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PREDICT User`s Manual

1. Header or Comment Line 1 0 1 0E 07 5 2E 06 1 8E 07 1 5E 01 8 2E 00 2 7E 01 1 5E 01 7 7E 02 2 6E 01 2 3E 01 1 2E 01 4 0E 01 7 7E 02 4 1E 02 1 4E 01 1 2E 01 6 2E 02 2 1E 01 2 6E 01 1 4E 01 4 6E 01 4 0E 01 2 1E 0 7 1E 0 2 3E 01 1 2E 01 4 0E 01 4 2E 01 2 2E 0 7 4E 01 1 2E 0 6 2E 02 2 1E 0 2 2E 0 2E 0 3 9E 01 4 0E 0 2 1E 01 7 1E 0 7 4E 01 3 9E 0 1 3E 00 2 0 1 0E 07 5 2E 06 1 8E 07 3 2E 01 1 7E 01 5 7E 01 1 8E 00 9 6E 01 3 2E 00 1 7E 00 9 1E 0 3 1E 00 9 6E 01 5 0E 01 1 7E 00 9 1E 01 4 8E 0 1 6E 00 3 2E 00 1 7E 00 5 7E 00 3 1E 00 1 6E 00 5 4E 00 1 7E 00 9 1E 01 3 1E 00 1 7E 00 8 8E 01 3 0E 00 9 1E 01 4 8E 01 1 6E 00 8 8E 01 4 6E 01 1 6E 00 3 1E 00 1 6E 00 5 4E 00 3 0E 00 1 6E 00 5 3E 00 29 7 3 5 Stops Data Block The stops data block is used to request an output file set for each of the desired impact altitudes The parameters are a list of the desired impact altitudes More than one impact altitude may be specified This feature is useful for aircraft safety studies PREDICT sorts the requested output altitude levels into decreasing order Thus there is no need for the user to worry about the order Below is an example of a request for two output file sets The first parameter specifies impacts at the ground while the second
2. wind The title begins with the first nonblank character following the title keyword and extends to the next valid data block keyword In the example above the title extends from the word This to just before the wind keyword thus a title may contain any text except for data block keywords All data block keywords begin with an asterisk so difficulties can be avoided by not putting asterisks in front of a word in the title 7 3 Propagate Data Block The propagate data block is used to define the breakup model s the off nominal covariance matrices and the file names and desired altitudes for the computed impact data The allowable data blocks following propagate are atmos montecarlo wind covariance stops breakup and intercept Resulting impact data files will be created by PREDICT with the file names automatically generated The file names for a breakup data block will be of the form BK_ breakup_model_name FT_ failure time ALT_ impact_altitude pdf The failure time will be rounded to the nearest whole second To prevent overwriting of files the pdf extension will be incremented pdf7 for a maximum of six files filename pdf filename pafl filename pdf2 filename pdf3 filename pdf4 filename pdf5 For example suppose a breakup state vector file contains state vectors for failure times of 2 seconds and 4 seconds and each of these failures uses a breakup model called stage1 In addition the user has requested i
3. 15 Table 7 1 Standard Atmosphere Models ici il a is edad 23 Table 7 2 RCC Atmosphere Py pes so cstes venus Id cis 24 3 DOF 6 DOF ARSC Ec ECFC ECI FTS TIP KTF LHS MHPCC PDF PI RCC Body 3 2 1 rotation Breakup time Failure mode Failure time Failure trajectory Fragment class Intact breakup model Local geodetic frame Nomenclature 3 Degrees Of Freedom point mass 6 Degrees Of Freedom Arctic Region Supercomputing Center Expected casualties Earth Centered and Fixed Cartesian coordinate system axis 1 through Greenwich meridian axis 3 through North Pole Earth Centered Inertial Cartesian coordinate system ECFC frame frozen at some instant in time Flight Termination System Instantaneous Impact Point Kauai Test Facility Latin Hypercube Sampling Maui High Performance Computing Center Probability Density Function Probability of Impact Range Commander s Council A rotation sequence to orient frame B with respect to frame A I align frames A and Bso axis 1 of A aligns with axis 1 of B etc II rotate B about axis 3 of B to arrive at frame B III rotate B about axis 2 of B to arrive at frame B IV rotate B about axis 1 of B to arrive at frame B Time the missile destructs Type of failure e g stuck nozzle Time a failure e g stuck nozzle occurs Trajectory flown after a failure occurs Type of fragment e g bolt Breakup model for nominal flight e
4. Jordan Culler Larry Rollstin Walter Rutledge Walter Wolfe William Millard and John Morris Naval Air Warfare Center have all helped define the information required to make PREDICT a tool that is used during missile launch operations A large thanks goes to David Salguero author of the TAOS software which was used as the basis for the propagation section of PREDICT An additional thanks goes to Terry Jordan Culler for reviewing and improving this document NH nan Rh W Contents YRC HG A ii 6 Impact Location Generation cessscsscsssccssscssscssecssecsssscnccensccsseceecssceesees 8 2 1 Breakup State V SCtors oe nck seen tian etnies eae era seeks 10 22 Breakup Models tt di tt hn dle eat de 12 Dido Wind Models ta Lerdo ll ds a dto lec 12 DA COV APACS Models e e E da Sead Noses NOPE fs 12 Probability of Impact Computati0NS c conciso 13 Risk to Aircraft Computations cecssscsscsssscssecssecssecsscessccsseesseesseess 16 Output Data Analysis isi a 17 PREDICT Execution e o 17 Gok KIDD Intercept RUNS o eee e e e el ee 17 6 2 High Performance Computing Centers ccccccccscesssscsesesesseseseeteesteneseens 18 6 3 Maui High Performance Computing Center ccccccceeseeeseseseeteseeeeeens 18 6 4 Arctic Region Supercomputing Center ceccccesesscsesseeseeseseeeesesteneseees 19 Problem Files une esessccccccecesessscsecesesesecsssssesesssssesececcessssesesesessssesesesececs 19 A eta aAa Nea Tas Me ae fe ig hoa Renee Tole at a
5. Nominal nomtraj dat Offnominal offnomtrajs dat Tmax 50 Tmin 10 Output covmat cvr End File nomtraj dat has the following form 49 project XYZ nominal trajectory file t sec x ft y ft z ft vx ft s vy ft s vz ft s 0 0 10000213 41 5240947 08 17559643 51 0 00 0 00 0 10 0 10001067 35 5241514 10 17561026 08 181 66 145 81 279 20 0 10004094 56 5244595 48 17565374 52 442 77 506 23 600 30 0 10010255 16 5252280 08 17573292 08 797 45 1054 72 983 40 0 10020169 39 5266117 44 17585017 83 1188 22 1728 03 1356 50 0 10034021 47 5287045 57 17600270 92 1589 37 2477 63 1695 60 0 10052203 17 5316228 49 17619049 18 2023 89 3328 97 2030 70 0 10073213 54 5351629 95 17639506 98 2219 43 3824 80 2097 File offnomtrajs dat has the following form project XYZ 2 off nominaltrajectories time sec x ft y ft z ft vx ft s vy ft s vz ft s 0 0 10000213 41 5240947 08 17559643 51 0 00 0 00 10 0 10001095 50 5241539 76 17561065 43 187 60 153 08 286 20 0 10004220 61 5244762 17 17565527 88 457 05 527 97 616 30 0 10010567 60 5252744 16 17573642 08 820 50 1092 56 1007 40 0 10020757 17 5267042 85 17585641 90 1219 46 1781 28 1386 50 0 10034964 83 5288584 33 17601236 58 1630 80 2549 28 1734 60 0 10053588 03 5318533 94 17620432 43 2046 46 3370 76 2050 0 0 10000213 41 5240947 08 17559643 51 0 00 0 00 10 0 10001039 11 5241488 62 17560986 72 175 70 138 58 271 20 0 10003968 89 52444
6. Sturgis 15414 MS 0825 W P Wolfe 9115 MS 0933 L W Young 10823 MS 9018 Central Technical Files 8945 1 MS 0899 Technical Library 9616 MS 0612 Review amp Approval Desk 9612 for DOE OSTI MS 0161 Patent amp Licensing Office 11500 32
7. matrix does not exist at the desired breakup time the covariance matrix corresponding to the nearest breakup time will be used The parameter following the covariance keyword is the name of the file containing the covariance matrices as a function of time This file may be created by the user or computed by PREDICT in a separate run as described in Section 7 5 7 The format of a covariance file is as follows 28 one header or comment line a line defining the time in seconds corresponding to this covariance matrix This line may also include the nominal ECFC state vector at this time but this information is not required a 6x6 matrix of numbers defining the covariance matrix in the following form PxPx PyPx PzPx VxPx VyPx VzPx where PxPy PxPz PyPy PyPz PzPy PzPz VxPy VxPz VyPy VyPz VzPy VzPz Px Vx PyVx PzVx VxVx VyVx VzVx PxVy PyVy PzVy VxVy VyVy VzVy Px Vz PyVz PzVz VxVz VyVz VzVz Px variance in ECFC x position ft Py variance in ECFC y position ft Pz variance in ECFC z position ft Vx variance in ECFC x velocity ft sec Vy variance in ECFC y velocity ft sec Vz variance in ECFC z velocity ft sec The seven lines consisting of the time and 6x6 matrix are repeated for each time desired An example of a covariance matrix containing only two time tags with the ECFC state vector included on the line containing the time is shown below
8. there will be many failure trajectories for the missile These trajectories are generated before PREDICT is executed They are typically six degree of freedom 6 DOF trajectories and are flown using software that includes representative guidance and control algorithms For each failure trajectory the missile is flown along its nominal path until the failure time for that trajectory is reached At that time the failure mode for that trajectory is activated e g a nozzle becomes stuck and the resulting trajectory is calculated Once the set of failure trajectories is obtained the set is checked for violations of the destruct criteria HP limit angle of attack limit etc If a failure trajectory violates any of the destruct criteria the FTS is activated and the missile state at breakup is recorded to the breakup state vector file If no destruct criteria 10 are violated the breakup state vector recorded to the breakup state vector file is the state vector at the end of powered flight This process is summarized in Figure 2 2 The entire process described in this section is performed before PREDICT is executed If a missile strikes a target vehicle an intercept case the breakup state vector file is not needed Instead a debris generation code KIDD or FASTT is called by PREDICT to provide initial fragment state vector information Missile flies a nominal path until failure time is reached e g nozzle sticks at failure time
9. 0 4 0 5 0 6 0 cd 1 578 1 584 2 40 2 89 3 12 3 18 3 06 2 874 2 797 2 76 dMass time age 0 047 xe OO 5507 104 05 E 207 20 04 253 0 80 20 392 0 ALO AD 2505 05 A 00 610 61 133 61 134 75 0 mass 0 0 2 2 18 0 1657 0 3339 0 5106 0 6979 0 8982 0 10995 0 12938 0 14751 0 16396 0 17939 0 19442 0 20696 0 20803 0 20814 0 0 0 0 0 7 3 6 1 1 Piece Data Block The piece data block must be used to define each fragment in the breakup model The first parameter after the piece keyword is the fragment name Delimiters are not allowed in the fragment name Additional parameters for this data block are number wet sref throw_dir ballistic ballistic_sigma cd dv dv_sigma and dmass Number This parameter defines how many of this kind of fragment are present at breakup This value is used by the impact probability computation For example if there are three identical bolts that will be present at breakup only one piece data block will be defined for the three bolts and number will be set to 3 The number parameter defaults to l Wegt This parameter defines the fragment s weight in pounds Sref This parameter defines the reference area of the fragment in ft This parameter is only required if a Cd table is defined Throw_dir This parameter defines the throw direction of the fragment in the missile s body fixed frame A value of 0 through 360 will result in the fragment being thrown in
10. parameter specifies impacts at an altitude of 30 000 feet Stops 0 30000 7 3 6 Breakup Data Block The breakup data block is used to define the breakup model for the problem It may include four additional data blocks model piece statevectors and roll 7 3 6 1 Model Data Block The model data block defines the breakup model files to use The first parameter after the model keyword is the breakup model identifier The breakup model identifiers must be identical to those used in the breakup state vector file described in Section 7 3 6 2 The second parameter is the name of the file containing the breakup model definition associated with the breakup model identifier Below is an example of a breakup model file Suppose this file is one of the breakup model files specified in the example of Section 7 3 For example it could be the file named breakup3 dat In the example of Section 7 3 the breakup model identifier associated with this file is Stg3 When a line in the breakup state vector file that contains Stg3 is read the fragments described below will be used to compute impact locations for that breakup state vector piece Fin wgt 50 ballistic 35 ballistic sigma 0 5 throw dir 90 piece Payload wgt 500 ballistic 135 ballistic sigma 2 5 throw dir 0 dv o 20 TO 25 40 50 30 dv_sigma 1 5 piece interstag wgt 24118 1 sref 15 9 throw dir 500 Cd mach 0 0 0 6 1 0 1 4 1 8 2 0 3
11. the one specified in the example in Section 7 3 so its file name is s1 sv The breakup model names used in this example Stgl Stg3 Stg2 correspond to the names provided in the first parameter of the model keyword as described in Section 7 3 6 1 This breakup state vector file lists only three failure modes fm1 fm2 and fm3 and all of the failures are initiated at 10 seconds However their breakups occur at 18 14 and 15 seconds respectively project failures name prob failt time alt latgd long vel gam psi pitch yaw roll Model fml le 6 10 0 18 0 51039 9 24 2 163 9 4902 2 86 4 239 0 78 1 121 6 0 0 Stgl fm2 le 8 10 0 14 0 31505 2 24 1 163 9 4445 2 72 8 98 7 72 7 116 0 25 0 Stg3 fm3 le 7 10 0 15 0 33943 8 24 1 163 9 4806 3 50 2 79 1 46 3 82 1 60 0 stg2 7 3 6 3 Roll Data Block Sometimes the roll orientation of the body at the time of breakup is not well known The roll data block option is used to vary the roll angle between the body fixed frame and the local geodetic frame for each Monte Carlo run The roll angle will begin at 0 for the first Monte Carlo run and will be incremented by 360 divided by the number of Monte Carlo runs For example if ten Monte Carlo runs are requested then the roll angle for the first Monte Carlo run will be 0 the second Monte Carlo run will use 36 the third Monte Carlo run will use 72 etc If this option is chosen any roll angle defined in the breakup state ve
12. time entry followed by the mass loss entry If no extrapolation outside the table is desired always define a time after the final time and repeat the previous table value Use the same approach for the earliest time with a repetition of the first table value 7 3 6 2 Statevectors Data Block The statevectors data block is used to define the state vector at breakup The first parameter is the file name of the breakup state vector file The only limit to the number of breakup state vectors that can be included in the state vector file is the memory limit on the particular computer being used The format of the state vector file is as follows e two header lines for comments and labels e data for each breakup state vector Data are assumed to be in the local geodetic coordinate frame Units are in seconds ft ft sec and degrees Euler angles are 32 for a body 3 2 1 yaw pitch roll order between the body fixed frame and the local geodetic frame The column order is Unique failure mode name 50 characters maximum Failure mode probability rate per second corresponds to a failure mode at a specific failure time Failure time State vector time breakup time Altitude Latitude Longitude Velocity Vertical flight path angle Horizontal flight path angle Pitch Yaw Roll Breakup model name A simple example of a breakup state vector file is shown below The lines have been wrapped to fit on the page Suppose this file is
13. views and opinions expressed herein do not necessarily state or reflect those of the United States Government any agency thereof or any of their contractors Printed in the United States of America This report has been reproduced directly from the best available copy Available to DOE and DOE contractors from U S Department of Energy Office of Scientific and Technical Information P O Box 62 Oak Ridge TN 37831 Telephone 865 576 8401 Facsimile 865 576 5728 E Mail reports adonis osti gov Online ordering http www doe gov bridge Available to the public from U S Department of Commerce National Technical Information Service 5285 Port Royal Rd Springfield VA 22161 Telephone 800 553 6847 Facsimile 703 605 6900 E Mail orders ntis fedworld gov Online order http www ntis gov ordering htm SAND2002 2398 Unlimited Release Printed July 2002 PREDICT User s Manual Larry W Young Mechanical and Structural Engineering Department Beverly R Sturgis Applied Engineering and Technology Development Department Sandia National Laboratories P O Box 5800 Albuquerque New Mexico 87185 0933 Abstract Sandia National Laboratories has developed a Near Real Time Range Safety Analysis Tool named PREDICT that is based upon a probabilistic range safety analysis process Probabilistic calculations of risk may be used in place of the total containment of potentially hazardous debris during a missile launch o
14. 165 164 163 162 161 160 159 158 Figure 7 2 Defining a Computational Box Path Ai Comp Box amp Plot Box For this example all points inside the Plot Box are computed and output into the plot file However if any point is outside the Comp Box its value will be set to zero The user 39 may also define the Plot Box by defining the MaxLatitude MinLatitude MaxLongitude and MinLongitude A warning is issued to inform the user if the requested Plot Box does not encompass the entire Comp Box This method is useful when values over a specific grid are required but reduced computational time is desired 7 43 Include Data Block This data block defines special input files to be included in the plot output file These files may be map files of surface features that the user wishes to display on any post processed plots to be produced Any files to be included must be in the format required by the plotting software package This keyword is followed by a list of the file names to be appended to the plot output file 7 4 4 Contours Data Block This data block defines the output file names and contour levels produced PREDICT will extract contours for each requested contour level and place the latitude and longitude coordinates in the desired output file Each file name should be followed by a value denoting the desired contour level The only other option for this keyword is the scale parameter Sc
15. 2 Union Data Block This data block defines a combination of multiple impact probability files into one file The combination may be accomplished either by adding the probability of impact values from each file at corresponding grid points using the add data block or by searching the files to find the maximum probability of impact value at each grid point using the max data block Both add and max have the same definition parameters files output minLatitude maxLatitude incLatitude minLongitude maxLongitude and incLongitude If minLatitude maxLatitude incLatitude minLongitude maxLongitude and incLongitude are not defined the output file s size will correspond to the size of the largest dimensions and smallest increment of the input files 43 Files This parameter provides the list of impact probability files to be combined Output This parameter defines the name of the combined file This file will be in Tecplot format and the size will correspond to the extremes of all the input impact probability files and the smallest increment MinLatitude This parameter defines the most southerly latitude of the output file MaxLatitude This parameter defines the most northerly latitude of the output file IncLatitude This parameter defines the latitude increment of the output file MinLongitude This parameter defines the most westerly longitude of the output file MaxLongitude This parameter defines
16. 29 21 17565222 01 428 62 484 50 584 30 0 10009943 01 5251815 30 17572943 32 774 47 1016 68 960 40 0 10019582 48 5265187 91 17584398 02 1156 93 1674 12 1326 50 0 10033079 94 5285497 55 17599315 20 1548 31 2405 81 1656 60 0 10050801 51 5313873 28 17617664 03 1991 78 3270 05 2002 7 6 End Data Block The end data block is used to define the end of a problem 50 0 00 38 48 70 48 09 85 95 00 89 24 20 85 65 24 0 86 00 78 45 34 56 60 References 1 D E Salguero Trajectory Analysis and Optimization Software TAOS SAND99 0811 Revised Sandia National Laboratories Albuquerque NM June 2001 2 KIDD Kernel Version 3 5 3 Report No N TR 99 052 Nichols Research Huntsville AL April 1999 3 McKnight D Maher R and Nagl L Fragmentation Algorithms for Strategic and Theater Targets FASTT Empirical Breakup Model Ver 3 0 DNA TR 94 104 December 1994 51 Distribution Re pid 10 10 10 Commander NAWCWD Code 521300E 575 I Ave Suite 1 Point Mugu CA 93042 5049 Attn J Morris Commander Navy Region Hawaii Care Of Pacific Missile Range Facility Attention Code N814 Box 128 Kekaha HI 96752 0128 Attn S Hudson Code 7331 William A Millard 450 Sunnyside Ridge Road Sandpoint ID 83864 MS 0825 T M Jordan Culler 15414 MS 0825 M W Kniskern 15414 MS 0825 L R Rollstin 15414 MS 1174 W H Rutledge 15414 MS 0825 B R
17. 75 North January Cold 30jan U S 30 North January 75warm U S 75 North January Warm 30july U S 30 North July 75july U S 75 North July 45jan U S 45 North January ttrwinter Sandia Tonopah Winter 45july U S 45 North July ttrspring Sandia Tonopah Spring A45springfall U S 45 North Spring Fall ttrsummer Sandia Tonopah Summer 60jan U S 60 North January ttrfall Sandia Tonopah Fall 60cold U S 60 North January Cold kwaj Sandia Kwajalein Mean Annual 60warm U S 60 North January Warm These atmosphere models extend to a geodetic altitude of 1000 km however above an altitude of 150 km all the models are the same as the 1976 U S standard atmosphere Below sea level 0 altitude temperature is extrapolated based on the temperature gradient at sea level and pressure is held constant at the sea level value Other atmospheric properties are computed from the temperature and pressure Some of the atmosphere models in Table 7 1 are defined only to an altitude of 30 km 80 km or 120 km Above 120 km they all transition to the 1976 U S standard by 150 km Above 30 km in some cases and 80 km in other cases they transition to an atmosphere at the nearest latitude Thus the 75 North atmospheres which are defined only to 30 km transition to the 60 North atmospheres above 30 km The 60 North warm and cold atmospheres are defined only to 80 km so they transition to the 60 July and January atmospher
18. Failure mode e g stuck nozzle is activated and trajectory continues along altered path no Destruct criteria violated e g IIP yes limit angle of attack limit etc No FTS action results FTS action results breakup state vector breakup state vector is state SA is state vector at time of FTS action vector at end of powered appropriate breakup model is chosen flight intact breakup model is pprop p chosen Breakup state vector info and breakup model name are written to state vector file for use in PREDICT Figure 2 2 Generation of Breakup State Vectors 11 2 2 Breakup Models The breakup model tells PREDICT which fragments are created when the missile is destroyed and gives information about each of those fragments Two cases exist that require different methods for supplying vehicle breakup information One case is an intercept scenario in which two impacting bodies break into fragments because of their collision In this case the user does not provide breakup models Instead the intercept data block is used and either the KIDD or FASTT breakup model is called from PREDICT to generate the debris from the collision The user tells PREDICT which debris generation code to call by using either the FASTT or the KIDD data block after the intercept data block The other case is a breakup scenario in which the missile is destroyed because of structural breakup or an FTS action This type of scenario is spec
19. June vafb jan Vandenburg AFB January ktf jul Kauai Test Facility July vafb jul Vandenburg AFB July ktf aug Kauai Test Facility August wallops annual NASA Wallops Annual ktf sep Kauai Test Facility wallops jan NASA Wallops January September ktf oct Kauai Test Facility October wallops jul NASA Wallops July ktf nov Kauai Test Facility November wsmr annual White Sands Annual 24 ktf dec Kauai Test Facility December wsmr jan White Sands January cape Cape Canaveral Annual wsmr jul White Sands July annual RCC atmospheres are selected with the keyword rcc following the atmos keyword The rcc keyword is followed by the RCC atmosphere type for example the data block atmos ree ktf dec selects the Kauai Test Facility KTF December atmosphere from the Barking Sands Kauai RCC 370 83 report 7 3 1 3 Sonde Measured Atmospheres This atmosphere model is useful when modeling atmospheric properties measured at a test site This type of information is often measured with a weather balloon equipped with a radio sonde Sonde measured data requires only temperature pressure and density as a function of altitude The set of tabulated data is interpolated with an exponential function which means that fewer points are required to represent a realistic atmosphere Sonde measured atmospheric data are input by the keyword sonde following the atmos keyword The sonde keyword is followed by the name of the file containing the sonde m
20. SANDIA REPORT SAND2002 2398 Unlimited Release Printed July 2002 PREDICT User s Manual Larry W Young and Beverly R Sturgis Prepared by Sandia National Laboratories Albuquerque New Mexico 87185 and Livermore California 94550 Sandia is a multiprogram laboratory operated by Sandia Corporation a Lockheed Martin Company for the United States Department of Energy under Contract DE AC04 94AL85000 Approved for public release further dissemination unlimited h Sandia National Laboratories Issued by Sandia National Laboratories operated for the United States Department of Energy by Sandia Corporation NOTICE This report was prepared as an account of work sponsored by an agency of the United States Government Neither the United States Government nor any agency thereof nor any of their employees nor any of their contractors subcontractors or their employees make any warranty express or implied or assume any legal liability or responsibility for the accuracy completeness or usefulness of any information apparatus product or process disclosed or represent that its use would not infringe privately owned rights Reference herein to any specific commercial product process or service by trade name trademark manufacturer or otherwise does not necessarily constitute or imply its endorsement recommendation or favoring by the United States Government any agency thereof or any of their contractors or subcontractors The
21. The sum of these values must equal 1 Min_beta This parameter defines the minimum ballistic coefficient kg m fragment to be included in the impact data The following defaults are used by PREDICT when it calls the KIDD program Mass conservation kinetic energy calculations mass integration for bins and explicit scaled momentum conservation are turned on There are no thermal energy calculations thermal calculations or high explosive detonations The RV is modeled as a strategic nuclear warhead with no booster attached A lethal hit with a zero miss distance is assumed An example of a propagation run using a KIDD generated debris model is shown below KIDD run title KIDD breakup propagate atmos 60warm montecarlo seed 0 trials 30 lhs covariance sl cvr intercept KIDD intercept time 100 fragchoice 1 cutoffval 0 001 yaw 10 pitch S roll 210 rv dia 1 118 rv_mass 1440 96 rv_size 9 140 rv_eci 5560823 0 2032954 0 2774827 0 1733 3 713 4 21 69 nmat_rv 3 materid rv 1 3 4 materthick_rv 0 005 0 005 0 005 materfrac rv 0 4300 0 4900 0 0800 kv _ dia 1 118 kv_mass 18 15 kv size 0 561 kv_eci 5560823 0 2032954 0 2774827 0 456 451 2733 98 1668 07 nmat_kv 3 materid kv 1 3 4 materthick kv 0 005 0 005 0 005 36 materfrac_kv 0 450 0 180 0 370 min beta 0 1 stops 0 end 7 4 PDF Data Block The pdf keyword is used to define an impact probability calculation problem This data block has several sub d
22. Uae ena ea 40 TAG Miike Data BOCK taste di aahs a ian 40 TAT Minmy Data Block ssl tdt AESKA RERE 40 148 Time Data Block richa A OS 41 7 4 9 Popcenter Data Block 2 csi ciices uvaadtten css 41 AS AAA a tans a A eile Soca ed 42 1351 Popcenter Data Block asia aaae ar R aan AEEA 42 2 Unmion Data Bl OS 43 7 5 3 Contours Data BOCK accutane Race surcearn ds icuuseh aes cuestane wcshencecstwacseusessanceumtennsanmmenss 44 104 Pati Data Block ad 45 LOD RRAT Data Bloc 47 To PTE CPO F Data BIO at NO a E A eii 48 7 5 7 Cova riance Data Blockers a side tees Nadler aia 48 7 6 End Data Bloc iia eera O O 50 Figures Figure 1 1 Generic Range Safety Analysis ra des ti 7 Figure 2 1 Internal Procedure to Initialize and Propagate Breakup Fragments 9 Figure 2 2 Generation of Breakup State Vectors ooooonooocinccnoocconncconaconnconccconocann cono ccnn conos 11 Figure 4 1 Example of Aircraft Probability of Impact vs Time ec eeeeeeseeeeeneeeeeees 16 Figure 7 1 Equal Probability Segments of Normal Distributi0N ooonoonnconcnincnnnnonancns 26 Figure 7 2 Defining a Computational BOX viii ad andas 39 Tables Table 3 1 Defining Parameters for the Impact Probability Density Functions oo o 14 Table 3 2 Bivariate Gaussian Density Function ccccsscccsscssssscssncessccsnscsseccssesseacessasenas 14 Table 3 3 Impact Density Function for an Arbitrary Longitude and Latitude 0 0
23. ale PREDICT currently outputs impact probability data in units of number of impacts per 32 ft The user may override this default value The value supplied should be in the units of impacts ft For example if a contour plot representing impacts 1000 ft were desired the entry would be Scale 1000 7 4 5 Plot Data Block This data block defines the output file names to use for the plotting software package selected Currently only the Tecplot plotting software format is supported Conversions to the format used by the RRAT program are discussed in Section 7 5 5 7 4 6 Minke Data Block The minke data block defines the minimum kinetic energy fragment to be considered in the impact probability calculations If this option is not defined no screening will be performed and all impact locations will be used 7 4 7 Minmv Data Block The minmv data block defines the minimum mass velocity fragment to be considered in the impact probability calculations If this option is not defined no screening will be performed and all impact locations will be used 40 7 4 8 Time Data Block The time data block defines the times at which to compute an impact probability grid This data block is used to produce time varying impact probability plots used in the evaluation of aircraft safety There are two input sets for this keyword the times at which to produce the plots and their corresponding time ranges These sets are defined by th
24. ata blocks files options include contours plot minmv minke time and popcenter Immediately following the pdf data block should be a value representing the altitude level at which to compute the impact probabilities If no value is provided a warning is issued and the altitude level is set to 0 feet An example of a problem file that executes a PDF run only is shown below The altitude of interest is ground level since the pdf keyword specifies an altitude of zero The six impact location files listed have been created by an earlier PREDICT run The latitude longitude grid of interest is set up and the desired output file name to be used by the Tecplot plotting program is provided problem B title range safety pdf 0 files BK_Stgl FT_2 ALT 0 pdf K_Stgl FT_4 ALT 0 pdf K Stgl FT_6 ALT 0 pdf K Stgl FT_8 ALT 0 pdf K Stgl FT_10 ALT 0 pdf K Stgl FT 12 ALT 0 pdf options pdfgrid minLatitude 18 0 maxLatitude 58 0 incLatitude 0 1 minLongitude 154 0 maxLongitude 122 0 incLongitude 0 1 plot S1 nowind 0 dat end w w w w wW 7 4 1 Files Data Block This data block defines the input files to use in impact probability calculations This keyword is followed by a list of the impact location file names to use This data block is not required if a propagate is defined in the problem prior to this pdf data block In that case the impact location data files generated during the propagation section wi
25. ctor file is ignored The roll block may be used in conjunction with the throw_dir parameter of the piece data block to allow a uniform scattering of the velocity 33 increment in the roll plane across a fragment s Monte Carlo runs See Section 7 3 6 1 1 for more information on this approach 7 3 7 Intercept Data Block The intercept data block is used to define a missile intercept case Either the KIDD or FASTT breakup models may be chosen 7 3 7 1 FASTT Data Block The data required for the FASTT option are specified with the following parameters Min_ dia This parameter defines the minimum diameter fragment to generate in units of meters Min_mass This parameter defines the minimum mass fragment to generate in units of kilograms Target Interceptor Target and Interceptor have a common set of parameters described below Wet This parameter defines the target or interceptor weight in kilograms Time This parameter defines the target or interceptor state vector time in seconds ECFC This parameter defines the target or interceptor ECFC state vector in km and km sec This parameter is followed by values defining the ECFC state vector position and velocity x y z components 7 3 7 2 KIDD Data Block The data required for the KIDD option are specified with the following parameters Intercept_time This parameter defines the time of the intercept in seconds Fragchoice This parameter define
26. e halle 19 Poles Data Blocks cscs a Ga ecb ed es hee ee eda 20 TAD Names and Values ecco e dd ear at To 20 TS COMME SA A A A ae Sa ee eee 20 72 te Data Bloc E ad Be es 20 7 3 Propagate Data Block a e did due o 21 73 1 Atmos Data Block oil ib is 22 7 3 1 1 Standard Atmospheres A udev auesunna easedstadncecsavescases 22 Td LZ2 ROC AGMOSpheres qe ito as 24 7 3 1 3 Sonde Measured Atmospheres ocooooocnoccnoncconncoonnonnnconccconocano cono cconncinns 25 7 3 2 Montecarlo Data Block oooooonnnnnnnccccncnninoncccnnnnonononnnncncnn cnn nononnnnoncnancnnnns 26 133 Wand Data Block ad a 27 7 3 3 1 Wind Table Format 0 ccccccccccccceceseecececececcacsscesesecccccccccaaeteceecececeees 27 7 3 4 Covariance Data Block o cccccececececcccccccsseseececececcccucesseescccccceceecuatesesececeeees 28 Mas Ops Data Bl il 30 1 3 0 Br akup Data Block AAA O A tena eeee 30 7 3 6 1 Model Data Block cococcncnononononononononononononononononononononononenonenoss 30 7 3 6 1 1 Piece Data Block dana 31 7 3 6 2 Statevectors Data Bla id oa 32 130 3 TROL Data Block si anan e a A E e AS 33 7 1 lnt rcept Data BlocKisispisisrs pie eia E REER Marana 34 Tool TFEASTT Data Bloc as 34 13 12 RIDD Data Bloc dia 34 TA PDE Data Blocs de ai encia do caco 37 PAA a IAN AA A A A AI 37 TAZ Options Data Block ascii 38 143 Include Data Block crias 40 TAR ACOMODO ad 40 TAS PlotData LOC ieee od Sat oo aa ari a a a
27. e parameters times and dt For example the following input would produce one impact probability plot based on all fragments that fall through 35 000 ft between 400 and 600 seconds 500 seconds 100 seconds and another impact probability plot for the fragments that fall through 35 000 ft between 700 and 1700 seconds 1200 seconds 500 seconds Pdf 35000 Time times 500 1200 dt 100 500 If this data block is not present in the problem definition then the impact probability plot produced will be time independent and will represent the impacts from all debris If this data block is defined the plot file names defined by the p ot keyword described in Section 7 4 5 will be modified by the addition of the time value 7 4 9 Popcenter Data Block This data block defines the file name of a list of population centers e g boats buildings used to compute the probability of impact and casualty expectations The first parameter is the name of the input file containing the population center information The second parameter is the desired output file name The format of the population center input file follows e two header lines for comments and labels After these two header lines any lines with a as the first character are taken as comments and copied directly into the output file e data with column order Longitude deg Latitude deg Reference Area ft Population Size Limit The format of the output file is as fo
28. e procedure to produce a range safety analysis may be divided into four parts Part 1 is the computation of the impact locations for all fragments in the breakup model For a missile destruct case the breakup is assumed to occur at many possible combinations of breakup times and failure modes For the intercept case the breakup is assumed to occur at a known location and intercept geometry Part 2 takes all of the impact location information computed during Part 1 and combines these locations with the failure probability of each failure trajectory to produce probability of impact data over a user specified latitude longitude grid Part 3 defines the aircraft safety study requirements Part 4 provides data analysis capabilities These parts are discussed in sections 2 through 5 below Figure 1 1 shows a generic range safety analysis flowchart PREDICT is a non interactive computer program All input data reside in one or more files created prior to running PREDICT As PREDICT runs it creates one or more output files These output files cannot be used until PREDICT has completed execution Each of the input and output files are text files that can be created inspected and modified with any text editor or word processor PREDICT uses a problem file to define all program input information The problem file uses a data block format as described in Section 7 The data blocks include all the instructions and file names necessary for PREDICT to execute the u
29. easured data for example the data block atmos sonde sonde dat says to retrieve sonde measured data from the file sonde dat The file sonde dat should contain tabulated data in the following format alt rho pres temp 0 FLT 665 1011 3 26 4 7500 929 22 754 54 9 8 15000 723 67 55 3423 27556 22500 55 6 57 397 60 24 2 30000 420 88 278 84 43 8 37500 306 23 190 74 D 0002 45000 212 17 127 98 63 1 52500 142 65 85 185 65 0 60000 93 686 56 807 61 8 67500 61 767 38 186 SO 75000 41 060 25 8 0 ES 82500 27 512 17 660 49 4 25 The units for a sonde measured atmosphere are a combination of English and metric units that are commonly used with radio sondes that is Variable Units alt ft rho g m pres mb temp deg C 7 3 2 Montecarlo Data Block The montecarlo data block provides information needed to initialize the random number generator set the number of runs and pick the type of random numbers used These values are set through three parameters seed trials and lhs Seed The seed parameter is used to initialize the random number generator If this parameter is not defined or is set to zero the time of day will be used for initialization Trials The trials parameter sets the number of Monte Carlo trajectory runs that will be made for each fragment This value is set to one by default LHS The LHS parameter results in the use of the Latin Hypercube Sampling method to generate rand
30. ed from the projected file inputs The Pi column is the impact probability computed at that instant in time The Ec column is the casualty expectation based on the computed Pi and the provided population The Cum Pi and Cum Ec are running totals for the previous two columns 7 5 5 RRAT Data Block This tool is used to convert a TecplotO formatted impact probability data file into a set of files in the format used by the RRAT code developed by ACTA RRAT can only accept maximum increments of 500 in either latitude or longitude Thus the incLatitude and incLongitude parameters are set internally to comply with this requirement The two output files generated have the same name as the output file with Pi grd and Ec grd added to the end of the file name If no Output block is defined the TecplotO file name is used The definition parameters are Tecplot minLatitude maxLatitude minLongitude maxLongitude Output Ec Tecplot_scale and Ec_scale Tecplot This parameter defines the input file name This file name should be the 32 ft file produced by PREDICT that is read by Tecplot to produce contour plots MinLatitude This parameter defines the most southerly latitude of the output file MaxLatitude This parameter defines the most northerly latitude of the output file MinLongitude This parameter defines the most westerly longitude of the output file MaxLongitude This parameter defines the most easterly l
31. ensity function time Using the impact probability over the latitude longitude grid of interest and the demographics for this grid the probability of impact PI for all assets and the expected casualties Ec for populated areas can be computed The expected casualty values assume that all fragments in the breakup models are hazardous and that each person occupies a distinct 32 ft area Impact within this area is assumed to result in a casualty Ship and aircraft impact probability calculations multiply the probability of impact per unit area by the craft area of interest The expected casualties associated with the craft are multiplied by the number of persons occupying the craft 15 4 Risk to Aircraft Computations Aircraft safety analysis is performed in a post processing mode The aircraft s path may be input through a file containing full information about the aircraft s position vs time or through a file containing its position heading and velocity at one instant in time In the latter case PREDICT projects the aircraft s path forward in time The output file provides instantaneous and cumulative probability of impact and expected casualties for the aircraft as a function of time If impact probability input files computed at different altitudes and or time periods are supplied the computed probability of impact will be based on interpolation between the appropriate altitude and time files If solutions are requested at times
32. es above 80 km This results in all atmospheres converging to the 1976 U S standard by an altitude of 150 km Standard atmospheres are selected by entering the appropriate atmosphere name following the atmos keyword For example the data block atmos standard 23 selects the 1976 U S standard atmosphere model while the data block atmos ttrfall selects the Tonopah Test Range TTR Fall atmosphere model The selected atmosphere model applies to all computations within a problem data block 7 3 1 2 RCC Atmospheres In addition to these standard atmosphere models PREDICT contains twenty eight Range Commander s Council RCC atmosphere models as shown in table 7 2 These models interpolate tabulated data from the RCC reports between sea level and an altitude of 70 km Between 70 km and 80 km the atmospheres transition to the 1976 U S standard atmosphere and above 80 km they are equivalent to the 1976 U S standard atmosphere These atmosphere models correspond to those available in TAOS Table 7 2 RCC Atmosphere Types ktf annual Kauai Test Facility Annual cape jan Cape Canaveral January ktf jan Kauai Test Facility January cape jul Cape Canaveral July ktf feb Kauai Test Facility February kmr annual Kwajalein Annual ktf mar Kauai Test Facility March kmr jan Kwajalein January ktf apr Kauai Test Facility April kmr jul Kwajalein July ktf may Kauai Test Facility May vafb annual Vandenburg AFB Annual ktf jun Kauai Test Facility
33. g spent 1 stage etc North east down coordinate system at current position 1 Introduction To produce a probabilistic range safety analysis for a missile launch or a missile intercept requires a vast amount of time and resources In the past several stand alone computer programs were used to perform a range safety analysis It was not uncommon to take several weeks using multiple individual central processing units to produce a set of probability impact data once all of the input data were available PREDICT was developed to reduce the time required to produce results so that day of launch decisions could be based upon the latest possible data The PREDICT computer program combines the stand alone programs used previously into a faster more user friendly program with the added capability described in this report To further enhance the computation speed it is possible to execute this program in a parallel computing environment The set of input data requirements is application dependent The user must supply some or all of the following information the missile system breakup model s the wind model the off nominal covariance matrices at various destruct times the state vectors at destruct or intercept and the probability of failure associated with each failure scenario For an intercept of two bodies colliding a fragmentation code is called by PREDICT to provide the breakup model and an initial state vector for each fragment Th
34. he IBM SP parallel computers located at the Maui High Performance Computing Center MHPCC and at the Arctic Region Supercomputing Center ARSC The breakup propagation and impact probability computations have been set up in a pseudo parallel manner such that they run on separate processors This significantly reduces run time Users of these computing centers must have an established account with adequate disk space for output files or they must operate from one of the scratch disk spaces The computing center must be contacted to establish a user account and to obtain current login procedures 6 3 Maui High Performance Computing Center At the time of this writing the IBM SP machine used at MHPCC is called tempest PREDICT is run on this machine with an interactive pre processing program named maui_all C An alias name is recommended to make the program easy to use For example if using the c shell the line alias PREDICT u brsturg maui_all exe can be added to the cshrc file in the user s home directory to define an alias called PREDICT that points to the pre processing program The pre processing program begins by displaying a main menu for example PREDICT PREDICT Version x x O Exit 1 Submit Job 2 Check Job Queue gt Option will prompt for the problem file name the status file name the number of processors needed an account number a time limit and an e mail address to use for notification A separa
35. ided in file projpath dat in the format described above test proj path tools path files nowind 30k T 325 dat nowind 30k T 555 dat nowind 30k T 785 dat nowind 30k T 1015 dat nowind 30k T 1245 dat projected projpath dat output projpath out end Points This option is used if the aircraft s path is known This parameter provides the name of the file containing the aircraft s trajectory The format for this file is as shown below e one header line e data in the following column order Time Alt Long Lat Ref Area Pop See Projected parameter above for descriptions of these entities A problem file example for this option is shown below The five files listed are impact probability files computed by PREDICT for five time baskets using the time feature described in Section 7 4 8 The aircraft s trajectory is provided in file AC _traj dat in the format described above aircraft tools path files nowind 30k T 325 dat nowind 30k T 555 dat nowind 30k T 785 dat nowind 30k T 1015 dat nowind 30k T 1245 dat points AC_traj dat output AC_ecpi out end Output This parameter defines the name of the output file The output file format will be as shown below e repeat of input file header line e column headers Time Altitude Longitude Latitude Pi Ec Cum Pi Cum Ec e output data 46 Each successive line will contain either the time altitude longitude and latitude provided in a points file or the data comput
36. ified by using the breakup data block In these situations the user must determine the fragments produced when the missile is destroyed For each fragment the weight ballistic coefficient any velocity increment and direction that may exist because of the destruct action and any change in the fragment s mass over time are defined Since many missile configurations may change during the course of flight it is likely that more than one breakup model will be defined For example the missile configuration during first stage burn differs from that during third stage burn and the fragments resulting from a breakup during these two segments of flight will differ from one other More discussion and examples of user defined breakup models are given in Section 7 3 6 Section 7 3 7 provides an example for an intercept case 2 3 Wind Models Atmospheric winds with respect to the earth s surface are defined with a wind data block Ifa wind data block is not input all wind velocities are set to zero Winds defined in a wind data block apply to the entire problem block in which the wind data block is defined By default wind components are aligned with the local geodetic coordinate system The wind is only a function of altitude and has no vertical or downward components The east wind component is positive when the wind is from the east moving from east to west and the north component is positive when the wind is from the north moving from nor
37. is the number of entries to be read for the next three parameters The maximum number of combinations is 20 Materid_rv This parameter defines the target s material ID array Aluminum 1 Uranium 2 Iron 3 Silica Phenolic 4 Materthick_rv This parameter defines the target s average material thickness m for each of the material combinations Materfrac_rv This parameter defines the fraction of the target mass for each material combination The sum of these values must equal 1 KV_ dia This parameter defines the maximum diameter of the interceptor in meters KV mass This parameter defines the mass of the interceptor in kilograms KV_ size This parameter defines the maximum dimension of the interceptor in meters KV _eci This parameter defines the interceptor ECIC position and velocity components in meters and meters second Nmat_kv This parameter defines the number of material thickness combinations for the interceptor This value is the number of entries to be read for the next three parameters The maximum number of combinations is 20 Materid_kv This parameter defines the material ID array Aluminum 1 Uranium 2 Iron 3 Silica Phenolic 4 35 Materthick_kv This parameter defines the interceptor s average material thickness m for each of the material combinations Materfrac_kv This parameter defines the fraction of the interceptor mass for each material combination
38. ll be used to supply the impact probability calculations 37 7 4 2 Options Data Block This data block defines the options to use in the definition of the computational grid for the impact probability calculations PdfGrid This parameter indicates that the user is defining the computation grid The values are in degrees The definition parameters are MinLatitude MaxLatitude IncLatitude MinLongitude MaxLongitude IncLongitude StartLatitude EndLatitude StartLongitude EndLongitude and Width MinLatitude This parameter defines the most southerly latitude of the PdfGrid region MaxLatitude This parameter defines the most northerly latitude of the PdfGrid region IncLatitude This parameter defines the latitude increment of the PdfGrid region MinLongitude This parameter defines the most westerly longitude of the PdfGrid region MaxLongitude This parameter defines the most easterly longitude of the PdfGrid region IncLongitude This parameter defines the longitude increment of the PdfGrid region StartLatitude This parameter defines the beginning latitude of a computation box EndLatitude This parameter defines the ending latitude of a computation box StartLongitude This parameter defines the beginning longitude of a computation box EndLongitude This parameter defines the ending longitude of a computation box Width This parameter defines the width of a computation bo
39. llows e acopy of the first header line from the input file e the output data with column order The first five columns are duplicates of the input file values 41 Longitude deg Latitude deg Reference area ft Population size Limit Impact probability impacts reference area Casualty expectation Maximum population that will still meet the defined limit An example of an input file is shown below The fishing boat in this example is assumed to carry 10 people and have a reference area of 1000 fi The probability of impact limit for this type of population center is 1e 6 Population Centers Longitude Latitude Ref Area Pop Size Limit Fishing Boat 159 722 22 178 1000 10 le 6 Skycreen 159 765944 22 070528 32 1 le 5 Range Assets 159 781256 22 061879 10000 1 le 3 Beach 159 761 22 088 32 20 le 6 159 754 22 094 32 10 le 6 7 5 Tools Data Block The tools data block is used to post process some of the output data The allowable data blocks following tools are popcenter union contours path rrat tecplot and covariance The tools data block has not been set up to operate in a parallel processing environment so only one processor is used for this data block 7 5 1 Popcenter Data Block This data block defines the file name of a list of population centers to compute the probability of impact and casualty expectations This data block is similar to that defined in Section 7 4 9 The definiti
40. lying covariance information to the position and velocity components of the breakup state vector In addition the user may choose to apply statistics to the fragment s ballistic coefficient velocity increment due to the destruct action and the wind profile through which the fragment will fly Once the fragment s initial conditions have been computed and any user specified statistics have been applied the three degree of freedom 3 DOF propagator in PREDICT propagates each fragment s instantaneous impact point IIP from breakup to all altitudes specified by the user The PREDICT propagator uses essentially the same methods employed by TAOS Modifications were made to the TAOS propagator to handle the multiple impact altitudes required for the aircraft safety studies The resulting ballistic trajectory has no propulsive forces and employs a user supplied drag coefficient or ballistic coefficient model for aerodynamics This initialization and propagation process is performed multiple times for each fragment to provide a Monte Carlo set of trajectories for each fragment Figure 2 1 summarizes this process for a non intercept scenario Each of the input files that the user must provide to PREDICT to compute impact locations at desired altitudes is discussed in the following sections Various altitudes are sometimes desired in order to determine risk to aircraft as well as risk to people and assets on the ground Obtain breakup state vector a
41. mpact altitudes of 0 and 10000 feet PREDICT will then create impact data files named BK_stagel FT_2 ALT_0 pdf BK_stagel FT_4 ALT_0 pdf BK_stagel FT_2 ALT_10000 pdf and BK_stagel FT_4 ALT_10000 pdf If a file called BK_stagel FT_2 ALT_0 pdf already exists then PREDICT will not overwrite that file but will create a file called BK_stagel FT_2 ALT_0 pdfl The same procedure is used for naming impact data files when either the FASTT or KIDD data blocks are used instead of a user defined breakup model The only difference is that the file name begins with FASTT or KIDD rather than BK An example of a problem file for a propagation run using a user supplied breakup model is given below This problem file chooses the 60 latitude warm season 60warm atmosphere model It specifies 30 Monte Carlo trajectories trials for each fragment of the breakup model and uses Latin Hypercube sampling LHS for the Monte Carlo process The covariance matrix as a function of time is supplied in file s1 cvr while the breakup state vectors are located in file s1 sv Four breakup models are supplied in the 21 model data block The fragments to be used for breakups during first stage flight are provided in the file breakup1 dat Breakup state vectors using this breakup model have the identifier Stg1 associated with them Similar setups exist for second and third stage breakup models For the cases where no failure occurs the only f
42. nd associated breakup model from breakup state vector file Obtain fragment information from breakup model Obtain wind profile and apply statistics if requested by user Apply covariance matrix to breakup state vector s position and velocity Adjust fragment ballistic coefficient with statistics if requested by user Adjust fragment delta velocity with statistics if requested by user Propagate fragment trajectory and store results Figure 2 1 Loop through number of Monte Carlo runs requested by user Loop through number of fragments in breakup model Internal Procedure to Initialize and Propagate Breakup Fragments 2 1 Breakup State Vectors For a missile destruct action the user must supply a breakup state vector file to PREDICT This file contains position velocity and attitude information about the missile at the time an FTS action or structural failure occurs For inclusion of the nominal trajectory without a destruct action this information reflects the missile s state vector at the end of powered flight State vector information includes the breakup time and the missile s position altitude latitude longitude velocity with respect to an earth fixed observer velocity magnitude horizontal and vertical flight path angles and attitude body 3 2 1 yaw pitch roll angles between the body fixed frame and the local geodetic frame Other information recorded in this file includes the failure mode
43. om numbers The default is random sampling Latin Hypercube Sampling breaks a normal distribution into segments of equal probability and selects one random value from each segment Figure 7 1 illustrates a normal distribution broken into six segments of equal probability The number of equal probability segments used by PREDICT for the LHS option is equal to the trials parameter above 0 4 0 35 0 3 0 25 0 2 0 15 0 1 0 05 Figure 7 1 Equal Probability Segments of Normal Distribution 26 7 3 3 Wind Data Block Atmospheric winds with respect to the earth s surface are defined with a wind data block Ifa wind data block is not input all wind velocities are set to zero By default wind components are aligned with the geodetic coordinate system The wind is only a function of altitude and has no vertical component All units are assumed to be in ft and ft sec The east wind component is positive when the wind is from the east moving from east to west The north component is positive when the wind is from the north moving from north to south The next parameter in the wind data block is the file name of the wind table Four additional parameters can be used inside a wind data block They are the standard deviation multipliers fixed_sigma sigma_north sigma_east and sigma_max These parameters should be followed by their desired value Fixed_Sigma The fixed_sigma parameter sets the east and north standard deviation m
44. on parameters are Pdf Centers and Output Pdf This parameter defines the impact probability file to be used to compute the probability of impact and expected casualties for the input population centers Centers This parameter defines the population centers input file name The format of the input file is as follows e two header lines for comments and labels After these two header lines any lines with a as the first character are taken as comments and copied directly into the output file e data with column order 42 Longitude deg Latitude deg Reference Area fi Population Size Limit Output This parameter defines the name of the output file The format of the output file is as follows e acopy of the first header line from the input file a line of column headers e the data with the following column order the first five columns are duplicates from the input file Longitude deg Latitude deg Reference area ft Population size Limit Impact probability impacts reference area Casualty expectation Maximum population that will still meet the defined limit A problem file example for this tool is given below casualties tools popcenter pdf nearlaunch dat centers pop dat output pop out end The file named nearlaunch dat is an impact probability file generated from a PREDICT odf run The population center file pop dat has the same form as the input file shown in Section 7 4 9 7 5
45. ongitude of the output file Output This parameter defines the name of the output file The Pi output file contains seven layers of data that are needed by the SIMDIS plot program developed by the Naval Research Laboratory The first and second layers correspond to 1000 ft The third through seventh layers correspond to three times the area of the previous layer For example the third layer corresponds to 3000 ft the fourth layer to 9000 ft etc The Ec output file is only one layer deep and corresponds to 1000 ft if no Tecplot_scale or Ec_scale inputs are used Ec This parameter flags the program to only generate an Ec file using the scale factors defined below Tecplot_scale This parameter defines the scale factor for the input TecplotO file The default value for this scale factor is number of impacts 32 ft This scale factor is only used if the Ec flag is set 47 Ec_scale This parameter defines the scale factor for the output Ec file This scale factor is only used if the Ec flag is set A problem file example for this tool is shown below for no Ec scaling conversion to RRAT title rrat grid tools RRAT Tecplot nowind 0 dat MinLatitude 18 0 MaxLatitude 58 0 MinLongitude 154 0 MaxLongitude 122 0 end 7 5 6 TECPLOT Data Block This tool converts an RRAT formatted impact probability data file into a TecplotO formatted data file The definition parameters are RRAT Ec Pi Al
46. ood of the failure mode occurring Table 3 3 This result provides the impact probability per unit area over the latitude longitude grid for all the fragments in a fragment class impacting within a grid node location for a single failure mode over all possible failure times Then these PDFs are summed for all fragment classes and all failure modes at each grid node location to obtain the total impact probability per unit area for all failure modes This process is repeated for every grid node location For the normal mission completion scenario no failures integration over time is not necessary Since all state vectors are associated with the end of powered flight for the normal mission completion a PDF is evaluated at the grid point and then multiplied by both the likelihood of normal mission completion and by the number of fragments The PDF for normal mission completion is summed at each grid point along with the failure PDFs although the PDF for normal completion becomes negligible as the distance from the nominal impact point increases The final result is a contour plot of impact probability per unit area with independent axes of longitude and latitude Table 3 3 Impact Density Function for an Arbitrary Longitude and Latitude id 2 98 Y NJ Y ile par 6 5 a jef ie fm i Where id impact density function longitude latitude fragment class number of fragments in the fragment class probability failure mode probability d
47. or altitudes outside of the values in the supplied input files the input files for the nearest time or altitude will be used For example if input files computed at 20 000 and 30 000 feet are supplied and the aircraft is currently at 32 000 feet the 30 000 foot input file will be used for the computation Figure 4 1 illustrates an example of a 2500 ft aircraft flying at an altitude of 25 000 feet The probabilities of impact shown were based on two time independent impact probability files computed at 20 000 and 30 000 feet 1 00E 05 TEPP Cumulative Instantaneous 1 00E 06 f 1 00E 07 i 0 20 40 60 80 100 120 140 160 Figure 4 1 Example of Aircraft Probability of Impact vs Time 16 5 Output Data Analysis The output data from PREDICT may be presented in several forms A contour plot of the impact probabilities is the most commonly used presentation form The capability exists to produce files to be used by display programs such as Tecplot Tabulation of impact probabilities for specific assets is another output format Several tools are available to assist with data analysis Each of these tools is discussed and examples are provided in Section 7 5 6 PREDICT Execution In general the PREDICT computer program is executed by entering a command that consists of the PREDICT executable file name followed by command line options The p option defines the input problem file name and the s option defines the output sta
48. path at one instant in time The definition parameters are Files Projected Points and Output Files This parameter defines the list of impact probability files to be used These files must have been previously computed for the altitudes and the latitude longitude grids the aircraft will be traversing Projected This option is used if only minimal information is known about the aircraft s trajectory PREDICT computes the aircraft s path and uses that information to get probability of impact and casualty expectations for the aircraft This parameter provides the name of the file containing the starting point information The format of this file is as shown below e one header line e data in the following column order Time Alt Long Lat Vel Heading VFPA dT maxT Ref Area Pop where Time current time sec Alt current altitude ft Long current longitude deg Lat current latitude deg Vel current velocity knots Heading current heading angle deg VFPA current vertical flight path angle deg dT desired delta time for path computation maxT maximum time to compute path over Ref Area reference area of this object ft Pop population of this object A problem file example for this option is shown below The five files listed are impact probability files computed by PREDICT for five time baskets using the time 45 feature described in section 7 4 8 One point of the aircraft s trajectory is prov
49. peration Impact probabilities are computed based upon probabilistic density functions Monte Carlo trajectories of dispersion events and missile failure scenarios Impact probabilities are then coupled with current demographics land populations commercial and military ship traffic and aircraft traffic to produce expected casualty predictions for a particular launch window Historically these calculations required days of computer time to finalize Sandia has developed a process that utilizes the IBM SP machines at the Maui High Performance Computing Center and at the Arctic Region Supercomputing Center to reduce the computation time from days to as little as an hour or two This analysis tool then allows the Missile Flight Safety Officer to make launch decisions based on the latest information winds ship and aircraft movements utilizing an intelligent risk management approach This report provides a user s manual for PREDICT version 3 3 The work described in this report was performed for the Pacific Missile Range Facility under project number 1539 tasks 1 2 3 and 4 Acknowledgments The process to produce probabilistic range safety analysis has been developed over a number of years with the contributions of several people Robert LaFarge Kenneth Cole David Outka William Millard and Floyd Spencer all developed early programs used to produce breakup fragment definitions impact propagations and impact probability calculations Terry
50. probability of impact files or it may be run with two or more sequential problem files where impact locations are computed in the first run and stored as output files These files become inputs for subsequent problem files to compute impact probabilities The impact data generated from Monte Carlo techniques can be used to develop a statistical model of the impact likelihood for an area on the earth s surface The statistical model is constructed from subsets of the impact data where each subset consists of all the impacts resulting from a given combination of the systematically varied impact mode parameters For impacts resulting from failures non intercept cases the systematically varied impact mode parameters are the failure time the fragment class and the failure mode The impact points vary because of the random variations in some flight parameters e g breakup time state vectors imparted fragment velocities and directions and the wind profile Since two or more of these variations are Gaussian in nature it can be expected that for each such subset the impact point variations will also approximate a Gaussian distribution Hence for each such subset five parameters describing the corresponding Gaussian impact point distribution function are computed mean longitude and latitude standard deviations in longitude and latitude and the correlation coefficient relating deviations from the mean in longitude with those in latitude The eq
51. ragments are those associated with normal completion of the mission such as the spent first stage etc These types of fragments are contained in the file named intact dat and the identifier Ipc is found in the breakup state vector file for these state vectors Impact locations stops on the ground 0 feet and at 30 000 feet are requested problem A title range safety propagate atmos 60warm montecarlo seed 0 trials 30 lhs covariance sl cvr breakup statevectors sl sv model tgl breakupl dat tg2 breakup2 dat del Stg3 breakup3 dat model lpc intact dat stops 30000 0 S O S O end 7 3 1 Atmos Data Block An atmosphere model defining temperature pressure density speed of sound and viscosity as a function of altitude is required to simulate flight through the atmosphere Atmospheric properties affect the aerodynamic forces and moments acting on a vehicle 7 3 1 1 Standard Atmospheres PREDICT contains the 1976 U S standard atmosphere model fourteen 1966 U S standard supplemental atmosphere models and five Sandia atmosphere models derived by Acurex Corporation as shown in Table 7 1 These atmosphere models correspond to those available in TAOS The default is the 1976 U S standard atmosphere 22 Table 7 1 Standard Atmosphere Models None No atmosphere 60july U S 60 North July Standard 1976 U S Standard 75jan U S 75 North January 15annual U S 15 North Annual 75cold U S
52. s that are lowercase Names and keywords entered in uppercase are automatically converted to lowercase so case is not important from a user s standpoint 7 1 2 Names and Values Names and values can be placed anywhere on a line They do not have to be in certain columns This free field style of input allows indentation to make it easier to visualize the problem file structure and to avoid input errors Numerical values can be input as integers without a decimal point as real numbers with a decimal point or as real numbers in scientific notation e format Note that delimiters cannot be embedded within a value so the value wet 10 000 Incorrect value is incorrect The comma is interpreted as a delimiter so PREDICT thinks there are two values instead of one In this case it reads 10 and 0 instead of 10000 7 1 3 Comments Comments starting with the special character can be placed anywhere in a problem file Comments extend from the character to the end of the line Blank lines are ignored so they can be used to put space between sections of information for easier reading 7 2 Title Data Block A problem title consisting of one or more lines of text is optional 20 A title can be used to help identify or document a problem There is no limit on the number of lines in a title title This is the first line of the title and this is the second line of the title and so on until the next data block name occurs
53. s the minimum fragment type to be defined by the parameter Cutoffval 1 minimum fragment mass 2 minimum fragment size Cutoffval This parameter defines the minimum size of fragment produced The units are defined by the Fragchoice parameter If Fragchoice 1 the value is the minimum mass in kilograms If Fragchoice 2 the value is the minimum fragment size in meters Yaw This parameter is the first angle in degrees of a body 3 2 1 Euler rotation set between the target s body fixed frame and the ECIC frame The ECIC frame is the same frame used in the RV_eci and KV_eci parameters below 34 Pitch This parameter is the second angle in degrees of a body 3 2 1 Euler rotation set between the ECIC frame and the target s body fixed frame Roll This parameter is the third angle in degrees of a body 3 2 1 Euler rotation set between the ECIC frame and the target s body fixed frame RV_dia This parameter defines the maximum diameter of the target in meters RV_mass This parameter defines the mass of the target in kilograms RV_ size This parameter defines the maximum dimension of the target in meters RV _eci This parameter defines the target ECIC position and velocity components in meters and meters second The order is x position y position z position x velocity y velocity z velocity Nmat_rv This parameter defines the number of material thickness combinations for the target This value
54. ser defined problem PREDICT is not an acronym rather it was chosen to describe how the flight safety analysis predicts the probable risk to people and assets Determine State Vectors at Destruct Action for Possible Failure Modes at Several Failure Times Apply Breakup Model Covariance Matrix Debris Wind Trajectory Model Simulations Failure Mode Probabilities Impact Probability Calculations Demographics Asset Locations Results Impact Probabilities Contour Plots Casualty Expectations User Inputs to PREDICT PREDICT Computations Figure 1 1 Generic Range Safety Analysis 2 Impact Location Generation A flying missile may be destroyed because of the following causes 1 an inadvertent flight termination system FTS action is taken while the missile is flying a near nominal trajectory 2 a failure causes the missile to fly off course and an FTS signal is sent to destroy it 3 the missile self destructs because of structural breakup or 4 the missile impacts a target vehicle In each of these cases fragments are created at the breakup location Information about each of the fragments is generated from the missile s state vector at the time of breakup and from the breakup model for the missile configuration at the time of breakup These data provide initial conditions for each fragment e g position velocity ballistic coefficient PREDICT alters the initial conditions by app
55. t Time and Tecplot RRAT This parameter defines the input RRAT formatted file name Ec This parameter defines the RRAT formatted file as an Ec file type Pi This parameter defines the RRAT formatted file as a Pi file type Alt This parameter defines the altitude of the RRAT formatted file Time This parameter defines the time of the RRAT formatted file The value supplied may be the time of the RRAT file or the value UNDEF for a time independent file Tecplot This parameter defines the output TecplotO formatted file name 7 5 7 Covariance Data Block This data block defines a tool to compute a covariance matrix based on a set of off nominal trajectories See Section 7 3 4 for more information on the covariance input file The definition parameters are Nominal Offnominal Tmin Tmax and Output Nominal This parameter defines the name of the nominal trajectory input file If this file is not defined a nominal trajectory will be based on the average of the off nominal trajectories Ifa nominal trajectory is supplied the format is the same as the off nominal trajectory format in the Offnominal parameter section 48 Offnominal This parameter defines the name of the file containing all the off nominal trajectories The format for this file is shown below Each Monte Carlo off nominal trajectory is placed immediately after the previous trajectory with no spaces in between e three header lines at top of file onl
56. te job must be submitted for each problem file The pre processing program then automatically submits the job to the IBM SP computer 18 Option 2 displays the status of the jobs that have been submitted After submitting a job it generally takes about a minute before it shows up in the queue When the job disappears from the queue it has finished An e mail message will be sent as a notification that the job has finished PREDICT creates output files on the root processor that are automatically copied to the user s directory A status file is created on each processor Each status file has a number attached to it corresponding to the processor that created it The pre processing program automatically deletes the files on each processor once these files have been copied back to the user s directory 6 4 Arctic Region Supercomputing Center At the time of publication the IBM SP machine used at ARSC is called icehawk The job submission procedure at ARSC is identical to that at MHPCC except that the interactive pre processing program is named arsc_all C 7 Problem Files 7 1 File Format Problem files contain the information required to compute a set of impact locations and or the impact probability data resulting from those impact locations A problem file may contain one or more problems Problem files are text files so they can be created with any standard text editor such as UNIX s vi or Windows Wordpad They may also be crea
57. ted with other software such as an interactive design code Each problem defines a propagation run a PDF run or a combination of the two A propagation run is used to define a breakup and compute the impact locations while a PDF run is used to compute the impact probabilities Each problem begins with the problem name contained in symbols and ends with a end statement A sample problem file for a propagation run is shown below This problem file contains a single propagation problem beginning with problem1 and ending with end probleml tdt le Example FTS breakup propagate montecarlo trials 60 stops 0 breakup statevectors f10 sv model chunks bkmodell dat end 19 7 1 1 Data Blocks Each set of information or data block in the problem file begins with an asterisk and a name for example title montecarlo model These are special PREDICT keywords that identify the type of information that follows Information from problem files is read into PREDICT one line at a time Each line of text contains some names and values separated by special characters such as spaces or commas These special characters are called delimiters Valid delimiters are white space characters space tab etc commas equal signs parentheses colons greater than signs and less than signs Because delimiters are used to separate names and values they cannot be embedded within a name or value Internally PREDICT requires name
58. ter is used to define the drag force coefficient table to be applied to the fragment as a function of Mach number If this parameter is used the Sref parameter must be defined The table format is a Mach number entry followed by the Cd entry Ifa Cd table is defined it will override any entries made through the ballistic and ballistic_sigma parameters If no extrapolation outside the table is desired always define a Mach number level above the highest level and repeat the previous table value Use the same approach for the lowest Mach number level with a repetition of the first table value Dv This parameter is used to define a table containing the incremental velocity applied to the fragment in ft sec as a function of time The table is linearly interpolated for a velocity increment at the current state vector time If no extrapolation outside the table is desired always define a time after the final time and repeat the previous table value Use the same approach for the earliest time with a repetition of the first table value Dv_sigma This parameter defines the variability to be applied to the delta velocity table Dv parameter Dmass This parameter is used to define the mass loss table to be applied to the fragment in pounds vs time The table is linearly interpolated for a delta mass for the current state vector time The fragment s weight is then reduced by the value determined from the table interpolation The table format is a
59. th to south If statistics are to be applied to the wind the user sets parameters in the wind data block to accomplish this action Section 7 3 3 provides examples and further discussion 2 4 Covariance Models PREDICT alters a fragment s initial conditions by applying a covariance matrix to the state vector obtained from the breakup state vector file The covariance matrix is a 6x6 matrix containing the covariance values in position and velocity The user must supply this covariance matrix as a function of time PREDICT is able to generate the covariance 12 matrix for the user in a separate run if so desired In this case the user supplies nominal and off nominal trajectories to PREDICT If a nominal trajectory is not provided PREDICT computes an average trajectory from the off nominal trajectories and uses it in place of a nominal trajectory in the formation of the covariance values An example of a covariance file is provided in Section 7 3 4 Section 7 5 7 describes the process that PREDICT uses to compute the covariance matrix in a separate run 3 Probability of Impact Computations Computation of the probability of impact contour plots requires the impact locations generated previously and the probability of failure associated with each failure trajectory The impact probability data are computed over a user specified latitude longitude grid PREDICT may be run with one single problem file that generates the impact locations and the
60. that direction in a plane perpendicular to the roll axis 0 y axis pitch axis 90 z axis yaw axis Values greater than 360 will be thrown forward along the positive roll axis x Values less than 360 will be thrown backward along the negative roll axis x If it is desired to scatter a fragment in a uniform fashion in the roll plane the plane perpendicular to the body roll axis use a throw_dir value between 0 and 360 and use the roll data block described in Section 7 3 6 3 The throw direction remains constant in the missile s body fixed frame but the use of rol causes the body fixed frame to be oriented in the local geodetic frame across the roll range of 0 through 360 If roll is used this scattering effect will be applied to all fragments in the breakup models that have throw_dir values of 0 through 360 31 Ballistic The ballistic parameter defines the ballistic coefficient for the fragment in Ib ft As an alternative to defining a ballistic coefficient a drag coefficient table versus Mach number may be defined see Cd parameter below Ballistic_sigma This parameter defines the variability in the ballistic coefficient The ballistic coefficient is determined by adding the input ballistic coefficient ballistic parameter above to the input variation multiplied by a uniform random number If this parameter does not appear the ballistic coefficient is held constant Cd This parame
61. the probability of the failure mode occurring the failure time the breakup time and the breakup model to be used for the breakup state vector An example of a breakup state vector file is given in Section 7 3 6 2 Failure modes are either destruct actions along the nominal flight path inadvertent FTS actions or system failures that cause the missile to fly off course Examples of system failures are stuck nozzles a computer failure or a guidance system failure Since impacts from a nominal trajectory e g impact of a spent first stage motor are also important nominal events may also be included in a breakup state vector file even though they are not really failures The failure time is the time a failure occurs For an inadvertent FTS action the failure time is the time the FTS action occurs For a stuck nozzle the failure time is the time the nozzle initially becomes stuck in place The breakup time is the time when the missile breaks into fragments This time is greater than or equal to the failure time since the missile may fly for some time after a failure occurs but before it is destroyed For example a nozzle might become stuck in place several seconds into a motor burn but other nozzles attempt to correct the error and a destruct action may not result until later in the trajectory A failure trajectory is the trajectory the missile flies after a failure occurs Since there are many possible failure modes and failure times
62. the most easterly longitude of the output file IncLongitude This parameter defines the longitude increment of the output file An example of a problem file using the add data block is shown below union example title PROJECT A tools union add files s1 _nowind 0 datla s1_nowind 0 datlb s1 nowind 0 datlc s1_nowind 0 datld output nowind 0 dat end 7 5 3 Contours Data Block This data block defines a tool to compute the probability of impact and casualty expectations for either a specific trajectory or an estimated simple trajectory based on a set of input parameters The definition parameters are Pdf Scale and Output Pdf This parameter defines the impact probability file to be used to compute the data for the input population centers 44 Scale This parameter defines the area used for the contour computations For example if a contour plot representing the number of impacts 1000 ft were desired the entry would be Scale 1000 Output This parameter defines the name of the output file followed by the contour level value The output file consists of a set of longitude and latitude points defining the contour If more than one contour at this level is present the individual fragments will be separated by a blank line 7 5 4 Path Data Block This tool is used in risk to aircraft studies by inputting either the aircraft s known trajectory or its projected trajectory based on knowledge of its
63. tus file name The status file is essentially a log of PREDICT s actions If no command line options are provided PREDICT uses the default file names of PROBLEM for the problem file name and PRINT for the status file name On many computers an alias link or path may be set up so that the command PREDICT runs the appropriate file PREDICT p file prb s file status If an alias is not used the full path and PREDICT executable name must be provided fullpath predict exe p file prb s file status 6 1 KIDD intercept Runs For operation on a UNIX or DOS operating system an environment variable must be set to locate the KIDD program executable For a UNIX operating system the following command must be added to the user s cshre file setenv KIDDEXE full path to the KIDD executable The single quotes around the path executable name must be included For a Windows environment the following steps are required Windows98 Start gt Settings gt Control Panel Double click on System icon Select the Environment tab 17 Create a new variable named KIDDEXE with a value that is the path to the KIDD executable Windows2000 Start gt Settings gt Control Panel Double click on System icon Select Advanced Select the Environment Variables option Create a new user variable named KIDDEXE with a value that is the path to the KIDD executable 6 2 High Performance Computing Centers PREDICT is available for execution on t
64. uations for defining parameters for the impact probability density functions PDFs are given in Table 3 1 Here A is the i impact longitude of the subset 3 is the i impact latitude of the subset and n is the number of impact points in the subset 13 Table 3 1 Defining Parameters for the Impact Probability Density Functions Mean longitude Mean latitude Standard deviation of longitude Correlation coefficient The value of the PDF function at an arbitrary longitude A and latitude 5 is given by the bivariate Gaussian density function as shown in Table 3 2 This function is an exponential function of the five defining parameters given in Table 3 1 Table 3 2 Bivariate Gaussian Density Function To obtain the impact probability density functions for all combinations of the time of failure fragment class and type of failure the subset of PDFs is combined numerically in the following manner First a grid of latitude longitude points in the area of interest is defined The number of impacts per unit area is computed at each of the grid points For each grid point and 14 combination of failure mode and fragment class the density of impacts expected for all times is obtained At each grid point the PDFs for a specific failure mode and fragment class are numerically integrated over the range of failure times and then multiplied by both the number of the fragments in each fragment class and the likelih
65. ultipliers to a fixed value e g three sigma for all Monte Carlo runs No random numbers are selected If this parameter is chosen the sigma_north sigma_east and sigma_max parameters should not be used Sigma_north The sigma_north parameter sets the north standard deviation multiplier to a fixed value for all Monte Carlo runs Random numbers are not selected If sigma_north is set to zero mean north winds are used This parameter may be used with the sigma_east parameter but the fixed_sigma and sigma_max parameters should not be used If the sigma_east parameter is specified but the sigma_north parameter is not then sigma_north is set to zero and mean north winds are used Sigma east The sigma east parameter sets the east standard deviation multiplier to a fixed value for all Monte Carlo runs Random numbers are not selected If sigma_east is set to zero mean east winds are used This parameter may be used with the sigma_north parameter but the fixed_sigma and sigma_max parameters should not be used If the sigma_north parameter is specified but the sigma_east parameter is not then sigma_east is set to zero and mean east winds are used Sigma_max The sigma_max option allows random sampling for the east and north standard deviation multiplier but limits the random number to the maximum value entered This option is useful when the user wants to limit the winds to 30 If this parameter is chosen the sigma_north sigma_east and fi
66. x There are two methods for defining the computation grid Either the lower left and upper right corners are defined or starting and stopping points with a width are defined In either case the step size or increment must be defined Most contour plotting packages require a grid of data over the entire region of interest The simplest method for defining the computational grid is to define the box that will be 38 plotted later For this method only the MinLatitude MaxLatitude IncLatitude MinLongitude MaxLongitude and IncLongitude parameters are required If the region of interest does not lie directly on a line along a north south or east west orientation it is potentially possible to reduce the computation time by using the second method By defining starting and stopping points along with a width a plot file will be produced that encompasses this box but does not compute the impact probabilities outside the defined computation box Figure 7 2 illustrates a plot of the region that would have computed values the area labeled Comp Box in comparison with the region that would be included in the plot file the area labeled Plot Box The following parameters were used to produce this example 28 27 4 26 y 25 4 24 23 y 22 21 PdfGrid StartLatitude 22 0 EndLatitude 27 0 IncLatitude 0 05 StartLongitude 159 0 EndLongitude 163 0 IncLongitude 0 05 Width 2 0 167 166
67. xed_sigma parameters should not be used 7 3 3 1 Wind Table Format The format of a wind table is as follows 21 e one header line for comments e asecond line providing the column labels Either North East velocities or total velocity and heading angle may be defined The column labels shown in parentheses below must be as shown and are case sensitive The data must be in order of increasing altitude The units must be in ft ft sec and degrees The column order and required labels shown in parentheses for North East velocities are Altitude Alt Mean East Velocity Emean East Velocity Standard Deviation stdE Mean North Velocity Nmean North Velocity Standard Deviation stdN The column order and required labels shown in parentheses for total velocity and heading are Altitude Alt Total Velocity Vel Total Velocity Standard Deviation stdV Heading Heading Heading Standard Deviation stdH An example of a wind table file using the North East form is shown below Barking Sands Annual Winds Alt Emean stdE Nmean stdN 16 1 48 4 53 0 72 6 40 16405 5 08 25 56 2 59 17 23 98430 23416 52 96 1 48 10 20 7 3 4 Covariance Data Block The covariance data block is used to supply the off nominal state vector covariance matrices as a function of time The covariance matrix is used to add position and velocity uncertainty into the fragment s initial state vector at the breakup time If a covariance
68. y e data with the following column order Time ECFCx ECFCy ECFCz ECFC Vx ECFC Vy ECFC Vz where Time current time sec ECFC x current ECFC x position ft ECFC y current ECFC y position ft ECFC z current ECFC z position ft ECFC Vx current ECFC velocity ft sec ECFC Vy current ECFC velocity ft sec ECFC Vz current ECFC velocity ft sec Tmin This parameter defines the desired starting time in the computed covariance matrix file Tmax This parameter defines the desired ending time in the computed covariance matrix file Output This parameter defines the name of the output file A brief example of a problem file used to create a covariance matrix file from a nominal trajectory and two off nominal trajectories is shown below The off nominal trajectories are contained in a file named offnomtrajs dat while the nominal trajectory is in file nomtraj dat PREDICT finds matching time values between the nominal and off nominal trajectories so it is important to provide files with times that match up in the time range of interest File covmat cvr is created by PREDICT and contains the output covariance matrix information The first covariance matrix in this file corresponds to a time of 10 seconds and the last covariance matrix to a time of 50 seconds Therefore only the information between 10 seconds and 50 seconds in the nominal and off nominal trajectories is used in this example COVAR Tools Covariance

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