0 1325315 8666961 2 -71 -29.29 87.7 136 -15.6 14.3 0 1328147 8692308 28 -71 -19.04 43.87 60.2 -37.5 0.8 0 1334747 8723832 1 -71 11.63 39.08 81.8 -45.4 3.6 0 1336075 8735973 15 -122 67.73 11.39 69.3 32.4 13.9 0 1336637 8744280 2 -122 50.07 13.87 52.8 -52.9 -11 0 1340837 8750031 28 -122 21.46 1.64 55.6 -26.8 -0.6 0 1343984 8785389 2 D7.63 68.4 27 152.4 -32.7 -14.6 0 1345765 8792205 40 -71 16.45 105.65 123 -67.6 57 0 1351147 8831397 15 -71 54.8 119.22 42.5 -91.3 23.8 0 1374062 8923200 15 -71 18.35 93.19 104.4 -55.9 39.6 0 1377125 8951103 15 -122 37.4 3.48 58.5 -8.4 1.4 0 1381104 8981775 2 -71 57.91 75.75 110.3 -22.2 28.2 0 1389468 9043332 15 -71 -33.6 91.63 74.9 92.6 -9 0.0012 1395613 9072513 26 -122 4.26 26.94 94.6 -67.5 47.5 0 1406932 9132153 2 -71 5.15 63.58 122.8 13.3 3.4 0 1407524 9142164 40 -122 58.53 7.34 57.4 16.1 6.4 0 1407524 9142164 2 B-49
Table B.2-3 (cont d) Randon Number Missile X Y Z X' Y Z P Number of Years Number -71 15.57 30.06 160 -36.7 -1 0 1411028 9150684 26 -122 40.43 8.52 59.3 -3.8 7.1 0 1423095 9220187 2 -71 15.44 63.3 159.9 -4.6 29 0 1431680 9300275 26 -71 14.6 80.69 116.9 -64.7 36.3 0 1432166 9308582 15 -122 40.78 12.87 76.1 -6.2 18.2 0 1434582 9345857 2 -71 63.43 89.46 142 -36.4 50.8 0 1438947 9359489 15 L18.41 50.04 27 -53.1 -34.5 -7.5 0 1448444 9399746 21 -71 23.11 114.97 179.1 29.6 76.9 0 1454468 9418916 15 l -71 27.52 64.57 112.5 -43.8 24.1 0 1455240 9427010 15 !-122 40.74 7.35 121.9 18.9 -2.6 0 1455428 9430631 26 -71 -33.97 132.25 20.1 120.9 34.9 0 1458110 9439364 15 -71 61 38.35 101.9 -27.7 2.8 0 1472902 9498365 15 j -71 13.64 75.77 109.4 -55.1 33.2 0 1475129 9513701 15 -71 30.27 42.26 125.4 -21.4 7.5 0 1485699 9587825 40 4 -122 39.47 9.98 67.7 -7.6 11.7 0 1488351 9607208 2 l -71 46.8 66.59 42.7 -42.7 -16.5 0 1504983 9713069 15 -122 28.6 1.96 53.9 -16.3 0.2 0 1509240 9746510 2 -71 66.01 92.34 11.7 -26.9 12.9 0 1510405 9760781 15 -71 -21.38 44.77 115 33.5 5.8 0 1516713 9793796 21 -71 -31.65 46.2 88.8 161 13.1 0 1521872 9821486 26 >88.42 -35.89 27 67.3 203.5 -5.2 0 1532331 9904130 24 -122 -32.97 0.96 39.7 -58.7 -3.7 0 1535664 9925856 2 -71 26.56 137.04 21.9 130.2 23.9 0 1537328 9954536 15 -71 43.26 92.94 165.8 32 16.5 0 1538315 9954824 16 -71 6.83 66.79 63.2 68.9 -2.8 0 1545743 9999341 15 Total 0.1609 B-50 5
Table B.2-4 Sussmary of Strikes on Water Intake Structure Random Number Missile I Y Z I' Y' 2* P Numbers of Years Number -180 148 1.49 101.5 -41.8 -10.5 0 297297 1924701 40 -192 94 5.5 -29.5 61.5 5.1 0 372698 2462280 2 -209 94 2.9 -36 37 2.9 0 537193 3499149 2 -239 94 15.4 74.5 33.2 -4.6 0 583873 3781347 40 -212 94 2.8 -45 54 3.6 0 622760 4045926 2 -228 148 7.7 66 -78 -7.7 0.0105 642264 4194813 26 -247 115.9 12.45 145.6 14.5 -1.6 0.0025 663494 4100924 26 -197 194 5.9 -33 60.9 0.5 0 667454 4370532 2 -247 100 6.8 9.87 6.4 1.3 0 668664 4392598 -40 -162.7 94 6.3 14.9 83.9 6.6 0 679124 4478316 2 -164.3 94 10.1 12.9 89.5 14.1 0 773385 5059593 2 -160 94 5.8 15.52 54.1 0.3 0 804561 5255766 2 0196.9 94 11.7 -36.4 73.8 9.1 0 852381 6070159 3 -192 148 0.363 -18.7 84.55 -5.8 0.00213 860907 5589744 2 -229 148 0.236 -1.6 87.88 -5.8 0 902689 5919594 21 -201 94 9.6 72.15 58.71 1.9 0.0004 916027 5984330 26 =243.8 94 10.8 32.1 152.3 -18.4 0.0265 924015 6680949 26 -172 94 2.4 68.8 160.5 -0.8 0.161 1022909 6644733 26 -247 129 14.5 95.9 27.3 -18.6 0 1071503 6810029 1 -247 145.3 11.2 82.4 -19.3 0.7 0 1137733 7234323 40 -147 126.6 16 -47 -34.4 -22 0 1186754 7638991 2 -145 104.3 13.5 -123.9 -22 -23.4 0.38 1199915 7757238 10 -247 125.5 8.9 153.8 -33.8 -14.1 0 1345764 8792199 40 -145 113.9 12.9 -163.9 17.6 -19.3 0.019 1365956 8874723 5 -172.9 94 4.2 13.3 25.5 4.2 0 1372242 8901455 21 B-51
Table B.2-4 (cont'd) Random Number Missile X Y Z X' Y' Z' P Number
of Years Number
-179.3 94 11.5 -14 85.6, 14.8 0.0025 1456165 9435092 2 s -176 94 6.07 -6.3 64.98 0.5 0 1465290 9465131 2 -145 105.75 15.69 -41.3 57.7 -1.2 0 1500515 9669490 2 -206 94 7.5 -38.4 36.16 -2 0 1512212 9974933 2 -175.4 148 14.4 78.6 -45.3 7.6 0 1512610 9871649 3 -152.6 148 13.13 22.9 -61.9 11.9 0 1525594 9855347 11 241.25 100.9 16 -16.7 186.2 -10.4 0 1532330 9904124 1 Total Prob. =.60453 Random Number identifies the particular trial in the simulation. l. e i 4 1 1 4 4 i B-52
air" vehicles has never been supported by hard evidence (L4). The extreme heights j predicted by the PILGRIMI code are due to the conservative wind model and missile j flight parameters. The effect on the results predicted herein is significant, but not dominating, however, because relatively few penetrate the auxiliary bay roof despite i the heights to which they are lofted. Using the' conditional probability (C ) of 0.5 for missile compromise of electrical f j conduits following wall penetration (with the exception of the south wall of the l water intake structure where it is assumed to be 1), along with the results from in I Tables B.2-3 and B.2-4, predicts a compromise rate of 1.3E-08 for the auxiliary bay and 5.0E-8 for the water intake structure. Even this number is very conservative i for the water intake structure because there were very few (if any) strikes in l regions which could impact the Class I conduits (i.e., C = 0). Couyuumise rate for i f l the water intake structure was totally dominated by two missile strikes (from the ) 40-ft long tree missile, No. 26, and the wide-flange I-beam, No.10). The I-beam comes from the construction materials originally modelled to account for possible l construction of a Unit 3, but left in the Pilgrim I analysis to compensate for those ) missiles generated from the new administration building. There were six strikes on the auxiliary bay roof by missiles which did not first l strike the containment and there were eight which struck the rolling steel vehicle j door. None of these penetrated. l The relative number of missile strikes (without considering perforation) on the two i regions is roughly pwevnional to their exposed areas as would be expected. The seeming anomaly of the higher penetration probability for the water intake structure is caused by the two missile strikes described above. Such fluctuation in rare event t { modelling is not uncommon, and since the probability numbers are so small, it is l no cause for concern. i Confidence limits of these predictions are discussed in Section 3. l ti i i B-53 e
r,,, x 1 'l 1 APPENDIX C COMPUTER CODE LISTING l l l I l l l
Figure C-1 is a listing of the main missile simulation code. The simulation code PILGRIM 1 consists of the main program and 9 subroutines which are described briefly on the next page and listed on the following pages. In addition, the subroutine BAYHITS has been addded which calculated the exact location of missile strikes on the auxiliary bay following impact on the outer plant " envelope" of PILGRIMI C-1
PROGRAM PILGRIM 1 This is the main program for the PILGRIM 1 code. Using random nurb;rs and tornedo parameter models, a tornado is created for cnolysis at each recurrance interval by this program. SUBROUTINE REDUCE 1 Subroutine REDUCE is called by PILGRIM 1. REDUCE scans the full ciccile list and selects out only those missiles that are within tha 75 mph of the tornado. REDUCE also will plot the plan view of tha tornado starting location and the missiles in its path if tha plot option of PILGRIM 1 is selected. SUBROUTINE VECTR Subroutine VECTR is called by PILGRIM 1. Using the various wind p;rcr2ter models of the tornado, VECTR calculates the wind / missile intsrection for each missile at each one tenth diameter step of tha tornado across the plant site. VECTR determines whether a Civ:n missile will fly and if so calls subroutine DIFEQ to perform 'I th2 numerical integration of the flight. VECTR also handles the cecounting of the missile termination statistics. SUBROUTINE DIFEQ1 Subroutine DIFEQ is called by VECTR. DIFEQ performs the Runge-Kutta numerical integration of the missile flight path until tha flight is terminated by one of the several termination conditions. DIFEQ stores or prints the data on the flight and torr.ination conditions of each missile in the tornado path. SUBROUTINE MCDWND Subroutine MCDWND is called by VECTR. MCDWND uses the Mcdonald wind codel to calculate the tangential, radial, and vertical wind velocities at any point in the tornado. SUBROUTINE RANDL Subroutine RANDL is called by RANDM. RANDL is the 'C' language rcndom number generator used throughout the program. SUBROUTINE RANINI pubroutine RANINI is called by PILGRIM 1. RANINI initializes the rcndom number generator, RANDL, to some preselected random number. SUBROUTINE RANDM Subroutine RANDM is called by several toutines. RANDM calls RANDL, returns the random number, and places the number of rcndom numbers used into common for use by other program units. $UBROUTINE SECOND l Jubroutine SECOND returns the system time with 10 millisecond resolution. C-2
l PILGRIM 1.FOR $ STORAGE:2 SNOFLOATCALLS C C--Interface subroutines to access system date and time. C INTERFACE TO SUBROUTINE TIME (LEN,STR) CHARACTER 410 STR [NEAR, REFERENCE] INTEGER 42 LEN [VALUE] END INTERFACE TO SUBROUTINE DATE (LEN,STR) CHARACTER 4 30 STR [NEAR, REFERENCE] INTEGER *2 LEN [VALUE] END C C--Start of main program. C } C .C--This program is for PILGRIM 1 C PROGRAM WIZ REAL
8 START,DIFF,CPTIME CHARACTER DSTR410, TSTR410, CDATE*10, CTIME*10 CHARACTER FNAME4 64, DATFILE*12 INTEGER

4 NRAN,NTRY,NYRS,ITOR,NRAN1,RSTART COMMON / FLY /NFT(2OOO)
COMMON / LOCATE /XMIS(1500),YMIS(1500),2 MIS (1500),ID(1500), +NMSL(1500),NMIS i COMMON /MSLTEMP/XTEMP(15DO),YTEMP(1500),2 TEMP (1500),ITEMP(3500), +NTEMP(1500),NM COMMON A(20),CDATE,CTIME,IDMSL,INMSL,MTYPS,MT6(45),NFTH(5) COMMON / COUNT /LINE,NPAGE COMMON / RANDOM /NRAN DIMENSION Q(25) INTEGER F, OPTION C GENERATE MAXIMUM WIND SPEED DATA AD.A1,B1,B2/2.30753,0.27063,0.99229,0.04481/ DATA CPTIME /1.0/ DATA DATFILE/'TORDATAX.DAT'/ CALL TIME (10,TSTR) CALL DATE(10,DSTR) CDATE = DSTR CTIME : TSTR C-3
PILGRIM 1.FOR WRITE (4,431) 433 FORMAT (IX,' Random number generator initialization.'/ 41X,' Enter one of the following:'// +' Negative random numbers to bypass;'/ +' "O" (2ero)" to to seed with zero;'/ +' Arbitrary positive seed;'// +' Enter.... '\\) READ (4,4)RSTART WRITE (4,432) 432 FORMAT (IX,' Enter maximum number of tornadoes.... '\\) RE AD(4,4 )NEND WRITE (*,433) 433 FORMAT (IX,' Enter minimum wind speed.... '\\) READ (t,4)VMIN WRITE (4,434) 434 FORMAT (IX,' Enter output format (0,1,2) '\\) READ (t,4)IPICT WRITE (4,436) 436 FORMAT (IX,' Enter number of years.... '\\) READ ( 4,4 ) NYRS MTYPS : 38 C C--DETERMINC WHERE OUTPUT IS TO GO C IF(IPICT .GT. O)THEN JO WRITE (4,400) 400 FORMAT (////JHO,' Output to:'//
41x, (J) Conso]e'/

41x, (2) Printer'/

41x, (3) File'//
41x,' Enter an option >> '\\) READ (4,4) OPTION IF(OPTION.LT. 2 .OR. OPTION.GT. 3)GOTO 10 IF(OPTION.EO. 1)THEN OPEN(e.,F3LE:' CON') ELSEIF(OPTION.EO. 2)THEN OFEN(6, FILE:'L PT J ') C C--Set printer to 17 char / inch and 8 lines / inch. C WRITE (6,409) CHAR (IS), CHAR (27), CHAR (40) 409 FORMAT (' ,3A) ELSE WRITE (4,420) 410 FORMAT (IHO,' Enter file name '\\) READ (4,420)FNAME OPEN(6. FILE =FNAME, STATUS:'NEW') ENDIF C-4 1
4u_4_. J,_A 4 r, 4._M.__ 4 a A_ a4,_4;.-_d. ,,A_4J_4_JA 34 As m_ .i.uJ._._=a: _ Aa.4,.3.a,_w.3424_ g2A,,4 .4__ag. .,._A_.- .a.sA,a a,. g, PILGRIM 1.FOR i 420 FORMAT (A) ENDIF C C--Open input missile data file -- 'MISLDATA' from RAMDISK E:' C 2 l OPEN(3, FILE:'E: PILGRIM 1f.DAT') i WRITE (4,411 ) 411 FORMAT (////20X,' Patience please... Loading missile data file.'//) C C--Put missile list into temporary array for analysis by subroutine C' REDUCE. C i i READ (3,301)NM i 301 FORMAT (I6) NLINES : NM/3 j DO 800 L : 1,NLINES i K = (L-1) 4 3 READ ( 3,302 ) ( XTEM P ( K + I ), YTEMP ( K 41 ),2 TEMP ( K 41 ), I TEMP ( K i l ), } +NTEMP(ktI), I: 1,3) { 800 CONTINUE l 302 FORMAT (3(2F6.0,F6.2,I3,I4)) l C { C--Open a] ternate output file -- TORDATA' C 1 4 DATFILE(J:1) CDATE(J:1) ) DATFILE(2:2) CDATE(2:2) DATFILE(3:3) CDATE(4:4) 3 DATFILE(4:4) CDATE(5:5) l DATFILE(5:5) C11ME(3:J) DATFILE(6:6) CTIME(2:2) l DATFILE(7:7) : CTIME(4:4) j DATFILE(8:8) : CTIME(5:5) f OPEN(9, FILE:DATFILE, STATUS : 'NEW') i WRITE (9,700)DATFILE,CDATE,CTIME,RSTART,NYRS i 700 FORMAT (' Fije ' A12,', started: AJO,', ,A10/ I +' after 19,' random numbers and ',19,' years.'//) ) wri t e (4,700) da tfi le, c da te, c t ime, rstar t, nyrs 4 RSITE:5280.0 DELT:5.0 i C READ (4,500)RSTART,NEND,VMIN,IPICT,MTYPS,NYRS 500 FORMAT (2IO,F8.0,3IO) C-5
PILGRIM 1.FOR NTRY:46948 LTOR=0 NTOR:0 NPAGE=1 CALL RANINI(RSTART,IPICT) CALL SECOND(START) Co*o************************************************************* C Start of master loop COOO**********'***************h************************************ DO 1001 ITOR=1,NTRY LINE=O NYRS:NYRS+213 140 RAND:0.0 CALL RANDM(RAND) NRAN1=NRAN P=0.5-RAND S: SIGN (1.0,P) P: ABS (P) IF(P.LT.1.E-4)P 1.E-4 TSQ:ALOG(1.0/(P*P)) T:SQRT(TSQ) 2:S*(T-(AO+Al*T)/(1.0+Bl*T+B2*TSQ)) WIND =98.742*EXP(0.3528*2) IF(WIND.GT.360.0)GOTO 140 IF(WIND.LT.75.0)GOTO 140 IF(WIND.LT.VMIN)GOTO 998 F= INT ((WIND /14.1)**(2.0/3.0)-2.0) C C GENERATE TRANSLATIONAL SPEED OF TORNADO C 5 RAND:0.0 CALL RANDM(RAND) P:0.5-RAND S: SIGN (1.0,P) P: ABS (P) IF(P.LT.I.OE-4)P:1.OE-4 TSQ:ALOG(1.0/(P*P)) T:SQRT(TS0) 2:S*(T-(AD+A14T)/(1.0+Bl*T+L2*TSO)) VTRANS 10.606642+37.5 IF((VTRANS.LT.5.0).OR.(VTRANS.GT.70))GOTO 5 DO 111 I:1,20 111 A(I):0.0 FTSEC=88.0/60.0 A(6):VTRANS4FTSEC A(12): WIND *FTSEC C SELECT PATH WIDTH RAND 0.0 CALL RANDM(RAND) R: RAND C-6
PILGRIM 1.FOR i IF(F.LT.O.OR.F.GT.5)GOTO 140 GOTO (20,30,40,50,60,70),F+1 20 IF(R.GT.O.995) GOTO 94 IF(R.GT.O.952) GOTO 93 IF(R.GT.O.865) GOTO 92 IF(R.GT.O.438) GOTO 91 GOTO 90 30 IF(R.GT.O.998) GOTO 95 IF(R.GT.O.987) GOTO 94 IF(R.GT.O.884) GOTO 93 -IF(R.GT.O.624) GOTO 92 IF(R.GT.O.144) GOTO 91 GOTO 90 40 IF(R.GT.O.996) GOTO 95 IF(R.GT.O.962) GOTO 94 IF(R.GT.O.737) GOTO 93 IF(R.GT.O.347) GOTO 92 IF(R.GT.O.038) GOTO 91 GOTO 90 50 IF(R.GT.O.991) GOTO 95 IF(R.GT.O.910) GOTO 94 IF(R.GT.O.487) GOTO 93 IF(R.GT.O.190) GOTO 92 IF(R.GT.O.023) GOTO 91 GOTO 90 60 IF(R.GT.O.967) GOTO 95 IF(R.GT.O.700) GOTO 94 IF(R.GT.O.183) GOTO 93 IF(R.GT.O.066) GOTO 92 GOTO 91 70 IF(R.GT.O.800) GOTO 94 IF(R.GT.O.400) GOTO 93 GOTO 92 95 WIDTH:6500.0 GOTO 100 94 WIDTH:2800.0 GOTO 100 93 WIDTH:870.0 GOTO 100 92 WIDTH:3OO.O GOTO 100 91 WIDTH:110.0 GOTO 100 90 WIDTH:35.0 C C SELECT TORNADO DIRECTION (HEADING IN RADIANS) 100 RAND:0.0 CALL RANDM(RAND) R= RAND PI:3.14159265 BETA:3.612831552 IF(R.LT. 91) BETA =2.827433388 IF(R.LT. 52) BETA =2.042035225 IF(R.LT. 20) BETA:1.256637061 IF(R.LT. 06) BETA:0.471238898 C-7
PILGRIM 1.FOR PHI: BETA-PI/2. IF(PHI.LT.O.0) PHI: PHI +2.O*PI RAND:0.0 CALL RANDM(RAND) R: RAND RTW:5280.0+ WIDTH /2.0 s DELR:2.O*(0.5-R)*RTW ALPHA 2:ACOS(DELR/RTW) i PATHL:2.O*SQRT(RTW*42.04 ABS (DELR)**2.0) STEP: WIDTH /10.0 DELT= STEP /A(6) IF(DELT.GE.O.1)GOTO 200 DELT:0.1 STEP:0.1*A(6) 200 CONTINUE NSTEP: INT (PATHL/ STEP)+2 XTOR:RTW*COS(BETA + ALPHA 2) YTOR:RTW4 SIN (BETA + ALPHA 2) A(7)=DELT A(11): WIDTH A(13): PHI VTM:2.O*(A(12)-A(6))/SQRT(5.) A(4):VTM C:0.G*(A(6)*A(6)-1.21E4) AA:A(11)413.57375 H1:0 H2=0 DO 300 I:90,179 ALPHA =3.1415927*I/180.0 8:-1.6*A(6)*(COS(ALPHA)/2.0+ SIN (ALPHA)) D2:AA* SIN (ALPHA)*(-B+SQRT(B*B-4.O*C))**(.625) IF(D2.GT.H2)H2:D2 BETA:6.2831853-ALPHA B :-1. 6* A ( 6 ) * ( COS (B ETA ) /2. 0+ SIN ( B ETA ) ) DI:AA* SIN (BETA)*(-B+SQRT(B*B-4.O*C))**(.625) IF(DI.LT.HI)H1:D1 300 CONTINUE A (15):H14 A (11 )/ (H2-H1 ) A(16):H24A(15)/H1 A(11):A(11)*A(11)/(H2-HI) RM:A(11)413.573754(2.O*VTM)*4(-0.625) IF(RM.GT.A(11)/2.0)RM=A(11)/2.0 A(5):RM IPASS=0 CALL REDUCE (XTOR,YTOR, PHI,IPASS,IPICT) DO 220 I:1,2000 220 NFT(I):0 i WRITE (9,610)NRANI,NMIS, WIND, WIDTH, PHI,VTRANS,A(4),A(5),NYRS IF(NMIS.EO.0)GOTO 999 C-8
PILGRIM 1.FOR IF(IPASS.EQ.1)GOTO 998 INDX1=MTYPS+5 DO 230 L1=1,INDX1 MT6(L1)=0 230 CONTINUE IF(IPICT.GT. O)THEN 1 WRITE (6,161)ITOR, WIND, WIDTH, PHI,VTRANS, STEP,A(16),A(15) +,A(4),A(5),A(11) 161 FORMAT (5H TRY:,I7,13H WIND VEL:,F7.2,13HMPH WIDTH:, 2 +F6.0,10HFT DIR:,F6.3,23HRADIANS TRANSLATION:,F5.2, +3HMPH,14H STEP SIZE:,F6.1,2HFT,/13X,17H75 MPH: LEFT SIDE =, +F7.1,15H RIGHT SIDE =,F8.1,' VTM=',F5.1 ) +,' RM:',F6.1,' A(11)',F6.1) 610 FORMAT (2I8,F8.2,F8.1,F8.3,F8.2,2F8.1,I8) i WRITE (6,162)CDATE,CTIME,NPAGE 1 NPAGE=NPAGE+1 162 FORMAT (IX,5HDATE:,A10,8H TIME:,A10,70X,5HPAGE,I3,/, +' MISSILE MISSILE LOC:',' INIT.WND. VEL 2 +' TORNADO LOC. MISL. LOC:END INT. TRM.MISL. VEL HEIGHT 2-DOT +' MISSILE DSPL. T.DSPL'/' NM/ TYPE START FT/DEG (FT/SEC)/DEG', +' FT/DEG FT/DEG TIME (FT/SEC)/DEG FT FT/SEC 'DIST/DIR DIST TIME NF EC TDEL'//) i ENDIF DO 190 J:1,NSTEP RANGE =SQRT(XTOR*XTOR+YTOR*YTOR) THETA =57.29578&ATAN2(YTOR,XTOR) l CALL VECTR(XTOR,YTOR,J,NSTEP,IPICT) XTOR=XTOR+ STEP *COS(PHI) YTOR=YTOR4 STEP
SIN (PHI) 190 CONTINUE CALL SECOND(CPTIME)
DIFF = CPTIME - START NTOR=NTOR+1 IF(NTOR.EQ.NEND)GOTO 1000 998 CONTINUE CALL SECOND(CPTIME) DIFF = CPTIME - START IF(IPICT.GT. O) WRITE (6,606)NRAN,DIFF,ITOR 100J CONTINUE C C--End of master loop. C ITOR=NTRY C-9
l PILGRIM 1.FOR 1C00 CONTINUE IF(IPICT.GT.0) WRITE (6,606)NRAN,DIFF,ITOR 606 FORMAT (' RANDM NUMBRS:',18,', TIME:',F12.1, +' SECONDS, AFTER',I6,' TORNADOES') j NRAN1:-NRAN1 WRITE (9,610)NRANI,NMIS, WIND, WIDTH, PHI,VTRANS,A(4),A(5) CLOSE (9) CLOSE (6) END C-10
REDUCE 1.FOR SSTORAGE:2 SNOFLOATCALLS SUBROUTINE REDUCE (XST,YST, PHI,IPASS,IPICT) CHARACTER IPLOT(180,132) 1 CHARACTER MLTR*40,CDATE*10,CTIME*10 DIMENSION NTYP(40),NTYP1(40) COMMON / LOCATE /XMIS(1500),YMIS(1500),2 MIS (1500),ID(1500), +NMSL(1500),NMIS COMMON /MSLTEMP/XTEMP(1500),YTEMP(1500),2 TEMP (1500),ITEMP(1500), +NTEMP(1500),NM COMMON A(20),CDATE,CTIME,IDMSL,INMSL,MTYPS,MT6(45),NFTH(5) i i DATA MLTR/'ABCDEFGHIJKLMNOPQRSTUVWXY2+2345678091=()'/ C DATA MLTR/1HA,1HB,1HC,1HD,1HE,1HF,1HG,1HH,1HI,1HJ,1HK,1HL, C +1HM,1HN,1HP,1HQ,1HR,1HO,1HS,1HT,IHU,1HV,1HW,1HX,1HY,1H2, -C +1H+,1H2,1H3,1H4,1H5,1H6,1H7,1H8,1HO,1H9,1H1,1H:,1H(,1H)/ REWIND 3 NMIS=0 NIDT=0 MSUM:0 MTOT=0 DO 4 I:1,MTYPS NTYP(I) 0 NTYP1(I)=0 4 CONTINUE IF(IPICT.NE. O)THEN DO 5 I:1,180 DO 6 K=1,132 IPLOT(I,K): 6 CONTINUE IPLOT(I,1):'*' IPLOT (I,132) = ' 4 ' 5 CONTINUE DO 8 K:1,132 IPLOT(1,K):'*' IPLOT(180,K):'#' 8 CONT.TNUE ENDIF 9 DO 7 I:1,2OOO XMIS(I)=0.0 C-11
l REDUCE 1.FOR YMIS(I)=0.0 ZM7G(I)=0.0 l ID(I)=0 7 CONTINUE SLOPE: TAN (PHI) BCEPT:YST-SLOPE *XST WTOR:-BCEPT/SQRT(SLOPE **2+1) j IF(PHI.GT.1.570796.AND. PHI.LT.4.712389)WTOR:-WTOR PWFCTR:1. 0+ ( A (12)-110. 0)/1933. 3 LEFT A(16)*PWFCTR RIGHT=A(15)*PWFCTR IF(LEFT.LT.200.0)LEFT:2OO.O IF(RIGHT.GT.-2OO.0)RIGHT -2OO.O i IF(WTOR.GT.LEFT.OR.WTOR.LT.RIGHT)IPASS=1 i IF(IPASS.EQ.1.AND.IPICT.EQ.0) RETURN IF(IPICT.EO. 2)THEN R:5280. RT:(A(16)-A(15))/2.0 THETA:0. DO 35 X:1,180 X:R*COS(THETA) Y:R* SIN (THETA) XT=RT*COS(THETA)+XST YT:RT* SIN (THETA)+YST INXT= INT (XT/60.+0.5)+90 INYT= INT (YT/60.+0.5)+110 THETA: THETA +3.14159/90. INX= INT (X/60.)+90 INY: INT (Y/60.)+110 IF(INX.GT.180.OR.INY.GT.132)GOTO 45 IPLOT(INX,INY):'*' 45 IF((INXT.LT.1).OR.(INXT.GT.180))GOTO 35 IF((INYT.LT.1).OR.(INYT.GT.132))GOTO 35 IPLOT(INXT,INYT):'.' 35 CONTINUE IPLOT(89,109):'.' IPLOT(89,110):'.' IPLOT(89,311):'.' IPLOT(90,109):'.' l IPLOT(90,110):'.' IPLOT(90,111):'.' IPLOT(91,109):'.' IPLOT(91,110)='.' IPLOT(91,111):'. ENDIF C i C--S31ect those missiles in temporary array that are in tornado pcth. C DO 20 I:1,NM IF(ITEMP(I).EO.0)GOTO 20 C-12 l
I REDUCE 1.FOR MTOT:MTOT+NTEMP(I) DIST:(YTEMP(I)-SLOPE *XTEMP(I)-BCEPT)/SQRT((SLOPE **2)+1) IF((PHI.GT.1.570796).AND.(PHI.LT.4.712389))DIST:-DIST 55 IF((DIST.GT.A(16)).OR.(DIST.LT.A(15)))GOTO 20 l i NMIS:NMIS+1 IF(NMIS.GT.15DO)GOTO 30 4 MSUM:MSUM+NTEMP(I) XMIS(NMIS):XTEMP(I) 4 YNIS(NMIS):YTEMP(I) 1 ZMIS(NMIS):ZTEMP(I) ID(NMIS):ITEMP(I) NMSL(NMIS):NTEMP(I) NTYP(ITEMP(I)):NTYP(ITEMP(I))+1 NTYP1(ITEMP(I)):NTYP1(ITEMP(I))+NTEMP(I) IF(IPICT.EQ. 2)THEN k INX= INT (XTEdr(I)/60)+90 i INY: INT (YTEMP(I)/60)+110 IPLOT(INX,INY):MLTR(ID(NMIS):ID(NMIS)) l ENDIF 20 CONTINUE IF(NMIS.EQ.O.OR.IPICT.EQ.0) RETURN j 30 CONTINUE IF(IPICT.EO. 2)THEN WRITE (6,262)CDATE,CTIME DO SO I:1,180 50 WRITE (6,603)(IPLOT(I,K),K:1,132) WRITE (6,601)NMIS,MTOT,MSUM,NEXT WRITE (6,261) (MLTR(I:I),I:1,19) 40 WRITE (6,602) (NTYP(I),I:1,19) WRITE (6,602) (NTYP1(I),I:1,19) WRITE (6,261) (MLTR(J:J),J:20,38) WRITE (6,602) (NTYP(J),J:20,38) WRITE (6,602) (NTYPI(J),J:20,38) ENDIF 601 FORMAT (IX,5HNMIS:,I6,7H MTOT,I6,7H MSUM:,I6,7H NEXT:,I6) i 261 FORMAT (/6X,19A6) 262 FORMAT (1H.5HDATE:,A10,8H TIME:,A10) 602 FORMAT (IX,1916) 603 FORMAT (IX,132A1) RETURN END C-13
-_.= VECTR.FOR $ STORAGE:2 $NOFLOATCALLS SUBROUTINE VECTR(XTOR,YTOR,J,NSTEP,IPICT) CHARACTER CDATE*10, CTIME*10 COMMON / FLY /NFT(2OOO) COMMON A(20),CDATE,CTIME,IDMSL,INMSL,MTYPS,MT6(45),NFTH(5) COMMON / COUNT /LINE,NPAGE COMMON / LOCATE /XMIS(1500),YMIS(15DO),2 MIS (1500),ID(1500), +NMSL(1500),NMIS COMMON / RANDOM /NRAN INTEGER
4 NRAN DIMENSION YO(25),CDAW(45),NSTOP(45,10),NTOTAL(10),ITOTAL(10)
DIMENSION 2MISH(5),NMSLH(5,5) COMPLEX UNITT,UNITRM,VTVECT,VRVECT,WNDVECT,MVECT,TVECT,RVECT, + ROT 90,TRVECT,UNITR DATA CDAW/.1643,.0461,.0349,.0257,.0374,.0546,.12,.0402, +.0384,.0338,.0523,.0166,.0137,.0053,.5542,.3657,.075,.075, +.163,.006,.129,.1263,.4356,.02,.0267 0595,.4244,.6829, +.04,.0836,.0788,.0042,.0809,.0384,.1956,.0978,.0452,.0317, 4.179,.15,.30,.3718 145,2*0.0/ DATA NMSLH/2,4,6,2,2,6,1,4,8,8,0,6,10,20,30, +240,10,20,30,3*0,2*1/ DATA 2MISH/5*7.0/ DATA NTOTAL/1040/ DATA NSTOP/45040/ XV: A(6) *COS( A (13) ) YV:A(6)* SIN (A(13)) TRVECT:CMPLX(XV,YV) ROT 90:(0.,1.) 624 FORMAT (1H,5HDATE:,A10,8H TIME:,A10,70X,5HPAGE,I3,/, +' MISSILE MISSILE LOC:',' INTT.WND. VEL 4' TORNADO LOC. MISL. LOC:END INT. TRM.MISL. VEL HEIGHT 2-DOT ', +' MISSILE DSPL. T.DSPL'/' NM/ TYPE START FT/DEG (FT/SEC)/DEG', +' FT/DEG FT/DEG TIME (FT/SEC)/DEG FT FT/SEC +'DIST/DIR DIST TIME NF EC TDEL'//) INDX1:MTYPS+5 DO 99 I:1,NMIS A(17):XMIS(I) A(18):YMIS(I) A(19):2 MIS (I) MH=O INMSL:NMSL(I) DO 31 K:1,5 31 NFTH(K):0 IDSW:0 IF(ID(I).EQ.27)IDSW:1 NHMSL:1+IDSW*4 C-14
j VECTR.FOR DO 98 IHMSL=1,NHMSL IDMSL:ID(I)+IDSW4(MTYPS-27+IHMSL) A(1):CDAW(IDMSL)*0.0765/2.0 IF(ID(I).EO.27)2 MIS (I):ZMISH(IHMSL) TVECT:CMPLX(XTOR,YTOR) NNSTEP 1 JJ:1 MTX:0 MT=0 MVECT:CMPLX( A (17), A (18) ) 50 CONTINUE DO 40 NFLY:JJ,NNSTEP IF((MT.EQ.0).AND.(MTX.EQ.0))GOTO 60 TVECT=TVECT+A(7)*TRVECT 60 DO 10 K:1,25 10 YO(K):0.0 IF(NFT(I).LT.0)GOTO 20 RT: CABS (TVECT) AT=57.29578*ATAN2(AIMAG(TVECT),REAL(TVECT)) 623 FORMAT (IH,5HNFLY:,I2,7H NJ:,I2,' RADIUS:',F6.1, +' ANGLE =',F6.1) RVECT:MVECT-TVECT YO(1)= CABS (RVECT) YO(3):ATAN2(AIMAG(RVECT),REAL(RVECT)) YO(5):ZMIS(I) CALL MCDWND(YO,VT,VR,V2) UNITR=RVECT/YO(1) UNITT:UNITR4 ROT 90 VTVECT:UNITT*VT VRVECT:UNITR4VR WNDVECT TRVECT+VTVECT+VRVECT WNDSPD: CABS (WNDVECT) IF(ID(I).NE.27)GOTO 65 IF(MH.EQ.1)GOTO 64 IF(WNDSPD.LT.161.33)GOTO 99 MWX:5 IF(WNDSPD.LT.366.67)MWX=4 IF(WNDSPD.LT.293.33)MWX:3 IF(WNDSPD.LT.234.67)MWX:2 IF(WNDSPD.LT.190.67)MWX:1 64 INMSL:NMSLH(MWX,IHMSL) IF(INMSL.EO.0)GOTO 98 65 CONTINUE IF(WNDSPD.LT.110.0)GOTO 40 WNDDIR:57.29578*ATAN2(AIMAG(WNDVECT),REAL(WNDVECT)) RR:YO(1) AR:YO(3) RM: CABS (MVECT) AM:57.295784ATAN2(AIMAG(MVECT),REAL(MVECT)) IF(MH.EQ.1.AND.MT.EQ.0)GOTO 201 KNOB 2:0 RAND:0.0 CALL RANDM(RAND) RN= RAND WNDR:WNDSPD/5'28.0 C-15
VECTR.FOR C THE FOLLOWING USES HALF THE PATH WIDTH-RM C WNDR:4.OtWNDSPD*A(6)*A(7)/(A(12)4((A(16)-A(15))/2.0-A(5))) C THE FOLLOWING USES D1-RM C WNDR=-4.O*WNDSPD4A(6)*A(7)/(A(12)*(A(15)+A(5))) IF(RN.LT.WNDR)GOTO 200 IF(ID(I).EO.27.AND.MH.EO.0)GOTO 99 IF(MT.EQ.0)GOTO 20 GOTO 40 200 IF(ID(I).EO.27)GOYO 201 IF(ZMIS(I).GT.2.0)GOTO 45 RWT:VT+A(6)4 SIN (A(13)-YO(3)) RWR:VR+ A (6)
COS ( A (13)-YO (3) )
RWZ:VZ D:SQRT(RWT*42+RWR*42+RWZ**2) IF(A(1)*D*RWZ-32.2.LT.-O.2)GOTO 40 45 CONTINUE NFT(I):NFT(I)+1 GOTO 202 201 NFTH(IHMSL):NFTH(IHMSL)+1 MH=1 202 CONTINUE 621 FORMAT (1H,14,1H/,I2,F7.1,1H/,F6.1,F6.1,1H/,F6.1,F7.1.1H/,F6.1) IF(LINE.LT.65)GOTO 30 IF(IPICT.GT. O) WRITE (6,624)CDATE,CTIME,NPAGE NPAGE:NPAGE+1 LINE 0 30 CONTINUE IF(IPICT.GT. O) WRITE (6,621)I,IDMSL,RM,AM,WNDSPD,WNDDIR,RT,AT C WRITE (6,622)(YO(K),K:1,6) 622 FORMAT (12H PRE-DIFEQ ,1P,6E10.3) CALL DIFEQ(YO,MVECT,MT,TVECT,TRVECT,I,IPICT) WRITE (4,630)NRAN 630 FORMAT (' # RANDOMS = ,I9,'. CTRL-C TO ABORT.') IF((NFLY.EO.NNSTEP).AND.(MTX.EO.1))GOTO 25 IF(MT.GT.2)GOTO 25 IF(MT.EQ.2)GOTO 40 IF(MT.EO.0)GOTO 20 XMIS(I):REAL(MVECT) YMIS(I):AIMAG(MVECT) TDISP: CABS (TVECT-CMPLX(XTOR,YTOR)) NJX: INT (TDISP/(A(7)*A(6))) JJ:J+NJX NNSTEP:NSTEP MTX:1 IF(JJ.GE.NSTEP)GOTO 25 GOTO 50 40 CONTINUE IF(MT.EO.0)GOTO 20 25 IF(ID(I).EO.27)GOTO 42 NFT(I):-NFT(I) GOTO 43 42 NFTH(IHMSL):-NFTH(IHMSL) 43 NSTOP(IDMSL MT+1):NSTOP(IDMSL,MT+1)+1 IF((MT.NE.6).AND.(MT.NE. 5).AND.(MT.NE. 7))GOTO 120 MT6(IDMSL):MT6(IDMSL)+INMSL C.16
VECTR.FOR 120 CONTINUE 20 IF(J.NE.NSTEP)GOTO 98 IF(I.NE.NMIS)GOTO 98 IF(IHMSL.NE.NHMSL)GOTO 98 IF(IPICT.GT. O)THEN DO 90 KM:1,2OOO IDSW:0 IF(ID(KM).EQ.27)IDSW:1 MSTOP=1+IDSW*4 DO 85 ISTOP:1,MSTOP IMMSL:ID(KM)+IDSW*(MTYPS-27+ISTOP) IF(IDSW.EQ.1)GOTO 55 IF(NFT(KM).NE.0)GOTO 85 GOTO 81 55 IF(NFTH(ISTOP).NE.0)GOTO 85 81 NSTOP(IMMSL,1):NSTOP(IMMSL,1)+1 85 CONTINUE 90 CONTINUE WRITE (6,626) INDX2=MTYPS+5 DO 70 ITYP 1,INDX2 70 WRITE (6,625)ITYP,(NSTOP(ITYP,JMT),JMT=1,10),MT6(ITYP) DO 73 JMT:1,10 73 ITOTAL(JMT):0 MT6T:D INDX3:MTYPS+5 DO 72 ITYP=1,INDX3 MT6T=MT6T+MT6(ITYP) DO 71 JMT:1,10 ITOTAL(JMT)=ITOTAL(JMT)+NSTOP(ITYP,JMT) NTOTAL(JMT):NTOTAL(JMT)+NSTOP(ITYP,JMT) NSTOP(ITYP,JMT):0 71 CONTINUE 72 CONTINUE MT6TT:MT6TT+MT6T WRITE (6,627)(ITOTAL(IMT), INT =1,10),MT6T WRITE (6,627)(NTOTAL(IMT),IMT=1,10),MT6TT ENDIF 625 FORMAT (I3,11I1O) 626 FORMAT (IH1//5H TYPE,10H NO-FLY ,10H REFLY +10H PASSED ,10H OUTSIDE 10H TIME +10H CTN' MENT,10H PLANT ,10H INTAKE-H,10H INTAKE-L +10H WATER ,10H TOTAL-6 /) 627 FORMAT (' TOTALS',I6,1DI1O) 628 FORMAT (IHI) 98 CONTINUE IF(ID(I).EO.27.AND.NHMSL.EO.5)NFT(I)=-1 99 CONTINUE RETURN END C-17
DIFEQ1.FOR SSYORAGE:2 SNOFLOATCALLS C C--This subroutine is for PILGRIM 1 C SUBROUTINE DIFEQ(YO,MVECT,MT,TVECT,TRVECT,IMSL,IPICT) CHARACTER CDATE*10, CTIME*10 REAL
8 CPTIME, TIME 1, TIME 2 COMMON / FLY /NFT(2OOO)
REAL MXDISP,MYDISP,MRDISP,MTDISP COMMON A(20),CDATE,CTIME,IDMSL,INMSL,MTYPS,MT6(45),NFTH(5) 4 COMMON / COUNT /LINE NPAGE DIMENSION YO(6),Y(6),ENDVTR(6),F1(6),F2(6),F3(6),F4(6),F5(6),YI(6) 2,YP(6),F(6),Y2(4),YTEMP(6) COMPLEX MVECT,TVECT,TRVECT,MDISP,YVECT,GVECT,Y2VECT,TFVECT CALL SECOND(TIME 1) C WRITE (*,700)MVECT,TVECT,TRVECT 700 FORMAT (' MVECT,TVECT,TRVECT:',6(IPE10.3)) C WRITE (*,701)(YO(I),I:1,6),MT,IMSL 701 FORMAT (' YO,MT,IMSL:',6(IPE10.3),2I3) EMAX=1.OE-2 ACCUR=.1 DELTA =1.0 A(14): DELTA XF:0.0 TDELM:0.0 FINAL:20.0 KNOB 3:1 DO2OI:1,6 YTEMP(I):YO(I) 20 YI(I):YO(I) IDO:0 ITT=0 GVECT:MVECT XMISI:REAL(GVECT) YNISI:AIMAG(GVECT) ZMISI:YO(5) XDOT:0.0 YDOT=0.0 2 DOT 0.0 TFVECT:CMPLX(0.,0.) A(8) A(4)/A(5) 10 Y6:YI(6) TDEL:0.0 DEL:0.0250 IDI=0 C SUBROUTINE RUNGE-KUTTA.
DIFEQ1.FOR 200 H: DEL IDO:ID0+1 C WRITE (6,8000) DEL,XF,TDEL,ID,IDI,IDO,ITT C WRITE (6,8010) (Y(I),YP(I),YI(I),I:1,6) 8010 FORMAT (6E15.8) 8000 FORMAT (3E12.5,4I6) H02=H40.5 H06:H/6. DO 1000I:1,6 4 1000 Y(I):YI(I) ID=1 C WIND NODEL. 2000 OY1:1.0/Y(1) IT:IT+1 IF(Y(1)-A(5).GT.ACCUR)GOTO 1005 VT=Y(1)*A(8) GOTO1020 1005 VT:110.4(0.5*A(11)*0Y1)**1.6 C 100:2 CD10 IF(IT.NE.1) GOTO 1015 C IDI:IDO CD15 IF(IDI.NE.IDO) GOTO 1420 1020 VR:-0.5*VT VZ:0.6666666667*VT C END OF WIND MODEL. C SUBROUTINE DE. RWT:VT-Y (4 )
Y (1 ) +A ( 6)

SIN ( A (13 )-Y ( 3 ) )
RWR=VR-Y(2)+A(6)*COS(A(13)-Y(3)) RWZ:V2-Y(6) D:SQRT(RWT*RWT+RWR*RWR+RWZ*RWZ) AD:A(1)*D F(1):Y(2) F(2):Y(1)*Y(4)4Y(4)+AD*RWR F(3):Y(4) F (4 ) (-2. 4 Y (2) *Y (4 ) +AD*RWT)
OY1 F(5):Y(6)
F(6)=-32.2+AD*RW2 C END OF SUBROUTINE DE. GOTO(1110,1120,1130.1140)ID 1110 DO 1050 I:1,6 1050 F1(I):F(I) GOTO 1210 1120 DO 1060 I:1,6 1060 F2(I):F(I) GOTO 1220 1130 DO 1070 I:1,6 1070 F3(I):F(I) GOTO 1230 1140 DO 1080 I:1,6 1080 F4(I):F(I) GOTO 1240 1210 DO 1310 I:1,6 1310 Y(I):Y(I)+H02*F1(I) ID=2 GOTO 2000 g,gg
1220 DO 1320 I=1,6 1320 Y(I):YI(I)+HO2*F2(I) ID=3 GOTO 2000 1230 DO 1330 I:1,6 1330 YP(I):YI (I) +H4F3(I) C CORRECTION AND TEST OF FOUR STEP RUNGE-KUTTA. ID=4 i GOTO 2000 s 1240 DO J340 I:1,6 Y (I ) :YI (I ) +HO6* (F1 (I ) +F2 (I) +F2 (I) +F3 (I ) +F3 (I ) +F4 (I ) ) IF(abs (Y(I)-YP(I)) -EMAX* ABS (YP(I)).GT.O.0) GOTO 1400 j 1340 CONTINUE GOTO 1500 1400 DEL: DEL 4.5 IDI:0 GOTO 200 1500 Do 1505I=1,6 1505 YI(I):Y(I) IDI:IDI+1 TDEL:TDEL+ DEL IF(Y(5).GT.ACCUR) GOTO 1520 ITT 1 GOTO 75 1520 IF(IDI.LT.4) GOTO 1525 IF(DELTA.LT.O.5)GOTO 1525 DEL: DEL + DEL IDI:0 1525 IF(TDEL.LT. DELTA) GOTO 200 C END OF RUNGE-KUTTA. 75 XF:XF4TDEL C START OF TERM SECTION YVECT:CMPLX(Y(1)*COS(Y(3)),Y(3)4 SIN (Y(3))) Y2VECT=YVECT-TDEL*TRVECT THETA 1=ATAN2(AIMAG(YVECT),REAL(YVECT)) THETA 2:ATAN2(AIMAG(Y2VECT),REAL(Y2VECT)) THETA =THETAJ-THETA 2 Y2(1): CABS (Y2VECT) Y2(3): THETA 2 SINTHA: SIN (THETA) COSTHA=COS(THETA) Y2(2):Y(2)4COSTHA-Y(1)*Y(4)*SINTHA Y2(4)=(Y(2)*SINTHA+Y(1)*Y(4)*COSTHA)/Y2(1) DO 300 I:1,4 300 YI(I):Y2(I) GVECT:TVECT+YVECT+TFVECT GREAL:REAL(GVECT) GAIMAG:AIMAG(GVECT) ENDVTR(5):Y(5) ENDVTR(6):Y(6) ENDVTR(1): CABS (GVECT) ENDVTR(3)=ATAN2(GAIMAG,GREAL) COSY 3:COS(YI(3)) SINY3: SIN (YI(3)) XVMG:YI(2)* COSY 3-YI(1)*YI(4)*SINY3 C-20
DIFEQ1.FOR YVMG=YI(2)*SINY3+YI(1)*YI(4)* COSY 3 ENDVTR(2)=SQRT(XVMG4XVMG+YVMG4YVMG) C write (*,777)yvmg,xvmg 777 format (' yvmg = ,1pe10.3,' xvmg = ' e10.3) C write (*,702)(y(i),1=1,4) C wri te (4,703) (y2 (i ), i = 1,4 ), thetal, the ta2 702 format (' y: ,4(1pe10.3)) 703 format (' y2,thetal, theta 2: ' 6(Ipe10.3)) ENDVTR(4)=ATAN2(YVMG,XVMG) C IF(IMSL.NE.345)GOTO 401 C WRITE (*,600)(Y(I),I:1,6) 600 FORMAT (' Y:',1P6E10.3) C WRITE (*,601)(ENDVTR(I),I:1.6) 601 FORMAT (' ENDVTR:',1P6E10.3) C WRITE (6,602)TDEL, THETA 1, THETA 2 602 FORMAT (' TDEL=',F6.3,' THETAl=',F8.3,' THETA 2=',F8.3/) 401 CONTINUE IF(ITT.EO.1) GOTO 202 IF(Y(5) .GT. 143.0)THEN GOTO 205 ELSEIF( (GREAL.GE. -73.0).AND.(GREAL.LE. 73.0).AND. + (GAIMAG.GE. -38.5).AND.(GAIMAG.LE. 73.5).AND. + + (Y(5) .GE. 85.0))THEN MT = 5 GOTO 80 ELSEIF( + (GREAL.GE. -136.0).AND.(GREAL.LE. 136.0).AND. (GAIMAG.GE. -210.0).AND.(GAIMAG.LE. 73.5).AND. + + (Y(5) .LE. 85.0))THEN MT=6 GOTO 80 ELSEIF( + (GREAL.GE. -247.0).AND.(GREAL.LE. -145.0).AND. + (GAIMAG.GE. 95.0).AND.(GAIMAG.LE. 159.0).AND. + (Y(5) .LE. 16.0))THEN MT=7 GOTO 80 ELSE GOTO 205 ENDIF 202 IF(ENDVTR(3).LT.O.226893)GOTO 205 IF(ENDVTR(1).LT.820.)GOTO 205 IF(ENDVTR(3).GT.2.6529.AND.ENDVTR(1).LT.3672.)GOTO 205 C.21
DIFEQ1.FOR IF(ENDVTR(3).LT.O.O.AND.ENDVTR(1).LT.3120.)GOTO 205 HT=9 GOTO 81 205 IF(ITT.EO.~1)GOTO 81 IF (XF.LT. FINAL) GOTO 206 IF (Y(6)-Y6.GT.O.0) GOTO 70 FINAL: FINAL +5.0 210 IF (FINAL.GT.42.5) GOTO hO 206 DO 230 I:1,6 230 YTEMP(I):YI(I) XMISI:GREAL YMISI:GAIMAG ZMIS1:Y(5) XDOT=XVMG YDOT:YVMG 2 DOT =Y(6) TFVECT=XF*TRVECT GOTO 10 80 IF(TDEL.LT.O.15)GOTO 82 XF=XF-TDEL DO 220 I:1,6 220 YI(I):YTEMP(I) DELTA:0.1 ITT:0 GOTO 10 70 MT=4 GOTO 81 82 WRITE (9,590)IDMSL,INMSL,XMIS1,YMIS1,2 MIS 1,XDOT,YDOT,2 DOT,MT WRITE (9,590)IDMSL,INMSL,GREAL,GAIMAG,Y(5),XVMG,YVMG,Y(6),MT 590 FORMAT (2IS,6F8.1,IS) 81 TYDISP:AIMAG(XF*TRVECT) TXDISP:REAL(XF4TRVECT) TRDISP:SQRT(TXDISP4*2+TYDISP**2) MXDISP:ENDVTR(1)*COS(ENDVTR(3))-REAL(MVECT) MYDISP=ENDVTR(1)* SIN (ENDVTR(3))-AIMAG(MVECT) MRDISP: SORT (MXDISP*42+MYDISP**2) MTDISP:57.295784ATAN2(NYDISP MXDISP) CALL SECOND(TIME 2) CPTIME: TIME 2-TIME 1 ENVTR3:57.29578+ENDVTR(3) ENVTR4:57.295784ENDVTR(4) IF(MT.GE.4)GOTO 40 PERPD:YI(1)* SIN (YI(3)-A(13)) IF(MRDISP.GT.85.)MT:1 IF((MRDISP.LE.85.).AND.(MT.EQ.1))MT=2 IF((PERPD.GT.A(16)).OR.(PERPD.LT.A(15)))MT 3 40 CONTINUE NFTI:NFT(IMSL) IF(IDMSL.GT.MTYPS)NFTI:NFTH(IDMSL-MTYPS) IF(IPICT.GT. O) WRITE (6,669)ENDVTR(1),ENVTR3,XF,ENDVTR(2),ENVTR4, +ENDVTR(5),ENDVTR(6), +MRDISP,MTDISP,TRDISP,CPTIME,NFTI,MT,TDEL,IDO LINE:LINE+1 IF(MT.NE.1) RETURN C-22
I DIFEQ1.FOR TVECT=TVECT+XF*TRVECT MDISP=CMPLX(MXDISP,MYDISP) MVECT=MVECT+MDISP MT=1 RETURN 669 FORMAT (1H+,48X,F7.1.1H/,F6.1 F5.1,F6.1,1H/,F6.1,F7.1, +F6.1,F7.1,1H/,F6.1,F7.1,' ' F4.1,I2,I2,F5.2,I4) END C.23 D
MCDWND.FOR { $ STORAGE:2 $NOFLOATCALLS SUBROUTINE MCDWND(Y,VT,VR,V2) C A(4):VTM NAXIMUM TANGENTIAL WIND VELOCITY C A(5):RM C A(6):VTRANS C A(11):PW C A(12):VH CHARACTER CDATE*10, CTIME*10 COMMON A(20),CDATE,CTIME,IDMSL,INMSL,MTYPS,MT6(45),NFTH(5) DIMENSION Y(25) IF(A(5).LT.Y(1))GOTO 5 VT Y(1)*A(4)/A(5) GOTO 10 5 VT:A(4)*(A(5)/Y(1))**1.6 10 VR :-VT/2. V2:2.4VT/3. RETURN END C-24
RANINI.FOR $ STORAGE:2 $NOFLOATCALLS INTERFACE TO SUBROUTINE RANZ[C](RAND [ REFERENCE]) REAL
O RAND END SUBROUTINE RANINI(K,IPICT)
REAL
8 RAND INTEGER

4 NRAN,K,I,LU COMMON / RANDOM /NRAN NRAN:0 IF(K) 3,6,2 2
RMIN=1.0/10.**K C CPU:SECOND(T) C CPU: CPU-INT (CPU) CPU = 0.456 5 RAND 0.0 CALL RANZ(RAND) R: RAND RCPU: ABS (R-CPU) IF(RCPU - RMIN)6,5,5 3 LU: -K RAND:0.0 DO 4 I:1 LU NRAN : NRAN + 1 4 CALL RANZ(RAND) 6 IF(IPICT.GT. O) WRITE (6,1061)NRAN RETURN 1061 FORMAT (12H START AFTER,I6,16H RANDOM NUMBERS) END C-25
RANDM.FOR $ DEBUG COO***************************************************************tt C C Name: RANDM C Type: Subroutine C Function: Calls 'C' module RANZ (File name: RANDL). Returns C a random number in [0,1]. Module used to put C the random number count into COMMON. C C By: Gaynor L. Abbott C 2633 Alpine Road C Menlo Park, CA 94025 C (415) 854-0754 C Co*O****************************************************************4 INTERFACE TO SUBROUTINE RANZ[C](RANO[ REFERENCE]) REAL
8 RAND END SUBROUTINE RANDM(RANMBR)
REAL48 RAND REAL*4 RANMBR COMMON / RANDOM /NRAN CALL RANZ(RAND) RANMBR = RAND C WRITE (*,100)RANMBR 100 FORMAT (' RAN NUM: ',F6.4) NRAN = NRAN + 1 RETURN END C-26
1 i 8 i
include < math.h>
Dinclude <stdio.h>
include <stdlib.h>
Ponz(rendon_numbr) double randon_numbr[]; l -{ long m; double halfa, atan(), sqrt(); static long m2 = 0; static long itwo = 2; static long ly, ic, mic, la; static double s; if (m2== 0) { iy = 0; a = 1; ?* while (m > m2)*/ do { m2 = m; a = itwo
m2;
} while (m > m2); halfa = (double) m2; la = 8 * (long) (halfa
atan(1.0)/8.0) + 5; ic = 2 * (long) (halfa * (0.5 - sqrt(3.0)/6.0)) + 1; nic = (m2 - ic) + m2; a = 0.5/halfa;
} iy *= is; if(iy > mic) ly = (iy - m2) -m2; iy+= ic; if(iy < 0) iy = (iy + m2) + m2; random _numbr[0] = (double) iy
s; return (0);
I, 1 C-27 d
SECOND.FOR $ STORAGE:2 $NOFLOATCALLS SUBROUTINE SECOND(SECS) REAL
8 SECS INTEGER

2 ITIME(8)
CALL DAYTIM(ITIME) SECS = DBLE(ITIME(3))*86400.DO + DBLE(ITIME(4))*3600.DO + + DBLE(ITIME(5))*60.DO + DBLE(ITIME(6)) + + DBLE(ITIME(7))/100.DO RETURN END I c-28
BAYHITS.FOR
storage: 2

nofloatcalls program bayhit character line*79, fname*12, outnam*12 integer

4 nran, years,id,mt real

4 t(4) write (*,100) 100 format (' Enter input file name... '\\)
read (*,'(a)')fname open(6,flie:fname) read (6,'(a)')line C C--Create output file name using file name of input file with ' HIT' C--cs extension. C do 200 i=1,9 outnam(i:i) = line(i+6:1+6) 200 continue outnam(10:12) = ' HIT' open(7, file =outnam, status = 'NEW') write (7,201)outnam 201 format (' This is file ',a12,' with aux bay = hit results from: '/) write (7,'(a)')line read (6,'(a)')line 4 write (7,'(a)')line read (6,'(a)')line read (6,'(a)')1ine write (7,'(/)') C 10 continue C C--Read in tornado data line. C read (6,110,end=1000)nran,nmis, wind, width, phi,vtrans,vtm,rm, years 110 format (218,6f8.0,i8) C C--Missile data line first entry is missile type (i.e. less than 100) C C-29
I BAYHITS.FOR if(nran.lt. 100)then backspace 6 backspace 6 read (6,110,end=1000)nran,nmis, wind, + width, phi,vtrans,vtm,rm, years else goto 10 endif wri te (7,120 ) n r an, n mis, win d, wi d th, phi, v t rans, vtm, rm, yea rs 120 format (218,f8.2 f8.1,f8.3,f8.2,2f8.1,i8) write (*,121) years 121 format (' Plant hits at ' 18,' years.') 20 continue read (6,130,end=1000)id,nm,x,y,z,xdot,ydot,2 dot,mt C C--Last line has nran negative. C if(id.It. O)then write (4,99) 99 format (' Done.') stop endif C C--New tornado if first entry .gt. 100 C if(id.st. 100) goto 10 r ea d ( 6,130, en d= 1000) i dl, nml, x1, yl, zl, xdo tl, ydo tl, zdo tl, m t i 130 format (218,6f8.1,iB) C C--Dont bother with type 7 hits C if(xdot.eq.O.0) xdot=0.OOOOO1 if(ydot.eq.O.0) ydot=0.OOOOO1 if(zdot.eq.O.0) zdot:0.DOOODI if(mt.eq. 7)goto 20 C i C--Calculate minimum times to each wall C t(1) = (27.0 - z)/zdot C-30 l
BAYHITS.FOR t(2) (-122.0 - x)/xdot = t(3) = (-71.0 - x)/xdot t(4) = (71.0 - y)/ydot C C--Test at each wall C do 300 i=1,4 C C--Must be positive for wall hit. C if(t(i) .ge. 0.0)then C C--Calculate hit coords. C xh = x + xdot
t(i) yh = y + ydot

t(i) zh = z + 2 dot

t(i)
C C--Wall 1 test. C if(i .eq. 1)then if((abs (zh - 27.0) .it. 1.0).and. + ((-122.0.It. xh).and. (xh.It. -71.0)).and. + ((-36.0.It. yh).and. (yh.It. 71. 0) ) ) then write (7,130)id,nm,x,y,z,xdot,ydot,zdot,mt wri te (7,140)i, xh, yh, zh 140 format (5x,' Wall ',il,' hit coords: x= ' f7.2, + , y: ' f7.2,', z= ',f7.2/) endif C C--Wall 2 test. C elseif(i .eq. 2)then if((abs (xh + 122.0) .It. 1.0).and. + ((-36.0.It. yh).and. (yh.It. 71.0)).and. + ((0.0.It. zh).and. (zh.It. 27.0)))then write (7,130)1d,nm,x,y,z,xdot,ydot,zdot,mt write (7,140)i,xh,yh,zh endif C-31
1 i i BAYHITS.FOR C C--Wall 3 test. C elself(i .eq. 3)then i if((abs (xh + 71.0) .It. 1.0).and. + ((-36.0.It. yh).and. (yh.it. 71.0)).and. '1 + ((27.0.It. zh).and. (zh.it. 143.0)))then write (7,130)id,nm,x,y,2,xdot,ydot,zdot,mt write (7,140)i,xh,yh,zh endif else C C--Wall 4 test. C if((abs (yh - 71.0).it. 1.0).and. + ((0.0.It. zh).and. (zh.It. 22.0)).and. + ((-122.0.It. xh).and. (xh.it. -71.0)))then write (7,130)id,nm,x,y,z,xdot,ydot,zdot,mt write (7,140)i,xh,yh,zh endif endif l endif 300 continue goto 20 1000 continue close (6) close (7) I write (*,99) stop end C-32
REN strike locations and velocity composeats es water lateke 20 INPUf"r-theta parameters";37 30 PRIN7"if rt s 1 data is r-theta format" 35 PRINf"if rts0. data is is certesian format 40 IF Bfs0 TEEN 200 50 INPUf"rPs";RP 50 INPUT *tP";TP 70 INPUf"as";I 80 INPUT *rve";RT 90 INPUf"t,==;ft 300 INPUf"sve";27 101 Ast/57.3 302 TPafPsA i 103 TystysA t 330 IsRPsC05(TP) 4 320 TsRPes!N(TP) 330 ITsRVsCOS(TV) 140 YvsByssIN(TV) 150 SOTO 300 200 INPUf"as";I 230 INPUf"ys";Y 220 INPUT *ss";2 230 INPUT *sve*;IT 240 INPUT *yv";YT 250 INPUf"sys*;2y 300 REN celeu3ating sleisua times to reach each well 330 fis(16-2)/2V 320 72=(-247-I)/IT 330 73s(-345-I)/IT 340 74s(94-7)/YV 345 75s(348-Y)/YT 350 PRINT 350 PRINf"tle";f1 370 PRINf"tts";f2 380 PRINT *t3s*;f3 388 PRINf"t4=";f4 390 PRIN7"t5s*;f5 391 PRINf"c0 telle if hit is valid" 392 PRINf"if c0 = 0 se hit Possible* 393 INPUf"e0 =";c0 394 IF CO = 0 TREN 600 400 INPUf"tas*;fM 410 IIst+IVefN 420 TEsf+YvetM 430 Zest +IVsfM 440 PRINT 465 PMINT 470 PRINf"mbs";IE 475 PRINf"yks";YE 480 PRINf"shs";25 485 PRINf"c1 tells if hit is valid" 486 PRINT *J f cls 0 go back to 400 with new ts* 487 PRINf"if c1 = 1 ell tries exhausted, se hit possible 488 PRINT *1f e1 = 2. hit valid, Print Parameters
490 INPUf"cls";C1 493 IP C1s0 TREN 400 497 IF C1st TEEN SCO 500 PRINf" valid hit" 505 80f0 $50 800 PRINT " hit set possible" S5O PRINf"esterlag data is as fellows:"
880 PRINT *ms";I S70 PRIN7"ys";Y SSO PRINT"as";I 890 PRINf"ava*;It 700 PRINf"yve";ff 710 PRINT"sys";27 720 PRINf" hit locaties is" 730 PRINf" abs";IE 740 PRINf"ybs";YB 750 PRINf"she*;25 7s0NO Figure C.2 HITWAT Code for Calculating Strike Parameters C-33
REN calculating missile / steel-wall impacts REN imput missile parameters INPUT " missile area in sq. inches"; AN INPUT " missile perimeter in inches";PM INPUT " missile weight in pounds"; WM INPUT " steel wall thickness in inches"; TW INPUT " missile normal velocity in fps";VM INPUT"beco numerical missile designation =";BN PH:2/(1-EXP(.001338*VM)) l Al=AM+1.36*TW*SQR(AM) ) REM calculate m2 60 H2=.OOO91*AM*TW ,0 EC=292*AM*TW to ES=4500*TW^2*SQR(AM) 50 M1=WM/32.2 L0 E1=.5*H1*VM*2*(1-M1/(M1+M2)) K) TE=EC+ES b5 Q1=(Mi*VM/(M1+M2))^2 LO IF El ( EM THEN 300 65 PRINT 'O PRINT" wall does not fail in phase 1" 10 COTO 4DO !O M3=8.809999E-03*AM*TW
O M4=M2-M3 iO PRINT
,0 Q3=(M1+M2)*(M1+M3) 6 RT=01-2*Q2/03 0 VE=SQR(Q1)=SQR(RT) O PRINT 2 PRINT" phase 1 penetration" 5 PRINT" phase 1 exit velocity =";VE D GOTO 600 0 E2=.5*M1*VM*2*(M1/(M1+M2)) 5 PRINT"Nagg-Sankey modified for thin metal: D ET=208*(5*PM*TW+AM*TW) D IF E2)ET THEN 500 D PRINT 5 PRINT" wall beach prevented" D COTO 532 D EV=SQR(01-ET/(M1+M2)) 1 PRINT"ql=";Q1 2 PRINT"m1=";M1 5 PRINT"m2=";M2 3 PRINT 3 PRINT" wall fails in phase 2" 3 PRINT" phase 2 exit velocity =";EV 2 PRINT" shear and compression energy capcity =";TE 5 PRINT" tensile energy capacity =";ET l PRINT" missile energy for shear and compr.=";El ~ E PRINT" missile energy avialable for overcoming tension =";E2 PRINT" energy values are in ft-lbs"
PRINT" impact area in sq inches =";AM PRINT" impact perhiphery in inches =";PM D PRINT" impact velocity in fps =";VM B PRINT"beco numerical missile designation =";BM D END Figure C-3 STEEL Code for Calculating Steel Perforation
L10 REM Penetration Probability for Concrete ) INPUT"misslie weight =";WM ) INPUT" missile minimum impact area =";AM ) INPUT" missile mean width =";TM ) INPUT" missile length =";LM ) INPUT" wall thickness in inches =";T ) INPUT" concrete compressive strength in psi =";SC i REM x velocity component is that normal to the wall struck i INPUT"x velocity =";XV 10 INPUT"y velocity =";YV .0 INPUT"z velocity =";2V 'O VT=SQR(XV^2+YV^2+2V^2) LO TP=T*VT/XV O T1=WM*2*VT'3 ,0 T2=(SC"-1.5)*(TP^-4) O AP=1.3*T1*T2 <1 PRINT O PRINT O PRINT"ap=";AP O IF AP ( AM THEN 300 5 PRINT"tm*1m=";TM*LM 6 PRINT"ap-an=";AP-AM D IF AP > 7H*LM THEN 320 0 T3=(AP-AM)/(TH*LM) D AC=ATN(T3/SQR(1-T3^2))*57.29578 D T4=SOR(1-T3^2) D T5=(AP-AM*T4)/(TM*LM) 3 AD=ATN(T5/SQR(1-T5^2))*57.29578 1 PRINT
2. PRINT"t3=";T3 3 PRINT"t5=";T5 4 PRINT"ac=";AC 5 PRINT"ad=";AD 3 PRINT 3 P=AC/90 L Pl=AD/90 5 PRINT"wa=";WM
) GOTO 340 3 P=0 P P7=VX^2-XP^2 ) GOTO 340 ) P=1 ) PRINT I PRINT" penetration probability =";P i PRINT"first iterate penetration probability =";P1 i PRINT i PRINT" angle =";AC I PRINT" maximum impact area =";AP 1 PRINT" total velocity =";VT I PRINT"x velocity =";XV i PRINT"y velocity =";YV i PRINT"z velocity =";2V END Figure C-4 COMPEN Code for Calculating Concrete Perforation and Associated Probability C-35
( Figure C-5 BASIC Program for Calculating Normal Windspeeds on any Given Wall 10 REM calculate normal velocity components on walls of aux bay and wa ter intakestructure 20 INPUT " tornado r location in feet =";TR 30 INPUT " tornado theta locat(on in degrees =";TT 40 INPUT " tornado direction da radians =" TD
3 INPUT " tornado translatida speed in sph =";ST 50 INPUT " tornado max tangential wind velocity in aph =";VM 60 INPUT " tornado width in feet =";TW 70 REM aux bay west wall r is rb 80 REM aux bay west wall theta is tb 90 REM water intake south wall r is rs 100 REM water intake south wall theta is ta 110 REM water intake east wall theta is to 120 REM water intake east wall r is re 130 REM radius of maximum wind in tornado is rm 140 RM = (TW / 2) * (75 / VM) *.625 143 REM r7 is the outer radius of 217 mph winds 145 R7 = (TW / 2) *.514785 146 REN r6 is the inner radius of 217 aph winds 147 R6 = (217 / VM)
RM 150 RB = 122 160 TB =
- 174.4 170 RS = 217.4 180 TS = 154 190 RE = 188.9 200 TE = 140 220 PRINT 223 PRINT "r6=" R6 224 PRINT "rs=";RM 225 PRINT "r7.";R7 230 M = TAN (TD) 240 IT = TR
COS (TT / 57.3) 250 YT = TR

SIN (TT / 57.3) 260 YI - YT - M

IT 270 II = IT - YT / M 280 PRINT 282 PRINT "xt=";IT 283 PRINT "yt=";YT 284 ' PRINT "m="
M 290 PRINT "xi=" II 300 PRINT "yi=";YI 301 REM if input c is O stop calc 302 INPUT "c ";C 303 IF C = 0 THEN GOTO 755 310 I(1) = RB
COS (TB / 57.3) 320 Y(1) = RB

SIN (TB / 57.3) 330 1(2) = RS

COS (TS / 57.3) 340 Y(2) = RS

SIN (TS / 57.3) 350 I(3) = RE

COS (TE / 57.3) 360 Y(3) = RE

SIN (TE / 57.3)
C-36
i Figure C-5 Continued 370 FOR I = 1 TO 3 380 A = 1 + M ' 2 390 B = - 2
I(I) - 2

Y(I)

M + 2

YI

M 400 C = (I(I))

2 + (Y(I)) ' 2 + YI

2 - 2

YI

Y(I) - RM ' 2 410 DI = B

2 - 4

A

C 420 IF (DI < 0) THEN GOTO 6d0 l
430 IC(I) = ( - B + SQR (DI)) / (2
A) 435 YC(I) = IC(I)

M + YI t
440 ID(I) = ( - B - SQR (DI)) / (2
A) 445 YD(I) = ID(I)

M + YI 450 PRINT 460 PRINT "i=";I 470 PRINT "xc(i)=";IC(I) 480 PRINT "xd(i)=";ID(I) 490 GOTO 620 600 PRINT "i=";I 610 PRINT "217 aph wind does not hit" 620 NEXT 622 INPUT "c=";C 624 IF C = 0 THEN GOTO 755 630 IB = I(1) 640 YB = Y(1) 650 IS = I(2) 660 YI - Y(2) 670 IE = I(3) 680 YE = Y(3) 690 PRINT 700 FOR I = 1 TO 3 710 PRINT "i=";I 720 PRINT "x(1)=";I(I) 725 PRINT "y(i)=";Y(I) 730 PRINT "xc(1)=";IC(I) 735 PRINT "yc(1)=";YC(I) 740 PRINT "xd(1)=";ID(I) 745 PRINT "yd(1)=";YD(I) 750 NEIT 751 INPUT "c=";C 752 IF (C = 0) THEN GOTO 755 753 GOTO 765 755 PRINT 756 PRINT " stopped calculation early" 760 GOTO 1060 765 REM Calculate Velocity on Walls 770 N = Y(1) - YC(1) 771 D = I(1) - IC(1) 772 GOSUB 2000 780 A1 =
ATN (N / D) + AZ 790 VI = VM
COS (A1) + ST

COS (TD) 800 PRINT 805 PRINT "First normal velocity printed is usually from trailing edge of tornadoand the second one is from leading edge" C-37
Figure C-5 Continued 809 PRINT 810 PRINT " normal velocity on aux bay wall =";VI 815 D = I(1) - ID(1) 820 N = Y(1) - YD(1) 821 GOSUB 2000 822 B1 = ATN (N / D) + AZ 830 IV = VM
COS (81) + ST

COS (TD) 850 PRINT "second normal vel on aux bay wall =";IV 860 N = Y(2) - YC(2) 870 D = X(2) - XC(2) 875 GOSUB 2000 880 A2 =
ATN (N / D) + AZ 890 V2 = VM
SIN (A2) + ST

SIN (TD) 900 PRINT " normal velocity on south wall of water intake =";V2 910 N = Y(2) - YD(2) 920 D = X(2) - ID(2) 925 GOSUB 2000 930 B2 =
ATN (N / D) + AZ 940 SV = VM
SIN (B2) + ST

SIN (TD) 950 PRINT "second normal velocity on south water intake =";SV 960 N = Y(3) - YC(3) 970 D = 1(3) - IC(3) 975 GOSUB 2000 980 B3 =
ATN (N / D) + AZ 990 V3 = - VM
COS (B3) - ST

COS (TD) 1000 PRINT " normal velcity on east water intake =";V3 1010 N = Y(3) - YD(3) 1020 D = X(3) - ID(3) 1025 GOSUB 2000 1030 B4 =
ATN (N / D) + AZ 1040 V4 = - VM
COS (B4) - ST

COS (TD) 1050 PRINT "second normal vel on east water intake =";V4 1060 END 2000 IF (N > 0) AND (D > 0) THEN AZ = 1.5709 2010 IF (N < 0) AND (D > 0) THEN AZ = 1.5706 2020 IF (N < 0) AND (D < 0) THEN AZ =
- 1.5708 2030 IF (N > 0) AND (D < 0) THEN AZ = - 1.5708 2040 RETURN C-38
APPENDIX D COMPARISON OF PILGRIM 1 METHODOLOGY WITH TORMIS METHODOLOGY l
1 l 1 1 l The following table was excerpted from Appendix K of Reference 4, and summarizes 1 the comparison of the EPRI developeri TORMIS methodology with the PILDRIMI methodology. t i i l i 1, e i i 4 I N 4 4 l 4 I e i i l I 4 ,t b i i D-1 i f
Compar1 Con cf EPRI cnd 8AI Studico Parameter EPRI SAI Comments i 2 2 Tbenado frequency 4.3-4 (m1 -yr)~I 4.9-4 (m1 -yr)~I SAI data are specific to plant, EPRI data are generic for tornado region 13 SAI data are more conservative. Rneuerence intervel 432 years 335 years Depende both on tornado-damage area and for tornadoes at (for plant A) ef fective plant area (Section K3.1): l plant SAI data are more conserestive. ( Spectrum of missile Many generie typee Many specific types Data very aimilar for the two studies. types Number of candidate 6000 75,000 SAI datn are more conservative. + missilee { Miselle-laydown 2000-ft radius 5290-ft radius Both studies based on elaulation trials area (geometric of missile flights to determine maximum distribution of translational distance of missiles. candidate Both studies conclude that -translation miselles) 9 beyond 2000 f t is extremely rare. SAI ( y study concluded that a 1-mile redine was required to include all poselble flights because a few 4000-ft translations were observed. SAI data are more conserva-tive. windfield model several Bechtel model RPRI model is more detailed, and EPRI did perform sensitivity studies on the wind-field. Cannot tell which model is more conservative (see. the comparison of mis-site velocity distributions below). Missile-injection Based on wind toed Based on probabillette Both methode produce essentially the same (flight initia-exceeding a spe-model proportional effect, and both allow control on tinn) mechanism cifiable factor 'to local wind speed whether or not most miselles are in-times miestle with verlable pro-jected at low or high wind speed. weight portionality constant e
CompariCon of EPRI and SAI Studies (Centinued) Parameter EPRI RAI comments Mise 11e-flight %ree drag coeffi-A single drag coefft- [ modeling ciente derived cient applicable to for each type relative wind is of minelle used Misette damage Considered only lo-Mots of Bechtel sup-SAI method much more detailed. Signifi-cat damage (per-plied detailed mod-cent contribution to the safety-foration and elling of perfora-compromise probability came from struc-spallation): used tion, spallation, tural damage. PfDRC formula and punching shear, and Rots formulatione structural daeage velocity distrihu-see comments see commente ne statistical distrihetton of miselle tion of minelles velocities impinging on the plant region impacting plant is nearly equivalent for the two studies (see Table 21. Y Frequency of mis-1.23-4 yr'I 1.61-4 yr"I hese results are similar despite the great W elles striking 5.4-2 per tornado 5.4-2 per tornado disparity in the number of candidate plant missile and their initial distance range from the plant. 8 Prohahility of 1.96-5 t 1.27-5 3.9-6 1 1-7 Difference here le attributable to the SAI danaging any study's emeller total safety-related safety-related area. area b Prohah111ty of not computed 5-7 i 3-7 For the SAI data this le an upper limit on safety the probehility of sustaining unaccept-comprosten able damage. 8%is value is from Tahle 3-15 of the EPRI (1978) report, bnis value le for the case with 12-in. target roof and 0-in. nontarget roof with 24-in. exterior walle. t ~. -- -. .Y}}

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1.0 INTRODUCTION

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1.0 INTRODUCTION

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1.0 INTRODUCTION

1.1 Background

5.0 REFERENCES

SUMMARY

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1.0 INTRODUCTION

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