Source Code

027016,000002: ## Copyright: Public domain. 027017,000003: ## Filename: TIME_OF_FREE-FALL_CALCULATIONS.agc 027018,000004: ## Purpose: Part of the source code for Solarium build 55. This 027019,000005: ## is for the Command Module's (CM) Apollo Guidance 027020,000006: ## Computer (AGC), for Apollo 6. 027021,000007: ## Assembler: yaYUL --block1 027022,000008: ## Contact: Jim Lawton <jim DOT lawton AT gmail DOT com> 027023,000009: ## Website: www.ibiblio.org/apollo/index.html 027024,000010: ## Page Scans: www.ibiblio.org/apollo/ScansForConversion/Solarium055/ 027025,000011: ## Mod history: 2009-10-04 JL Created. 027026,000012: ## 2016-08-20 RSB Typos. 027027,000013: ## 2016-12-28 RSB Proofed comment text using octopus/ProoferComments, 027028,000014: ## and fixed errors found. 027029,000015:

Page 682 (empty page)

027032,000018: 

Page 683

027034,000020: 
027035,000021:                                                                                                  #  CONIC TIME OF FLIGHT CALCULATION.   PROGRAM CALCULATES THE FREE-FALL TIME OF FLIGHT FROM PRESENT POSITION RN
027036,000022:                                                                                                  #  AND VELOCITY VN TO A RADIUS SPECIFIED BY RTERM, CORRESPONDING TO 280K OR400K FEET ALTITUDE.
027037,000023:                                                                                                  #  THE POSITION  RN MAY BE ON EITHER SIDE OF THE ELLIPSE, BUT  RTERM  IS   CONSIDERED ON THE INBOUND SIDE.
027038,000024: 
027039,000025:                                                                                                  #  THE EQUATION IS       TFF = ( DEL E - (Q2-Q1) ) / (ALFA SQRT( ALFA MUE) )
027040,000026: 
027041,000027:                                                                                                  #  AND                   Q2 = -SQRT( RTERM ALFA (2-RTERM ALFA) -LCP ALFA )       (INBOUND SIDE)          LEQ +/-  LCE
027042,000028:                                                                                                  #                             -  -
027043,000029:                                                                                                  #                        Q1 = RN.VN  SQRT(ALFA/MUE)                                                      LEQ +/-  LCE
027044,000030: 
027045,000031:                                                                                                  #  PROGRAM REQUIREMENTS ON ENTERING.
027046,000032:                                                                                                  #        1.  PUSHDOWN LIST IS ZEROED
027047,000033:                                                                                                  #        2.  INPUTS: POSITION  RN 2(-24) M,  VELOCITY  VN  2(-7)  M/CS
027048,000034: 
027049,000035:                                                                                                  #  THE PROGRAM EXITS WITH ONE OF THE FOLLOWING IN TFF.
027050,000036:                                                                                                  #                        A. TFF = FLIGHT TIME.  NORMAL CASE FOR POSITIVE FLIGHT  TIME LESS THAN ONE ORBITAL PERIOD.
027051,000037:                                                                                                  #                        B. TFF=+0.  THIS INDICATES THAT THE TRAJECTORY HAS GONE PAST RTERM AND THE PRESENT ALTITUDE IS
027052,000038:                                                                                                  #                           LESS THAN THE SPECIFIED TERMINAL ALTITUDE.
027053,000039:                                                                                                  #                        C. TFF = POSMAX.  THIS INDICATES THAT THE ELLIPTICAL CONIC FROM THE PRESENT POSITION WILL NOT
027054,000040:                                                                                                  #                           RETURN TO THE SPECIFIED ALTITUDE.
027055,000041:                                                                                                  #  THE FOLLOWING QUANTITIES REMAIN IN THE PUSHLIST
027056,000042:                                                                                                  #        ALFA                    2(+21) IN PDL 10D
027057,000043:                                                                                                  #        (2-RTERM ALFA)          2(-3)  IN PDL 6
027058,000044:                                                                                                  #        RTERM ALFA              2(-3)  IN PDL 4
027059,000045:                                                                                                  #        LCP ALFA                2(-6)  IN PDL 2
027060,000046: 
027061,000047:                                                                                                  #  THUS THE CALLING PROGRAM CAN CALCULATE TERMINAL VELOCITY, VTERM, AND COS GAMMA OR SIN GAMMA USING RESIDUE FROM
027062,000048:                                                                                                  #  CALCTFF.
027063,000049: 
027064,000050:                                                                                                  #             2
027065,000051:                                                                                                  #        VTERM  (RTERM/MUE) = (2-RTERM ALFA)
027066,000052: 
027067,000053:                                                                                                  #           2
027068,000054:                                                                                                  #        SIN GAMMA = 1 - (LCP ALFA / RTERM ALFA(2-RTERM ALFA)  )
027069,000055: 
027070,000056:                                                                                                  #           2
027071,000057:                                                                                                  #        COS GAMMA = LCP ALFA /(RTERM ALFA (2-RTERM ALFA)  )
027072,000058: 
027073,000059:                                                                                                  #  QUANTITIES ARE NORMALIZED BY LCE TO OBTAIN BEST ACCURACY IN COMPUTING, ESPACIALLY FOR SPARCTAN.  PROGRAM
027074,000060:                                                                                                  #  ACCEPTS LCE  LEQ 1.0.  THE SMALLEST LCE WHICH IS  NORMALIZED IS 2(-4),  ALTHOUGH THIS MAY BE EXTENDED IF
027075,000061:                                                                                                  #  DESIRED.  (LCE  L  2(-3) ALL HAVE SAME SCALING)
027076,000062: 

Page 684

027078,000064: 
027079,000065:                                                                                                  #  TEMPORARY ERASABLE ASSIGNMENTS FOR TFF COMPUTATIONS                   PUSHLIST 00 - 19D, X1
027080,000066: 
027081,000067: 26,7711                        RTERM              =        14D                                   
027082,000068: 
027083,000069: 31,6000                                           BANK     31                                    
027084,000070: 31,6000           77576        CALCTFF            EXIT     0                                     
027085,000071: 
027086,000072: 31,6001           11723                           CCS      REFSWTCH                              #  SEE IF GROUND DESIRES 280K FF REFERENCE
027087,000073: 31,6002           06006                           TC       +4                                    #  NO
027088,000074: 31,6003           06006                           TC       +3                                    
027089,000075: 31,6004           35501                           CAF      ZERO                                  
027090,000076: 31,6005           06012                           TC       +5                                    
027091,000077: 
027092,000078: 31,6006           36320                           CAF      NOMBURN                               #  TEST IF ANY NOMINAL BURN (SPS1,SPS2,
027093,000079: 31,6007           70647                           MASK     FLAGWRD2                              #  SPS3, SPS4, ARRST) FLAG SET
027094,000080: 31,6010           10000                           CCS      A                                     
027095,000081: 31,6011           45503                           CS       TWO                                   
027096,000082: 31,6012           20067                           INDEX    FIXLOC                                #  X1=-2 FOR 400K FT. AND 0 FOR 280K FT.
027097,000083: 31,6013           50046                           TS       X1                                    
027098,000084: 31,6014           04000                           TC       INTPRET                               
027099,000085: 31,6015           44175                           DMOVE*   1                                     
027100,000086: 31,6016           76576                           RTB                                            
027101,000087: 31,6017           33607                                    R280K,1                               
027102,000088: 31,6020           20265                                    FRESHPD                               
027103,000089: 31,6021           32017                           STORE    RTERM                                 #   2(-24)
027104,000090: 
027105,000091: 31,6022           67174                           VSQ      2                                     
027106,000092: 31,6023           64722                           DMP      DMP                                   
027107,000093: 31,6024           63726                           TSLT     BDSU                                  
027108,000094: 31,6025           00774                                    VN                                    #  VEL  2 (-7)
027109,000095: 31,6026           22307                                    1/MUE                                 #  2 (+35)
027110,000096: 31,6027           01024                                    RMAG                                  #  2(-25)
027111,000097: 31,6030           00002                                    1                                     
027112,000098: 31,6031           06304                                    DP1/4                                 #  RMAG ALFA   2 (-3)            TO PDL 0,1
027113,000099: 
027114,000100: 31,6032           47575                           NOLOD    1                                     
027115,000101: 31,6033           56712                           TSRT     DDV                                   
027116,000102: 31,6034           00002                                    1                                     
027117,000103: 31,6035           01024                                    RMAG                                  
027118,000104: 31,6036           32013                           STORE    10D                                   
027119,000105: 
027120,000106: 31,6037           47575                           NOLOD    1                                     
027121,000107: 31,6040           73776                           BMN                                            
027122,000108: 31,6041           22465                                    HIECC                                 
027123,000109: 
027124,000110: 31,6042           64774                           DMP      2                                     
027125,000111: 31,6043           53122                           SQRT     DMP                                   
027126,000112: 31,6044           57706                           TSLC     BDDV                                  
027127,000113: 31,6045           00013                                    10D                                   #  ALFA  2(+21)
027128,000114: 31,6046           22311                                    MUE(37)                               

Page 685

027130,000116: 31,6047           00013                                    10D                                   #  ALFA
027131,000117: 31,6050           00024                                    19D                                   #  -N. SAVE FOR GETTFF1
027132,000118: 31,6051           22313                                    DP2PI/16                              
027133,000119: 31,6052           32015                           STORE    12D                                   #  ORB PERIOD  2PI/ALFA SQRT(ALFA MUE)
027134,000120:                                                                                                  #  2(-17-N)
027135,000121: 31,6053           41773                           VXV      3                                     
027136,000122: 31,6054           44733                           VSLT     VSQ                                   
027137,000123: 31,6055           64722                           DMP      DMP                                   
027138,000124: 31,6056           76576                           RTB                                            
027139,000125: 31,6057           00766                                    RN                                    
027140,000126: 31,6060           00774                                    VN                                    #  MTRS/CS   2(-7)
027141,000127: 31,6061           00002                                    1                                     
027142,000128: 31,6062           22307                                    1/MUE                                 #  2(+35)
027143,000129: 31,6063           00013                                    10D                                   #  ALFA  2(+21)
027144,000130: 31,6064           22255                                    NORMBYE                               #  GET NORM COUNT BASED ON LCE SQ.
027145,000131:                                                                                                  #  LCP ALFA  2(-6)               TO PDL 2,3
027146,000132: 
027147,000133: 31,6065           47575                           NOLOD    1                                     
027148,000134: 31,6066           66616                           DSU      BPL                                   
027149,000135: 31,6067           15710                                    DP.36                                 
027150,000136: 31,6070           22077                                    LOECC                                 
027151,000137: 
027152,000138: 31,6071           66775                           DSU      1                                     
027153,000139: 31,6072           73776                           BMN                                            
027154,000140: 31,6073           00013                                    10D                                   
027155,000141: 31,6074           22322                                    ALFALIM                               
027156,000142: 31,6075           22465                                    HIECC                                 
027157,000143: 
027158,000144: 31,6076           64776        LOECC              DMP      0                                     
027159,000145: 31,6077           00017                                    RTERM                                 #  2(-24)
027160,000146: 31,6100           00013                                    10D                                   #  ALFA  2(+21)
027161,000147:                                                                                                  #  RTERM ALFA  2(-3)             TO PDL 4,5
027162,000148: 
027163,000149: 31,6101           66776                           DSU      0                                     
027164,000150: 31,6102           06304                                    DP1/4                                 
027165,000151: 31,6103           00005                                    4                                     #  RTERM ALFA  2(-3)
027166,000152:                                                                                                  #  (2-RTERM ALFA)  2(-3)         TO PDL 6,7
027167,000153: 
027168,000154: 31,6104           64775                           DMP      1                                     
027169,000155: 31,6105           53176                           SQRT                                           
027170,000156: 31,6106           00013                                    10D                                   #  ALFA  2(+21)
027171,000157: 31,6107           22307                                    1/MUE                                 #  2(+35)                        TO PDL 8,9
027172,000158: 
027173,000159: 31,6110           42774                           DOT      2                                     
027174,000160: 31,6111           63722                           TSLT     DMP                                   
027175,000161: 31,6112           76576                           RTB                                            
027176,000162: 31,6113           00766                                    RN                                    
027177,000163: 31,6114           00774                                    VN                                    #  2(-7)
027178,000164: 31,6115           00002                                    1                                     
027179,000165: 31,6116           77777                                    -                                     #  LEAVE Q1  2(-3) IN MPAC

Page 686

027181,000167: 31,6117           22143                                    ARGQ1                                 #  SAVE  MPAC FOR GONE PAST TEST. , NORMLZE
027182,000168: 31,6120           32011                           STORE    8D                                    #  Q1  (OR Q1/2 OR 2Q1 OR 4Q1)
027183,000169: 
027184,000170: 31,6121           64774                           DMP      2                                     #   CALCULATE Q2
027185,000171: 31,6122           66771                           DSU      RTB                                   
027186,000172: 31,6123           70776                           DAD                                            
027187,000173: 31,6124           77777                                    -                                     #  (2-RTERM ALFA) 2(-3) FROM PDL 6,7
027188,000174: 31,6125           77777                                    -                                     #  RTERM ALFA 2(-3) FROM PDL 4,5
027189,000175: 31,6126           77777                                    -                                     #  LCP ALFA 2(-6) FROM PDL 2,3
027190,000176: 31,6127           22155                                    ARGQ2                                 #  TEST SGN, TAKE ROOT  (RT DOT NEG)
027191,000177:                                                                                                  #  RETURN -Q2 (OR -Q2/2 OR -2Q2 OR -4Q2)
027192,000178: 31,6130           00011                                    8D                                    #  Q1  (AT SIMILAR SCALE)
027193,000179: 31,6131           32011                           STORE    8D                                    #  Q1-Q2  ( OR /2 OR2 OR4)
027194,000180:                                                                                                  #  LEQ +/- 2LCE  (OR 1 OR 4 OR 8)
027195,000181: 
027196,000182: 31,6132           66775                           DSU      1                                     
027197,000183: 31,6133           76522                           RTB      DMP                                   
027198,000184: 31,6134           00007                                    6                                     #  2-RTERM ALFA 2(-3)
027199,000185: 31,6135           77777                                    -                                     #  2-RTERM ALFA-RMAG ALFA  2(-3) IN MPAC
027200,000186: 31,6136           22213                                    GETTFF                                #  C(MPAC) = DEN  2(-3)
027201,000187: 31,6137           00015                                    12D                                   #  ORB PERIOD    2(-17-N)
027202,000188: 31,6140           33457                           STORE    TFF                                   
027203,000189: 31,6141           40576                           ITCQ     0                                     
027204,000190: 31,6142           20067        ARGQ1              INDEX    FIXLOC                                
027205,000191: 31,6143           20020                           INDEX    16D                                   #  COUNT BY ONES
027206,000192: 31,6144           34513                           CAF      BIT4                                  #  EFFECTIVE SH L 3  ( 2 OR 4 OR 5)
027207,000193: 31,6145           05416                           TC       SHORTMP                               
027208,000194: 31,6146           30117                           XCH      MPAC       +2                         #  MOVE UP
027209,000195: 31,6147           30116                           XCH      MPAC       +1                         
027210,000196: 31,6150           50115                           TS       MPAC                                  #  MPAC IS L .5 AS REQD BY TEST LATER.
027211,000197: 31,6151           20067                           INDEX    FIXLOC                                
027212,000198: 31,6152           50022                           TS       18D                                   #  SAVE FOR GONE PAST TEST.
027213,000199: 31,6153           04024                           TC       DANZIG                                
027214,000200: 
027215,000201: 31,6154           20067        ARGQ2              INDEX    FIXLOC                                
027216,000202: 31,6155           20021                           INDEX    17D                                   #  SH L BY 2,S
027217,000203: 31,6156           34510                           CAF      BIT7                                  #  DO EFFECTIVE SHL 6    (4 OR 8 OR 10)
027218,000204: 31,6157           05416                           TC       SHORTMP                               #  TP ENTRY , C(MPAC+2) VALID.
027219,000205: 31,6160           35501                           CAF      ZERO                                  
027220,000206: 31,6161           30117                           XCH      MPAC       +2                         
027221,000207: 31,6162           30116                           XCH      MPAC       +1                         
027222,000208: 31,6163           50115                           TS       MPAC                                  
027223,000209: 
027224,000210: 31,6164           10115                           CCS      MPAC                                  
027225,000211: 31,6165           06177                           TC       Q2ROOT                                
027226,000212: 31,6166           06170                           TC       +2                                    
027227,000213: 31,6167           06202                           TC       NEGQ2                                 #  NO FREEFALL CONIC TO RTERM FROM HERE.
027228,000214: 
027229,000215: 31,6170           10116                           CCS      MPAC       +1                         #  CK LO WORD. IF NEG, ASSUME ROUNDOFF.
027230,000216: 31,6171           06177                           TC       Q2ROOT                                

Page 687

027232,000218: 31,6172           04024                           TC       DANZIG                                
027233,000219: 31,6173           35501        NOROOT             CAF      ZERO                                  #  NEG ARG FROM ROUNDOFF. SET =0.
027234,000220: 31,6174           50115                           TS       MPAC                                  
027235,000221: 31,6175           50116                           TS       MPAC       +1                         
027236,000222: 31,6176           04024                           TC       DANZIG                                
027237,000223: 
027238,000224: 31,6177           05654        Q2ROOT             TC       BANKCALL                              #  GO TAKE DP SQRT
027239,000225: 31,6200           07322                           CADR     SQRT3                                 #  C(MPAC +2) =0
027240,000226: 31,6201           04024                           TC       DANZIG                                
027241,000227: 
027242,000228: 31,6202           34476        NEGQ2              CAF      POSMAX                                #  THIS WILL LEAVE PUSHLOC AT PDL2
027243,000229: 31,6203           51456                           TS       TFF                                   
027244,000230: 31,6204           51457                           TS       TFF        +1                         
027245,000231: 31,6205           40067                           CS       FIXLOC                                #  BUT RESET IT.
027246,000232: 31,6206           40000                           COM                                            
027247,000233: 31,6207           50123                           TS       PUSHLOC                               
027248,000234: 
027249,000235: 31,6210           04000                           TC       INTPRET                               
027250,000236: 
027251,000237: 31,6211           40576                           ITCQ     0                                     #  AND RETURN TO CALLING PROGRAM.
027252,000238: 
027253,000239:                                                                                                  #  ENTER WITH (2-RTERM ALFA-RMAG ALFA) 2(-3) IN MPAC,+1. Q1-Q2 IN PDL 8,9
027254,000240: 
027255,000241: 31,6212           20067        GETTFF             INDEX    FIXLOC                                
027256,000242: 31,6213           20020                           INDEX    16D                                   #  COUNT BY 1,5
027257,000243: 31,6214           34513                           CAF      BIT4                                  #  EFFECTIVE SL 3  (2 OR 4 OR 5 )
027258,000244: 31,6215           05416                           TC       SHORTMP                               #  C(MPAC +1,+2) = DEN    ON RETURN.
027259,000245: 31,6216           20067                           INDEX    FIXLOC                                #  (UNSCALD NUM AND DEN LEQ +/- 2 LCE)
027260,000246: 31,6217           40010                           CS       8D                                    
027261,000247: 31,6220           30116                           XCH      MPAC       +1                         #  SAVE Q2-Q1,  GET DEN
027262,000248: 31,6221           50115                           TS       MPAC                                  #  AND SAVE.
027263,000249: 31,6222           20067                           INDEX    FIXLOC                                
027264,000250: 31,6223           20020                           INDEX    16D                                   #  COUNT BY 1,5
027265,000251: 31,6224           36316                           CAF      -1/2PI                                
027266,000252: 31,6225           25777                           EXTEND                                         
027267,000253: 31,6226           40116                           MP       MPAC       +1                         
027268,000254: 31,6227           50117                           TS       MPAC       +2                         #  -(Q2-Q1) /2PI    SAVED
027269,000255: 
027270,000256: 31,6230           06323                           TC       SPARCTAN                              #  NUM=C(MPAC+1),DEN=C(MPAC)
027271,000257:                                                                                                  #  RETURN WITH DEL ECC. ANOM/2PI IN A
027272,000258:                                                                                                  #  RANGE (0,1)
027273,000259: 31,6231           60117                           AD       MPAC       +2                         
027274,000260: 31,6232           30115                           XCH      MPAC                                  #  TFF NORM=(DEL E:(Q2:Q1))/2PI
027275,000261:                                                                                                  #  FOLLOWING TEST VALID WHEN SPTEM3 L .5
027276,000262: 31,6233           20067                           INDEX    FIXLOC                                
027277,000263: 31,6234           30022                           XCH      18D                                   #  IF BOTH SGN Q1 AND SGN ATAN ARE
027278,000264: 31,6235           66237                           AD       +2                                    #  NEG, THEN SET TFF, +1  =+0.  (-3/4+1 )
027279,000265: 31,6236           60072                           AD       SGNATAN                               #  LEFT BY SPARCTAN
027280,000266: 31,6237           50000                           TS       A                                     #  (=50K =-3/4 +1 FOR OVFL TEST) 
027281,000267: 31,6240           06243                           TC       GETTFF3                               #  OK, GO ON

Page 688

027283,000269: 31,6241           35501                           CAF      ZERO                                  
027284,000270: 31,6242           06203                           TC       NEGQ2      +1                         #  GONE PAST. SET TFF=0.
027285,000271: 
027286,000272: 31,6243           20067        GETTFF3            INDEX    FIXLOC                                
027287,000273: 31,6244           20023                           INDEX    19D                                   #  -N.  BIT4 BELOW VALID FOR N LEQ 10D.
027288,000274: 31,6245           34513                           CAF      BIT4                                  #  SCALE FACTOR,  2(-11+N)
027289,000275: 31,6246           25777                           EXTEND                                         
027290,000276: 31,6247           40115                           MP       MPAC                                  
027291,000277: 31,6250           50115                           TS       MPAC                                  
027292,000278: 31,6251           30003                           XCH      LP                                    
027293,000279: 31,6252           50116                           TS       MPAC       +1                         #  NOW READY TO MULT BY ORB PERIOD
027294,000280: 31,6253           04024                           TC       DANZIG                                
027295,000281: 
027296,000282:                                                                                                  #  TO IMPROVE PRECISION OF SPARCTAN AT SMALLER LCE, COME HERE TO GET NORMALIZATION FACTOR
027297,000283:                                                                                                  #  BASED ON SIZE OF LCE SQ.  SHIFT BY 2,S. SCALING RESULTING FROM BELOW YIELDS AT LEAST ONE LEAD ZERO IN
027298,000284:                                                                                                  #  NUM AND DEN USED IN SPARCTAN.
027299,000285: 
027300,000286: 31,6254           36303        NORMBYE            CAF      OCT37440                              #  BRACKET SIZE BY OVFL TESTS
027301,000287: 31,6255           60115                           AD       MPAC                                  #  C(MPAC) = (1-LCE SQ)  2(-6)
027302,000288: 31,6256           50000                           TS       A                                     
027303,000289: 31,6257           06275                           TC       ENORM0                                #  HERE IF LCE GEQ 2(-1)
027304,000290: 31,6260           66304                           AD       OCTNEG30                              #  (EFFECTIVE CONST  37410)
027305,000291: 31,6261           50000                           TS       A                                     
027306,000292: 31,6262           06277                           TC       ENORM1                                #  HERE IF LCE GEQ 2(-2)
027307,000293: 31,6263           66305                           AD       OCTNEG6                               #  (EFFECTIVE CONST  37402)
027308,000294: 31,6264           50000                           TS       A                                     
027309,000295: 31,6265           06301                           TC       ENORM2                                #  HERE IF LCE GEQ 2(-3)
027310,000296: 31,6266           44515                           CS       BIT2                                  #  HERE IF LCE  L  2(-3)
027311,000297: 31,6267           20067        ENORM3             INDEX    FIXLOC                                
027312,000298: 31,6270           50020                           TS       16D                                   #  COUNT FOR SL BY 1,S ALSO NEEDED
027313,000299: 31,6271           60000                           AD       A                                     
027314,000300: 31,6272           20067                           INDEX    FIXLOC                                
027315,000301: 31,6273           50021                           TS       17D                                   #  COUNT FOR SL BY 2,S.
027316,000302: 31,6274           04024                           TC       DANZIG                                
027317,000303: 
027318,000304: 31,6275           34516        ENORM0             CAF      BIT1                                  
027319,000305: 31,6276           06267                           TC       ENORM3                                
027320,000306: 31,6277           35501        ENORM1             CAF      ZERO                                  
027321,000307: 31,6300           06267                           TC       ENORM3                                
027322,000308: 31,6301           44516        ENORM2             CS       BIT1                                  
027323,000309: 31,6302           06267                           TC       ENORM3                                
027324,000310: 
027325,000311: 31,6303           37440        OCT37440           OCT      37440                                 
027326,000312: 31,6304           77747        OCTNEG30           OCT      -00030                                
027327,000313: 31,6305           77771        OCTNEG6            OCT      -00006                                
027328,000314: 
027329,000315: 31,6306           33453 02065  1/MUE              2DEC*    .250876044 E-10       B35*            #  CS SQ/M CUBE
027330,000316: 31,6310           11217 27040  MUE(37)            2DEC*    3.986032233 E10        B-37*           #  CS SQ/M CUBE

Page 689

027332,000318: 31,6312           14441 37327  DP2PI/16           2DEC     .39269909                             
027333,000319: 31,6314           76563                           DEC      -.15915494 B-2                        
027334,000320: 31,6315           75347                           DEC      -.15915494 B-1                        
027335,000321: 31,6316           72717        -1/2PI             DEC      -.15915494                            
027336,000322: 31,6317           65640                           DEC      -.15915494 B1                         
027337,000323: 31,6320           00171        NOMBURN            OCT      00171                                 
027338,000324: 31,6321           04316 25750  ALFALIM            2DEC     6.562      E-8        B21             
027339,000325: 

Page 690

027341,000327: 
027342,000328:                                                                                                  #  INVERSE TANGENT.     THE SINGLE PRECISION ARCTAN IS BASED ON A HASTINGS  3 TERM POLYNOMIAL.  THE PROGRAM
027343,000329:                                                                                                  #  ACCEPTS  NUM  AND  DEN  , WHERE  TAN(THETA) = NUM/DEN, AND GIVES  THETA/PI  IN THE RANGE (0,1)
027344,000330:                                                                                                  #  ENTER WITH C(MPAC +1) = NUM, AND C(MPAC) = DEN.   NOTE THAT FOR CALCTFF, THETA = DEL E/2.
027345,000331:                                                                                                  #  SPARCTAN USES 3 SP TEMPORARIES:  SPTEMQ, SPTEM1, SPTEM2
027346,000332: 
027347,000333:                                                                                                  #  TEMPORARY ERASABLE ASSIGNMENTS FOR SPARCTAN ROUTINE
027348,000334: 
027349,000335: 31,6323     0071               SPTEMQ             =        VBUF                                  
027350,000336: 31,6323     0072               SPTEM1             =        VBUF       +1                         
027351,000337: 31,6323     0073               SPTEM2             =        VBUF       +2                         
027352,000338: 31,6323     0071               SPATANQ            EQUALS   SPTEMQ                                
027353,000339: 31,6323     0072               SGNATAN            EQUALS   SPTEM1                                
027354,000340: 
027355,000341: 31,6323           30001        SPARCTAN           XCH      Q                                     
027356,000342: 31,6324           50071                           TS       SPATANQ                               
027357,000343: 
027358,000344: 31,6325           34502                           CAF      BIT13                                 #  1/4 = PI/4
027359,000345: 31,6326           50073                           TS       SPTEM2                                
027360,000346: 31,6327           50072                           TS       SGNATAN                               #  IF NUM=0, THETA=0
027361,000347: 31,6330           10116                           CCS      MPAC       +1                         #  NUM
027362,000348: 31,6331           06341                           TC       TESTDEN                               #  IF DEN =0, THETA=90 DEG SGN(NUM)
027363,000349: 31,6332           06341                           TC       TESTDEN                               #  MUST STILL TEST DEN.
027364,000350: 31,6333           06335                           TC       +2                                    #  INDETERMINATE CASE 0/0 CONSIDERED AS 90D
027365,000351: 31,6334           06340                           TC       TESTDEN    -1                         
027366,000352: 31,6335           40072                           CS       SGNATAN                               
027367,000353: 31,6336           50072                           TS       SGNATAN                               
027368,000354: 31,6337           40116                           CS       MPAC       +1                         
027369,000355: 31,6340           50116                           TS       MPAC       +1                         #  ABVAL OF NUM.
027370,000356: 
027371,000357: 31,6341           10115        TESTDEN            CCS      MPAC                                  #  DEN
027372,000358: 31,6342           06355                           TC       SPATAN1                               
027373,000359: 31,6343           06434                           TC       SPATAN4                               #  90 DEG CASE
027374,000360: 31,6344           06346                           TC       +2                                    
027375,000361: 31,6345           06434                           TC       SPATAN4                               #  90 DEG CASE
027376,000362: 31,6346           40072                           CS       SGNATAN                               
027377,000363: 31,6347           50072                           TS       SGNATAN                               
027378,000364: 31,6350           40115                           CS       MPAC                                  
027379,000365: 31,6351           50115                           TS       MPAC                                  #  ABVAL OF DEN.
027380,000366: 
027381,000367: 31,6352           10116                           CCS      MPAC       +1                         #  EITHER POS OR +0. WAS NUM ZERO
027382,000368: 31,6353           06341                           TC       TESTDEN                               #  NO, GO ON
027383,000369: 31,6354           00071                           TC       SPATANQ                               #  YES, THETA =0      RETURN
027384,000370: 
027385,000371: 31,6355           25777        SPATAN1            EXTEND                                         #  HERE NEGLECT 1 BIT OF CCS. LOST IN MP.
027386,000372: 31,6356           46362                           MP       ITANC0                                #  POLY TRANSITION TEST.
027387,000373: 31,6357           60116                           AD       MPAC       +1                         #  NUM  (PNZ, SO +0 IN CCS IMPOSS)
027388,000374: 31,6360           10000                           CCS      A                                     #  IF NEG, USE Z=N/D FOR POLY.
027389,000375: 31,6361           06367                           TC       SPATAN2                               #  IF POS, USE Z=(N-D)/(N+D) FOR POLY.
027390,000376: 31,6362           67237        ITANC0             DEC      -.2714558                             #  =-(1-K)/(1+K), AND K=.573
027391,000377: 31,6363           35501                           CAF      ZERO                                  #  THIS FORM OF POLY HAS BETTER BEHAVIOR

Page 691

027393,000379: 31,6364           50073                           TS       SPTEM2                                #  NEAR ORIGIN. REPLACE PI/4 BY ZERO.
027394,000380: 31,6365           30116                           XCH      MPAC       +1                         #  SET +0 TO FIT IN WITH CALC BELOW.
027395,000381: 31,6366           06371                           TC       SPATAN3                               
027396,000382: 
027397,000383: 31,6367           40115        SPATAN2            CS       MPAC                                  #  N-D AND N+D WILL NOT OVFL IN AD IF LCE
027398,000384:                                                                                                  #  L 1.0 DUE TO NORMALIZATION BY LCE.
027399,000385: 31,6370           60116                           AD       MPAC       +1                         #  NUM
027400,000386: 31,6371           50021        SPATAN3            TS       SR                                    
027401,000387: 31,6372           30115                           XCH      MPAC                                  
027402,000388: 31,6373           60116                           AD       MPAC       +1                         
027403,000389: 31,6374           50000                           TS       A                                     #  DID IT OVFL..
027404,000390: 31,6375           06401                           TC       SPATAN5                               #  NO, GO DO DV.
027405,000391: 31,6376           30021                           XCH      SR                                    #  YES, SHIFT BOTH NUM AND DEN R1.
027406,000392: 31,6377           30021                           XCH      SR                                    #  (NUM-DEN)/4 IN SR
027407,000393: 31,6400           64522                           AD       HALF                                  #  (NUM+DEN)/2 IN A.
027408,000394: 
027409,000395: 31,6401           50115        SPATAN5            TS       MPAC                                  #  NORMALLY, (NUM+DEN)
027410,000396: 31,6402           30021                           XCH      SR                                    #  NORMALLY, (NUM-DEN) /2
027411,000397: 31,6403           25777                           EXTEND                                         
027412,000398: 31,6404           50115                           DV       MPAC                                  #  NO OVFL PROB.
027413,000399: 31,6405           50115                           TS       MPAC                                  #  Z/2= (NUM-DEN)/2(NUM+DEN)
027414,000400:                                                                                                  #  Z/2 = NUM/2DEN       NEAR ORIGIN
027415,000401: 
027416,000402: 31,6406           25777                           EXTEND                                         
027417,000403: 31,6407           40000                           SQUARE                                         
027418,000404: 31,6410           50116                           TS       MPAC       +1                         #  Z Z/4
027419,000405: 31,6411           25777                           EXTEND                                         
027420,000406: 31,6412           46441                           MP       ITANC7                                
027421,000407: 31,6413           66440                           AD       ITANC5                                
027422,000408: 31,6414           25777                           EXTEND                                         
027423,000409: 31,6415           40116                           MP       MPAC       +1                         
027424,000410: 31,6416           66437                           AD       ITANC3                                
027425,000411: 31,6417           25777                           EXTEND                                         
027426,000412: 31,6420           40116                           MP       MPAC       +1                         
027427,000413: 31,6421           66436                           AD       ITANC1                                
027428,000414: 31,6422           60000                           DOUBLE                                         
027429,000415: 31,6423           25777                           EXTEND                                         
027430,000416: 31,6424           40115                           MP       MPAC                                  
027431,000417: 31,6425           60073                           AD       SPTEM2                                #  EITHER 1/4=PI/4 OR 0
027432,000418: 31,6426           50001                           TS       Q                                     #  C(A)=THETA/PI ,RANGE( 0 ,.5) SEE NOTE
027433,000419: 31,6427           10072                           CCS      SGNATAN                               
027434,000420: 31,6430           30001                           XCH      Q                                     #  AFFIX SGN FOR POLY TO HAVE RANGE (-.5,.5
027435,000421: 31,6431           00071                           TC       SPATANQ                               
027436,000422: 31,6432           40001                           CS       Q                                     
027437,000423: 31,6433           64522                           AD       HALF                                  
027438,000424: 31,6434           64522        SPATAN4            AD       HALF                                  #  90 DEG CASE COME HERE
027439,000425: 31,6435           00071                           TC       SPATANQ                               #  RETURN WITH THETA/  PI IN A. RANGE(0,1)
027440,000426:                                                                                                  #  POLY GIVES THETA/ PI RANGE(-.5,+.5)
027441,000427: 
027442,000428:                                                                                                  #  NOTE *** RETURN TO CALCTFF  WITH  DEL E/2 PI IN A, RANGE (0,1).       SINCE THE OUTPUT OF  SPARCTAN ,

Page 692

027444,000430:                                                                                                  #  IS IN THE RANGE (0,1), THE +/- 90 DEG CASES ARE IDENTICAL.  FURTHER SINCE  FOR  CALCTFF, THE ANGLE THETA/PI
027445,000431:                                                                                                  #  EQUALS DEL E/2 PI,  SPARCTAN  CONSIDERS BOTH 0 DEG AND 180 DEG AS 0 DEG.  SHOULD PROGRAMS OTHER THAN  CALCTFF
027446,000432:                                                                                                  #  DESIRE ARC TANGENTS, THEN  SPARCTAN  CAN BE MADE GENERAL.
027447,000433: 
027448,000434: 31,6436           12133        ITANC1             DEC      .318060008                            #  =C1 /PI
027449,000435: 31,6437           62723        ITANC3             DEC      -.40894149                            #  = 4 C3/PI
027450,000436: 31,6440           27656        ITANC5             DEC      .7449806                              #  = 16 C5/PI
027451,000437: 31,6441           46450        ITANC7             DEC      -.79435682                            #  = 64 C5 /PI                                   74W
027452,000438: 

Page 693

027454,000440: 
027455,000441: 31,6442           73773        HIECC1             BMN      3                                     
027456,000442: 31,6443           71405                           LXC,1    LODON                                 
027457,000443: 31,6444           45070                           DMOVE    TSRT*                                 
027458,000444: 31,6445           76576                           RTB                                            
027459,000445: 31,6446           00017                                    14D                                   
027460,000446: 31,6447           22457                                    TFFMAX                                
027461,000447: 31,6450           00024                                    19D                                   
027462,000448: 31,6451           00015                                    12D                                   
027463,000449: 31,6452           00027                                    11D,1                                 
027464,000450: 31,6453           20265                                    FRESHPD                               
027465,000451: 31,6454           33457                           STORE    TFF                                   
027466,000452: 
027467,000453: 31,6455           40576                           ITCQ     0                                     
027468,000454: 
027469,000455: 31,6456           45175        TFFMAX             DMOVE    1                                     
027470,000456: 31,6457           76576                           RTB                                            
027471,000457: 31,6460           21043                                    NEARONE                               
027472,000458: 31,6461           20265                                    FRESHPD                               
027473,000459: 31,6462           33457                           STORE    TFF                                   
027474,000460: 
027475,000461: 31,6463           40576                           ITCQ     0                                     
027476,000462: 
027477,000463: 31,6464           45175        HIECC              DMOVE    1                                     
027478,000464: 31,6465           76576                           RTB                                            
027479,000465: 31,6466           00013                                    10D                                   
027480,000466: 31,6467           20265                                    FRESHPD                               
027481,000467: 31,6470           32017                           STORE    14D                                   
027482,000468: 
027483,000469: 31,6471           41775                           VXV      1                                     
027484,000470: 31,6472           71116                           ABVAL    TSLT                                  
027485,000471: 31,6473           00766                                    RN                                    
027486,000472: 31,6474           00774                                    VN                                    
027487,000473: 31,6475           00003                                    2                                     
027488,000474: 
027489,000475: 31,6476           47575                           NOLOD    1                                     
027490,000476: 31,6477           64716                           DMP      TSLT                                  
027491,000477: 31,6500           22307                                    1/MUE                                 
027492,000478: 31,6501           00002                                    1                                     #  H/MUE  B5  PD2,3
027493,000479: 
027494,000480: 31,6502           47575                           NOLOD    1                                     
027495,000481: 31,6503           64776                           DMP                                            
027496,000482: 31,6504           00001                                    0                                     #   H H/MUE  B-26  PD4,5
027497,000483: 31,6505           73174                           UNIT     2                                     
027498,000484: 31,6506           42722                           DOT      DMP                                   
027499,000485: 31,6507           63643                           TSLT     DSQ                                   
027500,000486: 31,6510           00766                                    RN                                    
027501,000487: 31,6511           00774                                    VN                                    
027502,000488: 31,6512           00003                                    2                                     
027503,000489: 31,6513           00003                                    2                                     
027504,000490: 31,6514           62774                           DDV      2                                     

Page 694

027506,000492: 31,6515           66643                           DSU      DSQ                                   
027507,000493: 31,6516           70653                           DAD      SQRT                                  
027508,000494: 31,6517           00005                                    4D                                    
027509,000495: 31,6520           01024                                    RMAG                                  
027510,000496: 31,6521           22674                                    TWO(-2)                               #  E  B-1  PD6,7
027511,000497: 
027512,000498: 31,6522           47576                           NOLOD    0                                     
027513,000499: 31,6523           33726                           STORE    ECC                                   
027514,000500: 
027515,000501: 31,6524           47575                           NOLOD    1                                     
027516,000502: 31,6525           65672                           BDSU     TSRT                                  
027517,000503: 31,6526           22674                                    TWO(-2)                               
027518,000504: 31,6527           00002                                    1                                     #  B-2    DEL    PD8,9
027519,000505: 
027520,000506: 31,6530           56776                           TSRT     0                                     
027521,000507: 31,6531           00005                                    4                                     
027522,000508: 31,6532           00002                                    1                                     #  PD10,11  B-27
027523,000509: 
027524,000510: 31,6533           66775                           DSU      1                                     
027525,000511: 31,6534           61776                           BDDV                                           
027526,000512: 31,6535           22674                                    TWO(-2)                               
027527,000513: 31,6536           00011                                    8D                                    #  H H/MUE(2-DEL)  B-25  =RPAR  PD10,11
027528,000514: 
027529,000515: 31,6537           56775                           TSRT     1                                     
027530,000516: 31,6540           65616                           BDSU     BPL                                   
027531,000517: 31,6541           15706                                    R400K                                 
027532,000518: 31,6542           00002                                    1                                     
027533,000519: 31,6543           00013                                    10D                                   
027534,000520: 31,6544           22457                                    TFFMAX                                
027535,000521: 
027536,000522: 31,6545           42775                           DOT      1                                     
027537,000523: 31,6546           43776                           BPL                                            
027538,000524: 31,6547           00766                                    RN                                    
027539,000525: 31,6550           00774                                    VN                                    
027540,000526: 31,6551           22443                                    HIECC1                                
027541,000527: 
027542,000528: 31,6552           62774                           DDV      2                                     
027543,000529: 31,6553           66672                           DSU      TSRT                                  
027544,000530: 31,6554           62776                           DDV                                            
027545,000531: 31,6555           00005                                    4D                                    
027546,000532: 31,6556           01024                                    RMAG                                  
027547,000533: 31,6557           22674                                    TWO(-2)                               
027548,000534: 31,6560           00002                                    1                                     
027549,000535: 31,6561           00007                                    6D                                    #  COSTH  PD12,13  B-1
027550,000536: 
027551,000537: 31,6562           47575                           NOLOD    1                                     
027552,000538: 31,6563           73726                           BMN      BDSU                                  
027553,000539: 31,6564           22457                                    TFFMAX                                
027554,000540: 31,6565           22674                                    TWO(-2)                               

Page 695

027556,000542: 31,6566           70774                           DAD      2                                     
027557,000543: 31,6567           61653                           BDDV     SQRT                                  
027558,000544: 31,6570           47176                           COMP                                           
027559,000545: 31,6571           22674                                    TWO(-2)                               
027560,000546: 31,6572           00015                                    12D                                   #  PD14,15 B0  TAN(TH/2)
027561,000547: 
027562,000548: 31,6573           56774                           TSRT     2                                     
027563,000549: 31,6574           61732                           BDDV     DSU                                   
027564,000550: 31,6575           56712                           TSRT     DDV                                   
027565,000551: 31,6576           15706                                    R400K                                 
027566,000552: 31,6577           00002                                    1                                     
027567,000553: 31,6600           00005                                    4D                                    
027568,000554: 31,6601           22674                                    TWO(-2)                               
027569,000555: 31,6602           00002                                    1                                     
027570,000556: 31,6603           00007                                    6D                                    
027571,000557: 
027572,000558: 31,6604           47575                           NOLOD    1                                     
027573,000559: 31,6605           73726                           BMN      BDSU                                  
027574,000560: 31,6606           22457                                    TFFMAX                                
027575,000561: 31,6607           22674                                    TWO(-2)                               
027576,000562: 
027577,000563: 31,6610           70774                           DAD      2                                     
027578,000564: 31,6611           61653                           BDDV     SQRT                                  
027579,000565: 31,6612           47176                           COMP                                           
027580,000566: 31,6613           22674                                    TWO(-2)                               
027581,000567: 31,6614           00021                                    16D                                   #  TAN(TH1/2)  PD18,19
027582,000568: 
027583,000569: 31,6615           56775                           TSRT     1                                     
027584,000570: 31,6616           70776                           DAD                                            
027585,000571: 31,6617           00011                                    8D                                    
027586,000572: 31,6620           00002                                    1                                     
027587,000573: 31,6621           22674                                    TWO(-2)                               
027588,000574: 
027589,000575: 31,6622           66775                           DSU      1                                     
027590,000576: 31,6623           73722                           BMN      DMP                                   
027591,000577: 31,6624           00023                                    18D                                   
027592,000578: 31,6625           00017                                    14D                                   
027593,000579: 31,6626           22665                                    TFF0                                  #  (1+DEL/4)(TANTH1/2)-TAN(TH/2))
027594,000580: 
027595,000581: 31,6627           51175                           DSQ      1                                     
027596,000582: 31,6630           64776                           DMP                                            
027597,000583: 31,6631           00023                                    18D                                   
027598,000584: 31,6632           00023                                    18D                                   #  (TAN(TH1/2))CUBED  PD22,23
027599,000585: 
027600,000586: 31,6633           51175                           DSQ      1                                     
027601,000587: 31,6634           64726                           DMP      BDSU                                  
027602,000588: 31,6635           00017                                    14D                                   
027603,000589: 31,6636           00017                                    14D                                   #  PD22,23   B0
027604,000590: 
027605,000591: 31,6637           56774                           TSRT     2                                     

Page 696

027607,000593: 31,6640           65722                           BDSU     DMP                                   
027608,000594: 31,6641           70776                           DAD                                            
027609,000595: 31,6642           00011                                    8D                                    
027610,000596: 31,6643           00002                                    1                                     
027611,000597: 31,6644           22676                                    DP1/3S                                
027612,000598: 31,6645           77777                                    -                                     
027613,000599: 31,6646           00025                                    20D                                   #  B-2   PD22,23
027614,000600: 
027615,000601: 31,6647           64773                           DMP      3                                     
027616,000602: 31,6650           63653                           TSLT     SQRT                                  
027617,000603: 31,6651           64722                           DMP      DMP                                   
027618,000604: 31,6652           56771                           TSRT     RTB                                   
027619,000605: 31,6653           00013                                    10D                                   
027620,000606: 31,6654           22307                                    1/MUE                                 
027621,000607: 31,6655           00002                                    1                                     
027622,000608: 31,6656           00013                                    10D                                   
027623,000609: 31,6657           00027                                    22D                                   
027624,000610: 31,6660           00010                                    7D                                    
027625,000611: 31,6661           20265                                    FRESHPD                               
027626,000612: 31,6662           33457                           STORE    TFF                                   
027627,000613: 
027628,000614: 31,6663           40576                           ITCQ     0                                     
027629,000615: 
027630,000616: 31,6664           45175        TFF0               DMOVE    1                                     
027631,000617: 31,6665           76576                           RTB                                            
027632,000618: 31,6666           05174                                    ZERODP                                
027633,000619: 31,6667           20265                                    FRESHPD                               
027634,000620: 31,6670           33457                           STORE    TFF                                   
027635,000621: 
027636,000622: 31,6671           40576                           ITCQ     0                                     
027637,000623: 
027638,000624: 31,6672           40576                           ITCQ     0                                     
027639,000625: 
027640,000626: 31,6673           20000 00000  TWO(-2)            2DEC     .5                                    
027641,000627: 31,6675           05252 25253  DP1/3S             2DEC     .3333333333 B-1                        

End of include-file TIME_OF_FREE-FALL_CALCULATIONS.agc.  Parent file is MAIN.agc