152ZFG Základy fyzikální geodézie - úloha3: Porovnání verzí

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(Není zobrazeno 45 mezilehlých verzí od 2 dalších uživatelů.)
Řádek 1: Řádek 1:
==Název úlohy==
Geodetická úloha na kouli a na elipsoidu
==Zadání úlohy==
==Zadání úlohy==
Pomocí osmi identických bodů se zadanými prostorovými souřadnicemi v kartézských souřadnicových systémech S1 a S2 vypočítejte transformační klíč Helmertovy prostorové transformace a body transformujte ze systému S1 do systému S2. Vypočítejte aposteriorní charakteristiky přesnosti plynoucí ze zavedení podmínky MNČ.
;Příklad 1
Je dána geodetická křivka na Besselově elipsoidu geodetickými souřadnicemi <math> B_A, L_A </math> bodu A a azimutem v tomto bodu <math> \alpha_A </math>. Vypočítejte pomocí vzorců sférické trigonometrie souřadnice <math> B_B, L_B </math> a azimut <math> \alpha_B </math> v bodě B, který leží na této geodetické křivce v zadané vzdálenosti <math> s_{AB} </math> od bodu A. Výpočet proveďte na náhradní referenční kouli; poloměr této referenční koule volte roven střednímu poloměru křivosti Besselova elipsoidu v bodě A. Výsledek porovnejte s výsledkem příkladu 2.
 
;Příklad 2
Je dána geodetická křivka na Besselově elipsoidu geodetickými souřadnicemi <math> B_A, L_A </math> bodu A a azimutem v tomto bodu <math> \alpha_A </math>. Vypočítejte souřadnice <math> B_B, L_B </math> a azimut <math> \alpha_B </math> v bodě B, který leží na této geodetické křivce ve vzdálenosti <math> s_{AB} </math> od bodu A. Dále pro zadanou geodetickou křivku vypočítejte průsečík s nultým poledníkem a azimut geodetické křivky v tomto bodě. Geodetickou úlohu řešte na Besselově elipsoidu; zadané numerické hodnoty jsou shodné se zadáním příkladu 1.
 
;Příklad 3
Je dána geodetická křivka na Besselově elipsoidu geodetickými souřadnicemi <math> B_A, L_A </math> bodu A a geodetickými souřadnicemi <math> B_B, L_B </math> bodu B (souřadnice jsou shodné se zadanými, resp. vypočtenými souřadnicemi bodů A, B z příkladu 2). Vypočítejte vzdálenost <math> s_{AB} </math> bodů A, B a azimuty <math> \alpha_A </math> a <math> \alpha_B </math> této geodetické křivky v bodech A, B. Geodetickou úlohu řešte na Besselově elipsoidu.
 
 
Výpočty provádějte s přesností na 0.001´´.
 
==Numerické zadání==
Numerické zadání s bodem A, azimutem <math>\alpha_A</math> a vzdáleností <math>s_{AB}</math> naleznete v adresáři ftp://athena.fsv.cvut.cz/ZFG/gu/zadani v souboru '''zfg_2014_u3_xx.m''', kde '''xx''' je číslo zadání. Číslo zadání studenta odpovídá číslování uvedenému na stránkách cvičení ZFG.
 
==Dokumenty ke stažení==
Parametry užívaných elipsoidů naleznete [ftp://athena.fsv.cvut.cz/ZFG/gu/elipsoidy.png zde].


==Numerické zadání úlohy==
Pro testování správnosti vašich výpočtů můžete využít modelové náhodně vygenerované zadání s přehledem výsledků [ftp://athena.fsv.cvut.cz/ZFG/gu/zfgul3_test.pdf zfgul3_test.pdf]. Pozn.: výsledky zatím neobsahují průsečík s Greenwichským poledníkem (časem opět doplním) - na vaše přání zveřejňuji již tyto dílčí výsledky.


Souřadnice transformovaných bodů v systému S2 jsou pro všechna zadání stejné:
<!--
{| class="border"
==Název úlohy==
|bod
Gravitační potenciál a jeho derivace
|x [m]
 
|y [m]
==Zadání úlohy==
|z [m]
;Příklad 3.1
|-
Zemské těleso lze v prvním přiblížení nahradit koulí téhož objemu pomocí středního průvodiče '''<math>R</math>''' a střední hustoty '''<math>\sigma</math>''' konstantní v celém objemu. Pro tuto homogenní kouli určete hodnoty gravitačního potenciálu a jeho první i druhé radiální derivace na jejím povrchu a ve vzdálenostech '''<math>r_i</math>''' od těžiště koule podle numerického zadání. Vypočtené hodnoty využijte k vykreslení průběhu těchto tří funkcí.
| A || 0,000 || 0,000 || 0,000
|-
| B || 100,000 || 0,000 || 0,000
|-
| C || 100,000 || 100,000 || 0,000
|-
| D || 0,000 || 100,000 || 0,000
|-
| E || 0,000 || 0,000 || 100,000
|-
| F || 100,000 || 0,000 || 100,000
|-
| G || 100,000 || 100,000 || 100,000
|-
| H || 0,000 || 100,000 || 100,000
|}


;Příklad 3.2
Zemské těleso aproximujte dvěma homogenními kulovými vrstvami o tloušťkách daných poloměry '''<math>R_1</math>''', '''<math>R_2</math>''', '''<math>R_3</math>''' a hustotách '''<math>\sigma_1</math>''' a '''<math>\sigma_2</math>'''. Spočtěte opět hodnoty gravitačního potenciálu a jeho první i druhé radiální derivace tohoto sféricky symetrického tělesa na rozhraních jednotlivých vrstev a ve vzdálenostech '''<math>r_i</math>''' od těžiště kulové dvojvrstvy; průběhy zkoumaných funkcí přehledně vykreslete a diskutujte. Popište jejich chování na rozhraních vrstev z hlediska spojitosti pomocí řešení limitních případů analytických vyjádření příslušných funkcí; v případě nespojitosti funkcí uveďte velikost skoku na daném rozhraní (analytické vyjádření velikosti skoku ověřte numericky). Porovnejte také případ koule a kulových vrstev.


Souřadnice transformovaných bodů v systému S1:
''Pozn.: Analytické řešení limitních případů pro jednotlivá rozhraní kulové dvojvrstvy postačí v TZ uvést pouze pro druhou radiální derivaci gravitačního potenciálu.''
{| class="border"
|číslo zadání
|bod
|x [m]
|y [m]
|z [m]
|číslo zadání
|bod
|x [m]
|y [m]
|z [m]
|-
|rowspan="8"  | 1 || A || 93,170 || -295,133 || 48,646 ||rowspan="8"  | 51 || A || 30,977 || -52,407 || 155,159
|-
| B || -1,411 || -280,864 || 24,723 || B || 25,958 || 9,966 || 203,122
|-
| C || -22,338 || -261,377 || 119,082 || C || 31,794 || -37,672 || 265,678
|-
| D || 72,244 || -275,639 || 143,002 || D || 36,814 || -100,045 || 217,715
|-
| E || 111,543 || -199,539 || 32,973 || E || 109,452 || -44,876 || 153,571
|-
| F || 16,961 || -185,277 || 9,045 || F || 104,430 || 17,496 || 201,538
|-
| G || -3,961 || -165,780 || 103,413 || G || 110,259 || -30,144 || 264,102
|-
| H || 90,619 || -180,041 || 127,335 || H || 115,281 || -92,510 || 216,133
|-
|rowspan="8"  | 2 || A || -30,662 || -150,076 || -11,197 ||rowspan="8"  | 52 || A || -58,386 || 179,416 || -139,345
|-
| B || -65,948 || -64,049 || -107,415 || B || 6,015 || 194,213 || -161,630
|-
| C || -154,799 || -152,591 || -154,001 || C || -17,000 || 254,451 || -188,161
|-
| D || -119,508 || -238,628 || -57,778 || D || -81,406 || 239,658 || -165,875
|-
| E || -124,284 || -98,472 || 69,285 || E || -44,756 || 211,279 || -78,829
|-
| F || -159,575 || -12,443 || -26,942 || F || 19,643 || 226,073 || -101,114
|-
| G || -248,427 || -100,991 || -73,525 || G || -3,379 || 286,308 || -127,643
|-
| H || -213,138 || -187,020 || 22,695 || H || -67,779 || 271,515 || -105,356
|-
|rowspan="8"  | 3 || A || -58,640 || 90,084 || -100,064 ||rowspan="8"  | 53 || A || 15,080 || 334,609 || -140,155
|-
| B || 0,229 || 66,547 || -170,125 || B || -10,561 || 301,188 || -205,519
|-
| C || 8,938 || 157,707 || -193,421 || C || -82,489 || 298,753 || -176,064
|-
| D || -49,932 || 181,236 || -123,365 || D || -56,837 || 332,171 || -110,696
|-
| E || 14,759 || 98,137 || -41,104 || E || 0,375 || 404,779 || -170,263
|-
| F || 73,625 || 74,606 || -111,166 || F || -25,273 || 371,357 || -235,635
|-
| G || 82,330 || 165,765 || -134,457 || G || -97,197 || 368,929 || -206,162
|-
| H || 23,463 || 189,294 || -64,400 || H || -71,549 || 402,343 || -140,802
|-
|rowspan="8"  | 4 || A || -22,297 || 366,540 || 79,651 ||rowspan="8"  | 54 || A || -8,488 || -143,002 || -28,202
|-
| B || 58,657 || 324,191 || 109,487 || B || 23,660 || -248,992 || 37,987
|-
| C || 81,716 || 304,082 || 18,377 || C || 137,422 || -252,463 || -22,818
|-
| D || 0,769 || 346,426 || -11,462 || D || 105,272 || -146,469 || -89,012
|-
| E || 24,086 || 450,435 || 72,867 || E || 43,249 || -69,502 || 64,376
|-
| F || 105,043 || 408,096 || 102,706 || F || 75,397 || -175,489 || 130,568
|-
| G || 128,106 || 387,984 || 11,597 || G || 189,146 || -178,964 || 69,760
|-
| H || 47,145 || 430,327 || -18,239 || H || 156,998 || -72,964 || 3,571
|-
|rowspan="8"  | 5 || A || -1,349 || -53,984 || 107,577 ||rowspan="8"  | 55 || A || -14,581 || 174,102 || 53,660
|-
| B || 12,440 || -86,892 || 148,631 || B || 28,563 || 70,321 || 134,653
|-
| C || 2,987 || -130,181 || 117,101 || C || -26,818 || -21,311 || 46,746
|-
| D || -10,801 || -97,276 || 76,046 || D || -69,968 || 82,470 || -34,241
|-
| E || 50,412 || -53,127 || 90,890 || E || 104,835 || 169,093 || -16,376
|-
| F || 64,199 || -86,029 || 131,941 || F || 147,989 || 65,326 || 64,612
|-
| G || 54,745 || -129,331 || 100,408 || G || 92,597 || -26,310 || -23,282
|-
| H || 40,963 || -96,415 || 59,353 || H || 49,448 || 77,466 || -104,272
|-
|rowspan="8"  | 6 || A || 20,503 || 393,620 || -122,535 ||rowspan="8"  | 56 || A || 52,342 || -91,495 || -67,506
|-
| B || -70,711 || 328,401 || -189,274 || B || 140,410 || -21,181 || -38,826
|-
| C || -110,464 || 271,128 || -78,977 || C || 115,863 || 46,740 || -129,970
|-
| D || -19,252 || 336,338 || -12,231 || D || 27,786 || -23,572 || -158,655
|-
| E || -63,906 || 491,048 || -102,367 || E || -19,532 || -28,522 || -1,227
|-
| F || -155,123 || 425,836 || -169,100 || F || 68,544 || 41,791 || 27,459
|-
| G || -194,875 || 368,565 || -58,798 || G || 43,995 || 109,719 || -63,687
|-
| H || -103,669 || 433,771 || 7,940 || H || -44,074 || 39,398 || -92,368
|-
|rowspan="8"  | 7 || A || 23,910 || 233,940 || -36,316 ||rowspan="8"  | 57 || A || 9,814 || 296,466 || 45,020
|-
| B || 47,640 || 328,518 || 31,422 || B || 28,940 || 250,611 || 2,156
|-
| C || 113,328 || 374,688 || -56,040 || C || -28,290 || 256,288 || -29,442
|-
| D || 89,611 || 280,104 || -123,782 || D || -47,417 || 302,135 || 13,430
|-
| E || -72,106 || 288,901 || -79,422 || E || 35,604 || 343,065 || 6,690
|-
| F || -48,378 || 383,477 || -11,686 || F || 54,720 || 297,210 || -36,181
|-
| G || 17,322 || 429,648 || -99,147 || G || -2,511 || 302,888 || -67,783
|-
| H || -6,403 || 335,061 || -166,890 || H || -21,628 || 348,742 || -24,913
|-
|rowspan="8"  | 8 || A || -20,027 || -70,648 || 74,791 ||rowspan="8"  | 58 || A || -3,202 || 109,027 || -276,757
|-
| B || -69,042 || -104,138 || -14,136 || B || 30,042 || 109,602 || -155,182
|-
| C || -1,308 || -46,278 || -73,262 || C || 68,834 || -9,904 || -165,220
|-
| D || 47,710 || -12,786 || 15,660 || D || 35,584 || -10,481 || -286,802
|-
| E || 46,612 || -154,089 || 69,484 || E || 112,022 || 149,085 || -308,451
|-
| F || -2,402 || -187,578 || -19,445 || F || 145,268 || 149,662 || -186,879
|-
| G || 65,327 || -129,720 || -78,576 || G || 184,049 || 30,157 || -196,919
|-
| H || 114,347 || -96,232 || 10,353 || H || 150,803 || 29,582 || -318,496
|-
|rowspan="8"  | 9 || A || 7,668 || 475,089 || 117,180 ||rowspan="8"  | 59 || A || -26,543 || -449,172 || 53,068
|-
| B || 55,432 || 448,741 || 105,023 || B || -94,065 || -405,727 || -12,443
|-
| C || 58,815 || 477,063 || 56,954 || C || -76,285 || -481,408 || -80,962
|-
| D || 11,051 || 503,407 || 69,119 || D || -8,756 || -524,847 || -15,459
|-
| E || 36,482 || 515,435 || 142,970 || E || -103,099 || -505,062 || 94,924
|-
| F || 84,247 || 489,084 || 130,818 || F || -170,629 || -461,617 || 29,420
|-
| G || 87,627 || 517,405 || 82,748 || G || -152,853 || -537,301 || -39,100
|-
| H || 39,864 || 543,748 || 94,911 || H || -85,317 || -580,741 || 26,406
|-
|rowspan="8"  | 10 || A || -10,754 || 207,875 || -47,920 ||rowspan="8"  | 60 || A || -64,418 || -97,966 || -83,457
|-
| B || -10,878 || 308,067 || -145,458 || B || -51,266 || -199,514 || 7,477
|-
| C || -7,130 || 210,560 || -245,610 || C || 62,152 || -242,037 || -56,400
|-
| D || -7,003 || 110,378 || -148,066 || D || 49,001 || -140,488 || -147,334
|-
| E || -150,523 || 205,165 || -50,514 || E || 11,196 || -16,528 || -3,437
|-
| F || -150,652 || 305,357 || -148,061 || F || 24,337 || -118,066 || 87,504
|-
| G || -146,903 || 207,851 || -248,211 || G || 137,753 || -160,591 || 23,619
|-
| H || -146,771 || 107,671 || -150,669 || H || 124,610 || -59,047 || -67,308
|-
|rowspan="8"  | 11 || A || 31,664 || -50,081 || 155,170 ||rowspan="8"  | 61 || A || 59,875 || 450,368 || 138,025
|-
| B || -52,182 || -140,593 || 125,299 || B || 108,055 || 323,175 || 152,809
|-
| C || -75,069 || -160,097 || 248,634 || C || 176,116 || 361,985 || 264,955
|-
| D || 8,775 || -69,583 || 278,506 || D || 127,936 || 489,180 || 250,175
|-
| E || -60,856 || 36,761 || 151,733 || E || -48,583 || 418,229 || 214,972
|-
| F || -144,707 || -53,750 || 121,860 || F || -0,408 || 291,039 || 229,751
|-
| G || -167,596 || -73,250 || 245,195 || G || 67,656 || 329,852 || 341,905
|-
| H || -83,752 || 17,258 || 275,064 || H || 19,475 || 457,043 || 327,126
|-
|rowspan="8"  | 12 || A || -31,701 || -485,743 || 57,217 ||rowspan="8"  | 62 || A || -41,024 || 66,815 || -130,056
|-
| B || 5,844 || -600,552 || 76,992 || B || -18,336 || 104,006 || -232,024
|-
| C || -20,037 || -629,030 || -39,214 || C || -19,825 || 208,263 || -194,326
|-
| D || -57,585 || -514,217 || -58,985 || D || -42,504 || 171,080 || -92,366
|-
| E || 81,893 || -454,272 || 24,212 || E || 67,502 || 60,479 || -108,230
|-
| F || 119,439 || -569,094 || 43,982 || F || 90,180 || 97,664 || -210,194
|-
| G || 93,561 || -597,560 || -72,223 || G || 88,697 || 201,923 || -172,495
|-
| H || 56,011 || -482,750 || -91,989 || H || 66,008 || 164,740 || -70,536
|-
|rowspan="8"  | 13 || A || -4,189 || -333,380 || 49,056 ||rowspan="8"  | 63 || A || -67,013 || -193,237 || -73,333
|-
| B || -55,985 || -366,730 || 75,963 || B || -1,556 || -96,768 || -147,320
|-
| C || -26,682 || -363,468 || 136,377 || C || -122,706 || -52,028 || -196,167
|-
| D || 25,102 || -330,118 || 109,463 || D || -188,163 || -148,493 || -122,181
|-
| E || -35,473 || -275,111 || 61,071 || E || -77,163 || -105,157 || 32,521
|-
| F || -87,257 || -308,459 || 87,990 || F || -11,703 || -8,693 || -41,464
|-
| G || -57,964 || -305,192 || 148,400 || G || -132,855 || 36,052 || -90,314
|-
| H || -6,168 || -271,852 || 121,488 || H || -198,312 || -60,423 || -16,332
|-
|rowspan="8"  | 14 || A || 88,609 || 12,300 || -33,202 ||rowspan="8"  | 64 || A || -31,542 || 143,668 || -143,998
|-
| B || 91,936 || 10,873 || 26,841 || B || 43,403 || 230,953 || -84,738
|-
| C || 96,089 || -49,117 || 25,201 || C || 135,993 || 141,681 || -70,361
|-
| D || 92,771 || -47,702 || -34,849 || D || 61,041 || 54,400 || -129,617
|-
| E || 148,531 || 16,538 || -36,427 || E || 19,035 || 177,739 || -258,154
|-
| F || 151,860 || 15,117 || 23,627 || F || 93,978 || 265,024 || -198,892
|-
| G || 156,018 || -44,875 || 21,979 || G || 186,571 || 175,750 || -184,503
|-
| H || 152,690 || -43,453 || -38,075 || H || 111,620 || 88,469 || -243,773
|-
|rowspan="8"  | 15 || A || 62,366 || -70,046 || -71,843 ||rowspan="8"  | 65 || A || 47,520 || 175,522 || 2,294
|-
| B || 62,519 || -17,971 || 27,704 || B || 99,131 || 108,969 || 9,227
|-
| C || 62,970 || -117,513 || 79,774 || C || 107,478 || 124,061 || 91,954
|-
| D || 62,813 || -169,587 || -19,771 || D || 55,870 || 190,620 || 85,014
|-
| E || 174,707 || -69,713 || -72,181 || E || -18,864 || 125,683 || 18,085
|-
| F || 174,861 || -17,641 || 27,364 || F || 32,738 || 59,132 || 25,015
|-
| G || 175,311 || -117,185 || 79,437 || G || 41,089 || 74,228 || 107,739
|-
| H || 175,152 || -169,256 || -20,106 || H || -10,523 || 140,780 || 100,805
|-
|rowspan="8"  | 16 || A || -72,703 || -75,016 || 102,975 ||rowspan="8"  | 66 || A || -53,662 || -192,983 || 45,141
|-
| B || -51,746 || -91,605 || -16,242 || B || -17,421 || -81,679 || 21,396
|-
| C || -39,883 || 29,111 || -30,955 || C || -32,369 || -101,732 || -95,398
|-
| D || -60,836 || 45,694 || 88,266 || D || -68,602 || -213,034 || -71,653
|-
| E || 47,073 || -84,070 || 125,289 || E || -166,488 || -154,580 || 52,981
|-
| F || 68,034 || -100,656 || 6,074 || F || -130,242 || -43,279 || 29,233
|-
| G || 79,896 || 20,048 || -8,640 || G || -145,191 || -63,324 || -87,552
|-
| H || 58,947 || 36,635 || 110,584 || H || -181,430 || -174,625 || -63,812
|-
|rowspan="8"  | 17 || A || -49,473 || -187,835 || -225,023 ||rowspan="8"  | 67 || A || 28,574 || -185,482 || -3,599
|-
| B || 11,721 || -96,543 || -173,052 || B || 112,033 || -165,763 || -24,837
|-
| C || 116,730 || -148,165 || -206,000 || C || 126,158 || -249,973 || -47,490
|-
| D || 55,542 || -239,454 || -257,974 || D || 42,708 || -269,694 || -26,245
|-
| E || -52,145 || -126,349 || -329,865 || E || 3,266 || -167,481 || -86,301
|-
| F || 9,042 || -35,066 || -277,895 || F || 86,727 || -147,756 || -107,547
|-
| G || 114,056 || -86,692 || -310,841 || G || 100,858 || -231,974 || -130,204
|-
| H || 52,868 || -177,982 || -362,815 || H || 17,398 || -251,697 || -108,962
|-
|rowspan="8"  | 18 || A || -3,291 || 58,392 || -67,764 ||rowspan="8"  | 68 || A || 29,360 || 117,807 || 150,925
|-
| B || -13,778 || 102,437 || -43,675 || B || 71,436 || 90,590 || 291,160
|-
| C || -5,168 || 128,262 || -87,137 || C || 69,409 || 236,665 || 320,118
|-
| D || 5,312 || 84,214 || -111,235 || D || 27,328 || 263,878 || 179,875
|-
| E || -52,753 || 53,542 || -80,440 || E || -113,483 || 107,712 || 191,829
|-
| F || -63,235 || 97,591 || -56,343 || F || -71,399 || 80,495 || 332,066
|-
| G || -54,637 || 123,415 || -99,809 || G || -73,438 || 226,569 || 361,027
|-
| H || -44,151 || 79,368 || -123,899 || H || -115,522 || 253,776 || 220,780
|-
|rowspan="8"  | 19 || A || -26,093 || -7,702 || -58,331 ||rowspan="8"  | 69 || A || -29,898 || -316,569 || -27,757
|-
| B || -9,516 || 50,270 || -87,212 || B || -3,303 || -231,839 || -96,619
|-
| C || 1,414 || 77,141 || -26,977 || C || -34,166 || -158,019 || -17,718
|-
| D || -15,165 || 19,167 || 1,901 || D || -60,770 || -242,744 || 51,144
|-
| E || 37,754 || -27,356 || -61,147 || E || 74,829 || -316,334 || 12,989
|-
| F || 54,321 || 30,622 || -90,023 || F || 101,434 || -231,605 || -55,870
|-
| G || 65,251 || 57,496 || -29,791 || G || 70,567 || -157,781 || 23,033
|-
| H || 48,679 || -0,478 || -0,919 || H || 43,957 || -242,502 || 91,900
|-
|rowspan="8"  | 20 || A || -19,714 || 149,429 || 242,552 ||rowspan="8"  | 70 || A || -6,324 || 9,528 || -76,129
|-
| B || 1,831 || 90,967 || 295,510 || B || 41,615 || 60,008 || 18,026
|-
| C || -28,051 || 34,114 || 244,886 || C || 111,580 || 123,170 || -51,458
|-
| D || -49,595 || 92,582 || 191,928 || D || 63,629 || 72,686 || -145,608
|-
| E || 53,299 || 143,413 || 206,219 || E || -87,062 || 94,230 || -80,430
|-
| F || 74,838 || 84,941 || 259,177 || F || -39,121 || 144,713 || 13,730
|-
| G || 44,962 || 28,098 || 208,556 || G || 30,844 || 207,863 || -55,761
|-
| H || 23,420 || 86,563 || 155,596 || H || -17,099 || 157,393 || -149,912
|-
|rowspan="8"  | 21 || A || -1,496 || 50,358 || 30,936 ||rowspan="8"  | 71 || A || -17,985 || -78,194 || -28,835
|-
| B || 27,698 || -33,805 || 72,754 || B || -26,841 || -37,289 || -60,085
|-
| C || 21,239 || -79,295 || -14,278 || C || -31,192 || -69,479 || -100,980
|-
| D || -7,960 || 4,866 || -56,097 || D || -22,337 || -110,381 || -69,738
|-
| E || 92,257 || 73,432 || 11,916 || E || -69,271 || -82,530 || -19,975
|-
| F || 121,451 || -10,729 || 53,733 || F || -78,128 || -41,630 || -51,220
|-
| G || 114,997 || -56,216 || -33,290 || G || -82,480 || -73,809 || -92,122
|-
| H || 85,798 || 27,943 || -75,111 || H || -73,620 || -114,708 || -60,875
|-
|rowspan="8"  | 22 || A || 1,996 || 57,819 || 135,802 ||rowspan="8"  | 72 || A || 21,689 || -401,128 || 108,706
|-
| B || -21,399 || -15,302 || 170,653 || B || 5,663 || -475,434 || 192,354
|-
| C || -80,895 || -24,407 || 111,614 || C || 55,901 || -404,719 || 264,808
|-
| D || -57,495 || 48,707 || 76,761 || D || 71,928 || -330,405 || 181,171
|-
| E || 56,972 || 16,835 || 86,737 || E || -78,288 || -353,674 || 131,716
|-
| F || 33,570 || -56,290 || 121,594 || F || -94,312 || -427,992 || 215,354
|-
| G || -25,921 || -65,389 || 62,542 || G || -44,075 || -357,269 || 287,815
|-
| H || -2,525 || 7,732 || 27,688 || H || -28,043 || -282,955 || 204,169
|-
|rowspan="8"  | 23 || A || 1,756 || -73,171 || 74,601 ||rowspan="8"  | 73 || A || 16,964 || 375,085 || 247,244
|-
| B || 2,774 || -40,542 || 124,645 || B || -0,723 || 487,938 || 239,053
|-
| C || 5,957 || -90,542 || 157,181 || C || -103,043 || 468,448 || 191,430
|-
| D || 4,927 || -123,176 || 107,143 || D || -85,357 || 355,597 || 199,631
|-
| E || 61,402 || -71,074 || 72,013 || E || -31,354 || 375,058 || 351,084
|-
| F || 62,425 || -38,444 || 122,050 || F || -49,041 || 487,912 || 342,883
|-
| G || 65,603 || -88,446 || 154,593 || G || -151,362 || 468,421 || 295,263
|-
| H || 64,585 || -121,078 || 104,550 || H || -133,668 || 355,563 || 303,466
|-
|rowspan="8"  | 24 || A || -58,762 || -191,413 || -8,972 ||rowspan="8"  | 74 || A || 7,716 || 107,422 || -66,020
|-
| B || -48,805 || -172,763 || 51,033 || B || -1,935 || 147,772 || -22,712
|-
| C || -106,418 || -194,311 || 67,296 || C || -46,907 || 114,225 || -1,494
|-
| D || -116,380 || -212,962 || 7,278 || D || -37,248 || 73,877 || -44,805
|-
| E || -33,681 || -248,301 || 4,548 || E || 46,209 || 78,358 || -30,361
|-
| F || -23,723 || -229,650 || 64,556 || F || 36,550 || 118,711 || 12,944
|-
| G || -81,343 || -251,196 || 80,810 || G || -8,424 || 85,168 || 34,161
|-
| H || -91,300 || -269,851 || 20,797 || H || 1,234 || 44,823 || -9,156
|-
|rowspan="8"  | 25 || A || -14,816 || 312,924 || -88,682 ||rowspan="8"  | 75 || A || -30,726 || -336,403 || 19,400
|-
| B || -99,513 || 377,487 || -176,113 || B || -8,274 || -403,305 || 91,613
|-
| C || -66,758 || 286,964 || -274,700 || C || -106,287 || -425,369 || 101,646
|-
| D || 17,936 || 222,392 || -187,261 || D || -128,739 || -358,470 || 29,430
|-
| E || -118,459 || 231,536 || -48,393 || E || -21,595 || -408,737 || -50,451
|-
| F || -203,157 || 296,104 || -135,819 || F || 0,859 || -475,635 || 21,764
|-
| G || -170,389 || 205,581 || -234,405 || G || -97,154 || -497,698 || 31,789
|-
| H || -85,696 || 141,016 || -146,977 || H || -119,608 || -430,804 || -40,424
|-
|rowspan="8"  | 26 || A || 48,259 || -41,077 || -191,310 ||rowspan="8"  | 76 || A || -43,660 || 204,215 || -164,580
|-
| B || 15,108 || 18,228 || -225,919 || B || -137,467 || 266,163 || -67,163
|-
| C || 22,176 || -17,052 || -293,135 || C || -80,085 || 400,105 || -97,083
|-
| D || 55,328 || -76,361 || -258,529 || D || 13,731 || 338,149 || -194,495
|-
| E || -20,040 || -73,506 || -181,453 || E || -143,830 || 222,926 || -272,945
|-
| F || -53,188 || -14,207 || -216,064 || F || -237,633 || 284,876 || -175,536
|-
| G || -46,122 || -49,489 || -283,288 || G || -180,246 || 418,814 || -205,454
|-
| H || -12,970 || -108,788 || -248,679 || H || -86,438 || 356,866 || -302,868
|-
|rowspan="8"  | 27 || A || 72,657 || -16,129 || -62,558 ||rowspan="8"  | 77 || A || 64,212 || 120,027 || -257,009
|-
| B || 49,381 || -127,697 || -84,673 || B || 80,180 || 174,246 || -367,841
|-
| C || 62,283 || -152,717 || 27,952 || C || 18,757 || 80,811 || -422,392
|-
| D || 85,557 || -41,144 || 50,077 || D || 2,797 || 26,594 || -311,568
|-
| E || -40,354 || 3,996 || -45,133 || E || -42,800 || 181,741 || -242,230
|-
| F || -63,620 || -107,567 || -67,253 || F || -26,827 || 235,964 || -353,060
|-
| G || -50,715 || -132,594 || 45,378 || G || -88,243 || 142,527 || -407,615
|-
| H || -27,446 || -21,031 || 67,494 || H || -104,216 || 88,314 || -296,791
|-
|rowspan="8"  | 28 || A || 70,548 || -98,767 || -97,987 ||rowspan="8"  | 78 || A || 15,590 || 20,752 || 87,279
|-
| B || 20,523 || -114,915 || -70,311 || B || 10,979 || 72,163 || 141,186
|-
| C || 1,148 || -140,518 || -120,289 || C || -63,119 || 63,468 || 143,145
|-
| D || 51,172 || -124,376 || -147,964 || D || -58,513 || 12,056 || 89,234
|-
| E || 96,057 || -149,887 || -81,691 || E || 23,218 || -32,646 || 138,865
|-
| F || 46,030 || -166,024 || -54,022 || F || 18,607 || 18,766 || 192,767
|-
| G || 26,651 || -191,631 || -103,995 || G || -55,487 || 10,075 || 194,725
|-
| H || 76,676 || -175,485 || -131,667 || H || -50,881 || -41,335 || 140,821
|-
|rowspan="8"  | 29 || A || 19,154 || 157,384 || 153,406 ||rowspan="8"  | 79 || A || 7,879 || -100,695 || 129,989
|-
| B || 78,894 || 47,638 || 170,584 || B || -72,908 || -136,829 || 155,646
|-
| C || -30,186 || -13,998 || 156,108 || C || -32,830 || -173,666 || 229,988
|-
| D || -89,920 || 95,745 || 138,927 || D || 47,968 || -137,537 || 204,328
|-
| E || 40,151 || 149,384 || 29,293 || E || -11,004 || -24,351 || 178,007
|-
| F || 99,887 || 39,643 || 46,473 || F || -91,798 || -60,488 || 203,669
|-
| G || -9,189 || -22,001 || 31,991 || G || -51,717 || -97,333 || 278,004
|-
| H || -68,929 || 87,746 || 14,814 || H || 29,074 || -61,199 || 252,351
|-
|rowspan="8"  | 30 || A || -0,832 || 148,123 || -55,062 ||rowspan="8"  | 80 || A || -82,391 || 19,624 || 195,867
|-
| B || -3,177 || 83,383 || -82,664 || B || -126,755 || 13,600 || 235,381
|-
| C || 4,481 || 55,693 || -18,369 || C || -155,874 || -21,964 || 197,277
|-
| D || 6,819 || 120,437 || 9,226 || D || -111,512 || -15,951 || 157,758
|-
| E || -70,802 || 147,260 || -47,104 || E || -55,013 || -27,965 || 219,355
|-
| F || -73,142 || 82,515 || -74,709 || F || -99,374 || -33,982 || 258,868
|-
| G || -65,481 || 54,832 || -10,407 || G || -128,500 || -69,550 || 220,760
|-
| H || -63,142 || 119,582 || 17,182 || H || -84,143 || -63,530 || 181,251
|-
|rowspan="8"  | 31 || A || -62,187 || -290,838 || 74,947 ||rowspan="8"  | 81 || A || -10,413 || 205,562 || -99,978
|-
| B || -148,419 || -277,181 || 52,556 || B || -20,573 || 98,681 || -113,175
|-
| C || -122,249 || -237,171 || -23,850 || C || 75,377 || 83,682 || -65,540
|-
| D || -36,007 || -250,826 || -1,461 || D || 85,534 || 190,557 || -52,338
|-
| E || -63,819 || -370,443 || 32,697 || E || -59,316 || 198,329 || -3,776
|-
| F || -150,059 || -356,788 || 10,309 || F || -69,474 || 91,448 || -16,972
|-
| G || -123,886 || -316,776 || -66,108 || G || 26,476 || 76,444 || 30,672
|-
| H || -37,641 || -330,428 || -43,713 || H || 36,626 || 183,327 || 43,869
|-
|rowspan="8"  | 32 || A || 21,688 || 24,157 || 173,270 ||rowspan="8"  | 82 || A || -45,436 || 279,685 || -163,035
|-
| B || 35,864 || 10,746 || 240,885 || B || -84,684 || 320,165 || -149,056
|-
| C || 51,742 || 78,562 || 251,010 || C || -51,030 || 361,055 || -172,936
|-
| D || 37,573 || 91,973 || 183,389 || D || -11,771 || 320,577 || -186,922
|-
| E || -45,394 || 37,383 || 189,943 || E || -71,915 || 271,648 || -214,121
|-
| F || -31,224 || 23,972 || 257,570 || F || -111,174 || 312,136 || -200,137
|-
| G || -15,339 || 91,783 || 267,694 || G || -77,514 || 353,016 || -224,014
|-
| H || -29,509 || 105,189 || 200,071 || H || -38,255 || 312,536 || -237,997
|-
|rowspan="8"  | 33 || A || 44,183 || -183,082 || -7,037 ||rowspan="8"  | 83 || A || -25,582 || -156,980 || 151,171
|-
| B || 38,428 || -219,288 || 83,764 || B || 36,128 || -53,249 || 236,515
|-
| C || 29,366 || -128,530 || 119,376 || C || 35,072 || -146,795 || 350,972
|-
| D || 35,115 || -92,329 || 28,585 || D || -26,636 || -250,524 || 265,628
|-
| E || -53,143 || -189,398 || -15,719 || E || 108,740 || -205,366 || 112,860
|-
| F || -58,891 || -225,601 || 75,075 || F || 170,451 || -101,635 || 198,212
|-
| G || -67,959 || -134,848 || 110,694 || G || 169,393 || -195,183 || 312,666
|-
| H || -62,213 || -98,642 || 19,902 || H || 107,685 || -298,907 || 227,318
|-
|rowspan="8"  | 34 || A || 39,453 || 117,439 || -16,522 ||rowspan="8"  | 84 || A || -46,635 || 166,791 || 13,631
|-
| B || 33,907 || 39,298 || 86,838 || B || -71,644 || 60,654 || 67,095
|-
| C || 42,312 || -64,157 || 9,066 || C || 46,747 || 43,133 || 87,695
|-
| D || 47,865 || 13,995 || -94,293 || D || 71,758 || 149,260 || 34,235
|-
| E || 168,764 || 120,807 || -7,024 || E || -56,922 || 223,156 || 120,711
|-
| F || 163,206 || 42,664 || 96,330 || F || -81,942 || 117,013 || 174,178
|-
| G || 171,612 || -60,794 || 18,564 || G || 36,453 || 99,495 || 194,776
|-
| H || 177,166 || 17,359 || -84,797 || H || 61,469 || 205,633 || 141,314
|-
|rowspan="8"  | 35 || A || 41,180 || 17,938 || -167,878 ||rowspan="8"  | 85 || A || -51,182 || -51,542 || 18,228
|-
| B || 37,801 || 67,734 || -245,735 || B || -118,414 || -85,354 || 130,674
|-
| C || 106,456 || 121,247 || -214,492 || C || -103,162 || -216,350 || 100,410
|-
| D || 109,831 || 71,451 || -136,634 || D || -35,929 || -182,537 || -12,038
|-
| E || 103,051 || -38,713 || -206,801 || E || 65,247 || -53,904 || 87,134
|-
| F || 99,674 || 11,090 || -284,655 || F || -1,994 || -87,717 || 199,581
|-
| G || 168,327 || 64,599 || -253,411 || G || 13,265 || -218,713 || 169,308
|-
| H || 171,707 || 14,805 || -175,566 || H || 80,501 || -184,899 || 56,863
|-
|rowspan="8"  | 36 || A || 18,551 || -42,342 || 65,222 ||rowspan="8"  | 86 || A || -10,928 || 153,829 || -86,720
|-
| B || 22,249 || -14,504 || -47,899 || B || -17,656 || 30,629 || -10,708
|-
| C || 81,529 || -112,378 || -70,056 || C || 125,085 || 37,646 || 13,298
|-
| D || 77,831 || -140,224 || 43,063 || D || 131,820 || 160,845 || -62,715
|-
| E || -81,736 || -99,169 || 47,947 || E || -35,020 || 229,818 || 34,307
|-
| F || -78,037 || -71,326 || -65,177 || F || -41,751 || 106,619 || 110,312
|-
| G || -18,748 || -169,207 || -87,320 || G || 100,994 || 113,639 || 134,323
|-
| H || -22,459 || -197,050 || 25,792 || H || 107,727 || 236,836 || 58,305
|-
|rowspan="8"  | 37 || A || 21,819 || 222,345 || 35,209 ||rowspan="8"  | 87 || A || 29,723 || -86,649 || -35,592
|-
| B || 64,934 || 299,487 || 73,760 || B || 17,622 || -41,898 || 100,238
|-
| C || 62,447 || 257,521 || 160,516 || C || -74,921 || 59,585 || 58,562
|-
| D || 19,334 || 180,377 || 121,968 || D || -62,830 || 14,829 || -77,269
|-
| E || 108,020 || 182,552 || 18,432 || E || -79,309 || -177,746 || -15,287
|-
| F || 151,129 || 259,692 || 56,978 || F || -91,403 || -132,992 || 120,547
|-
| G || 148,641 || 217,725 || 143,745 || G || -183,957 || -31,512 || 78,877
|-
| H || 105,528 || 140,591 || 105,197 || H || -171,861 || -76,268 || -56,958
|-
|rowspan="8"  | 38 || A || -16,265 || -55,427 || -71,646 ||rowspan="8"  | 88 || A || 50,033 || 278,002 || -139,931
|-
| B || -25,671 || -131,166 || -43,586 || B || 50,039 || 216,948 || -236,550
|-
| C || -106,270 || -124,213 || -51,827 || C || 50,034 || 313,571 || -297,607
|-
| D || -96,861 || -48,463 || -79,890 || D || 50,022 || 374,625 || -200,989
|-
| E || -10,987 || -84,193 || -147,527 || E || 164,336 || 278,018 || -139,927
|-
| F || -20,397 || -159,943 || -119,457 || F || 164,339 || 216,961 || -236,546
|-
| G || -100,991 || -152,981 || -127,706 || G || 164,335 || 313,582 || -297,603
|-
| H || -91,590 || -77,240 || -155,770 || H || 164,319 || 374,643 || -200,984
|-
|rowspan="8"  | 39 || A || -53,192 || 129,839 || 73,707 ||rowspan="8"  | 89 || A || 3,685 || 475,694 || -68,483
|-
| B || -23,735 || 106,391 || 30,249 || B || 50,250 || 450,269 || -84,841
|-
| C || 20,100 || 142,101 || 40,698 || C || 80,158 || 484,614 || -53,084
|-
| D || -9,356 || 165,552 || 84,151 || D || 33,588 || 510,041 || -36,721
|-
| E || -30,466 || 91,359 || 109,873 || E || -0,736 || 440,246 || -25,970
|-
| F || -1,001 || 67,914 || 66,420 || F || 45,829 || 414,815 || -42,337
|-
| G || 42,831 || 103,618 || 76,868 || G || 75,737 || 449,169 || -10,583
|-
| H || 13,370 || 127,067 || 120,318 || H || 29,166 || 474,598 || 5,778
|-
|rowspan="8"  | 40 || A || -47,254 || -39,090 || -47,292 ||rowspan="8"  | 90 || A || 40,806 || -248,916 || 46,046
|-
| B || -44,379 || -81,587 || -14,591 || B || 64,657 || -294,153 || 16,219
|-
| C || -95,649 || -74,176 || -0,454 || C || 71,528 || -259,296 || -31,137
|-
| D || -98,528 || -31,681 || -33,159 || D || 47,679 || -214,070 || -1,306
|-
| E || -62,953 || -71,075 || -87,471 || E || 94,554 || -233,299 || 65,333
|-
| F || -60,073 || -113,573 || -54,767 || F || 118,401 || -278,535 || 35,513
|-
| G || -111,345 || -106,159 || -40,627 || G || 125,272 || -243,676 || -11,850
|-
| H || -114,228 || -63,675 || -73,338 || H || 101,419 || -198,451 || 17,980
|-
|rowspan="8"  | 41 || A || -74,761 || 30,164 || 183,471 ||rowspan="8"  | 91 || A || -38,767 || 105,181 || -70,416
|-
| B || -70,723 || 95,811 || 316,035 || B || -15,246 || 102,931 || -130,225
|-
| C || -70,850 || 228,428 || 250,361 || C || -30,973 || 40,700 || -134,058
|-
| D || -74,898 || 162,771 || 117,799 || D || -54,488 || 42,950 || -74,264
|-
| E || -222,685 || 31,843 || 187,150 || E || -96,502 || 121,202 || -93,723
|-
| F || -218,651 || 97,487 || 319,713 || F || -72,998 || 118,953 || -153,533
|-
| G || -218,781 || 230,096 || 254,042 || G || -88,711 || 56,727 || -157,367
|-
| H || -222,817 || 164,453 || 121,479 || H || -112,223 || 58,978 || -97,562
|-
|rowspan="8"  | 42 || A || -41,878 || -226,942 || -3,086 ||rowspan="8"  | 92 || A || -6,294 || 255,663 || -231,651
|-
| B || -38,826 || -304,573 || -25,689 || B || 38,261 || 154,536 || -249,454
|-
| C || -107,693 || -295,222 || -67,118 || C || 116,077 || 175,124 || -171,665
|-
| D || -110,749 || -217,588 || -44,521 || D || 71,528 || 276,260 || -153,860
|-
| E || 0,483 || -206,134 || -68,822 || E || -73,289 || 212,332 || -153,138
|-
| F || 3,540 || -283,767 || -91,425 || F || -28,737 || 111,199 || -170,950
|-
| G || -65,337 || -274,417 || -132,855 || G || 49,081 || 131,789 || -93,168
|-
| H || -68,390 || -196,782 || -110,245 || H || 4,523 || 232,920 || -75,365
|-
|rowspan="8"  | 43 || A || -7,819 || -55,712 || 12,582 ||rowspan="8"  | 93 || A || -75,723 || 244,498 || -135,815
|-
| B || -60,330 || -80,620 || 3,655 || B || -82,559 || 229,007 || -46,701
|-
| C || -74,640 || -37,204 || -33,324 || C || -85,390 || 139,720 || -62,434
|-
| D || -22,133 || -12,297 || -24,402 || D || -78,555 || 155,200 || -151,551
|-
| E || 14,446 || -86,572 || -32,251 || E || 14,681 || 240,532 || -129,582
|-
| F || -38,074 || -111,488 || -41,174 || F || 7,850 || 225,046 || -40,465
|-
| G || -52,388 || -68,062 || -78,169 || G || 5,021 || 135,755 || -56,195
|-
| H || 0,130 || -43,150 || -69,240 || H || 11,847 || 151,234 || -145,314
|-
|rowspan="8"  | 44 || A || 12,124 || 29,493 || -61,344 ||rowspan="8"  | 94 || A || 26,421 || -45,661 || 265,356
|-
| B || 6,872 || 5,332 || 8,602 || B || 2,414 || 39,092 || 221,112
|-
| C || 80,039 || 14,134 || 17,146 || C || 59,763 || 15,365 || 144,530
|-
| D || 85,293 || 38,298 || -52,807 || D || 83,771 || -69,402 || 188,771
|-
| E || 1,041 || 99,080 || -38,137 || E || -50,083 || -90,051 || 221,820
|-
| F || -4,216 || 74,920 || 31,812 || F || -74,083 || -5,292 || 177,589
|-
| G || 68,953 || 83,727 || 40,347 || G || -16,738 || -29,019 || 100,998
|-
| H || 74,216 || 107,887 || -29,595 || H || 7,266 || -113,787 || 145,242
|-
|rowspan="8"  | 45 || A || -14,290 || 305,473 || -38,546 ||rowspan="8"  | 95 || A || 59,456 || 169,514 || -55,338
|-
| B || -33,289 || 244,676 || -26,483 || B || 72,883 || 88,087 || -110,613
|-
| C || -88,751 || 266,977 || -1,417 || C || 27,474 || 132,458 || -187,016
|-
| D || -69,763 || 327,772 || -13,482 || D || 14,051 || 213,898 || -131,738
|-
| E || -41,951 || 302,495 || -97,100 || E || 146,782 || 205,112 || -86,567
|-
| F || -60,942 || 241,699 || -85,042 || F || 160,205 || 123,674 || -141,848
|-
| G || -116,416 || 264,001 || -59,971 || G || 114,796 || 168,052 || -218,246
|-
| H || -97,415 || 324,801 || -72,038 || H || 101,372 || 249,496 || -162,967
|-
|rowspan="8"  | 46 || A || 42,815 || 56,809 || 65,624 ||rowspan="8"  | 96 || A || 87,799 || 9,898 || 157,693
|-
| B || 59,197 || 180,782 || 131,551 || B || 168,746 || 47,893 || 60,760
|-
| C || 42,456 || 248,403 || 8,546 || C || 118,896 || 169,835 || 66,937
|-
| D || 26,080 || 124,431 || -57,384 || D || 37,963 || 131,834 || 163,874
|-
| E || -96,594 || 63,254 || 88,136 || E || 179,213 || 42,745 || 246,898
|-
| F || -80,215 || 187,223 || 154,067 || F || 260,161 || 80,738 || 149,963
|-
| G || -96,957 || 254,856 || 31,063 || G || 210,308 || 202,685 || 156,145
|-
| H || -113,336 || 130,881 || -34,871 || H || 129,369 || 164,682 || 253,079
|-
|rowspan="8"  | 47 || A || 16,659 || 216,633 || -245,483 ||rowspan="8"  | 97 || A || 15,320 || 50,805 || 120,047
|-
| B || 69,269 || 215,380 || -216,984 || B || 16,360 || 122,350 || 229,948
|-
| C || 78,347 || 272,789 || -231,217 || C || 13,706 || 12,471 || 301,494
|-
| D || 25,740 || 274,043 || -259,713 || D || 12,665 || -59,065 || 191,589
|-
| E || -10,379 || 233,470 || -194,822 || E || 146,436 || 48,013 || 120,621
|-
| F || 42,217 || 232,216 || -166,326 || F || 147,467 || 119,556 || 230,527
|-
| G || 51,294 || 289,627 || -180,557 || G || 144,812 || 9,675 || 302,069
|-
| H || -1,311 || 290,873 || -209,051 || H || 143,779 || -61,856 || 192,165
|-
|rowspan="8"  | 48 || A || -85,888 || 301,572 || -21,383 ||rowspan="8"  | 98 || A || 24,696 || 289,570 || -67,006
|-
| B || -104,608 || 351,179 || -120,655 || B || -33,685 || 352,622 || -151,554
|-
| C || -200,846 || 394,044 || -81,085 || C || 67,752 || 359,704 || -216,316
|-
| D || -182,129 || 344,439 || 18,178 || D || 126,129 || 296,647 || -131,759
|-
| E || -30,635 || 393,030 || 13,903 || E || -4,212 || 187,067 || -123,498
|-
| F || -49,346 || 442,638 || -85,362 || F || -62,592 || 250,121 || -208,043
|-
| G || -145,584 || 485,510 || -45,798 || G || 38,848 || 257,198 || -272,797
|-
| H || -126,869 || 435,905 || 53,478 || H || 97,217 || 194,146 || -188,253
|-
|rowspan="8"  | 49 || A || 29,200 || -214,223 || 271,379 ||rowspan="8"  | 99 || A || -21,738 || -63,055 || 1,821
|-
| B || -20,130 || -197,446 || 186,408 || B || 54,881 || 4,990 || -19,130
|-
| C || 22,774 || -107,751 || 179,213 || C || 24,411 || 8,511 || -119,116
|-
| D || 72,106 || -124,541 || 264,192 || D || -52,202 || -59,530 || -98,175
|-
| E || 104,453 || -254,365 || 219,770 || E || -86,078 || 16,289 || 24,217
|-
| F || 55,119 || -237,577 || 134,791 || F || -9,475 || 84,337 || 3,277
|-
| G || 98,023 || -147,884 || 127,604 || G || -39,942 || 87,862 || -96,718
|-
| H || 147,360 || -164,667 || 212,581 || H || -116,549 || 19,814 || -75,767
|-


==Doplňkový materiál==
[http://web.ics.purdue.edu/~braile/edumod/threedearth/threedearth.htm O struktuře Země - sestavte si 3D model]


==Numerické zadání==
<math>G = 6,672.10^{-11}~m^{3}.kg^{-1}.s^{-2}</math>


<math>R = 6371~km</math>


<math>\sigma = 5520~kg.m^{-3}</math>


<math>r_i = [0, 20000]~km</math>, kde v uvedeném rozmezí zvolte dostatečný počet výpočetních bodů s ohledem na hladkost vykreslovaných křivek zkoumaných průběhů funkcí (např. 200 výpočetních bodů)


|rowspan="8"  | 50 || A || -46,150 || -37,165 || -63,817 ||rowspan="8" | 100 || A || -13,094 || -292,595 || -36,143
{|class="border"
|-
|-  
| B || -113,887 || -30,922 || -190,379 || B || 45,011 || -174,946 || -68,398
| '''R<sub>3</sub> =''' || R
|-
|-  
| C || -8,846 || 52,106 || -242,495 || C || 152,991 || -207,928 || 5,840
| '''R<sub>2</sub> =''' || R<sub>3</sub> - 3 . ( 10 + ''n'' ) <math>km</math>
|-
|-  
| D || 58,887 || 45,878 || -115,939 || D || 94,883 || -325,573 || 38,088
| '''R<sub>1</sub> =''' || R<sub>2</sub> - ( 400 + ''n'' ) <math>km</math>
|-
|-  
| E || 24,724 || -154,257 || -107,523 || E || 43,665 || -350,296 || -144,34
| '''<math>\sigma_2</math>'''[<math>kg.m^{-3}</math>] || <math>2,75.10^3</math>
|-
|-  
| F || -43,010 || -148,016 || -234,076 || F || 101,779 || -232,648 || -176,594
| '''<math>\sigma_1</math>'''[<math>kg.m^{-3}</math>] || <math>3,64.10^3</math>
|-
| G || 62,026 || -64,979 || -286,205 || G || 209,752 || -265,623 || -102,354
|-
| H || 129,768 || -71,222 || -159,642 || H || 151,649 || -383,269 || -70,100
|-
|rowspan="8" | 101 || A || -23,015 || -35,636 || -89,787 ||rowspan="8" | 102 || A || 74,487 || 131,213 || -147,528
|-
| B || 67,309 || -11,943 || -172,643 || B || 43,481 || 203,541 || -267,277
|-
| C || 129,377 || -113,094 || -133,901 || C || 28,144 || 79,865 || -338,002
|-
| D || 39,057 || -136,789 || -51,048 || D || 59,158 || 7,545 || -218,252
|-
| E || -82,804 || -104,861 || -174,752 || E || -64,564 || 128,730 || -113,025
|-
| F || 7,520 || -81,177 || -257,608 || F || -95,576 || 201,049 || -232,773
|-
| G || 69,593 || -182,324 || -218,864 || G || -110,905 || 77,375 || -303,500
|-
| H || -20,727 || -206,010 || -136,009 || H || -79,891 || 5,0560 || -183,744
|}
|}
[[Kategorie:Výuka]]
 
'''<math>\sigma_2</math>''' je hustota vnější vrstvy, '''<math>\sigma_1</math>''' je hustota vnitřní vrstvy.
 
Veličina ''n'' se rovná pořadovému číslu zadání studenta uvedenému na stránkách cvičení ZFG.
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Hustoty vrstev '''<math>\sigma</math><sub>1</sub>''' a '''<math>\sigma</math><sub>2</sub>''' převezměte z Bullenova hustotního modelu Země (typ A') podle toho, do které Bullenovy zóny modelu A' spadne vnitřní rozhraní vaší vrstvy. Numerické hodnoty Bullenova modelu A' naleznete [ftp://athena.fsv.cvut.cz/VG/FYG/uloha2/BullenAdash.jpg zde].
-->
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[[152ZFG Základy fyzikální geodézie | 152ZFG Základy fyzikální geodézie]]
{{Teoretická geodézie}}

Aktuální verze z 27. 3. 2014, 09:59

Název úlohy

Geodetická úloha na kouli a na elipsoidu

Zadání úlohy

Příklad 1

Je dána geodetická křivka na Besselově elipsoidu geodetickými souřadnicemi bodu A a azimutem v tomto bodu . Vypočítejte pomocí vzorců sférické trigonometrie souřadnice a azimut v bodě B, který leží na této geodetické křivce v zadané vzdálenosti od bodu A. Výpočet proveďte na náhradní referenční kouli; poloměr této referenční koule volte roven střednímu poloměru křivosti Besselova elipsoidu v bodě A. Výsledek porovnejte s výsledkem příkladu 2.

Příklad 2

Je dána geodetická křivka na Besselově elipsoidu geodetickými souřadnicemi bodu A a azimutem v tomto bodu . Vypočítejte souřadnice a azimut v bodě B, který leží na této geodetické křivce ve vzdálenosti od bodu A. Dále pro zadanou geodetickou křivku vypočítejte průsečík s nultým poledníkem a azimut geodetické křivky v tomto bodě. Geodetickou úlohu řešte na Besselově elipsoidu; zadané numerické hodnoty jsou shodné se zadáním příkladu 1.

Příklad 3

Je dána geodetická křivka na Besselově elipsoidu geodetickými souřadnicemi bodu A a geodetickými souřadnicemi bodu B (souřadnice jsou shodné se zadanými, resp. vypočtenými souřadnicemi bodů A, B z příkladu 2). Vypočítejte vzdálenost bodů A, B a azimuty a této geodetické křivky v bodech A, B. Geodetickou úlohu řešte na Besselově elipsoidu.


Výpočty provádějte s přesností na 0.001´´.

Numerické zadání

Numerické zadání s bodem A, azimutem a vzdáleností naleznete v adresáři ftp://athena.fsv.cvut.cz/ZFG/gu/zadani v souboru zfg_2014_u3_xx.m, kde xx je číslo zadání. Číslo zadání studenta odpovídá číslování uvedenému na stránkách cvičení ZFG.

Dokumenty ke stažení

Parametry užívaných elipsoidů naleznete zde.

Pro testování správnosti vašich výpočtů můžete využít modelové náhodně vygenerované zadání s přehledem výsledků zfgul3_test.pdf. Pozn.: výsledky zatím neobsahují průsečík s Greenwichským poledníkem (časem opět doplním) - na vaše přání zveřejňuji již tyto dílčí výsledky.


152ZFG Základy fyzikální geodézie