Uniwersytet Warmińsko-Mazurski w Olsztynie Olsztyn,16.12.2010r.
Wydział Geodezji i Gospodarki Przestrzennej
Kierunek : Geodezja i Kartografia
Specjalność: Geodezja i Geoinformatyka
Wyrównanie sieci geodezyjnej na elipsoidzie
Piotr Płókarz
Rok III, grupa 2
Wyrównanie sieci: metoda obliczenia wyrównanych współrzędnych punktów 2, 3, 4 w sieci.
Wykonanie zadań odwrotnych dla 6 linii metodą Gaussa.
Ułożenie układu równań poprawek V=AX+L
Eliminacja stałej orientacji.
Eliminacja niewiadomej z równania warunkowego.
Ułożenie układu równań normalnych (ATPA)X+ATPL=0
Rozwiązanie układu równań normalnych.
Obliczenie wyrównanych współrzędnych i ich błędów.
Kontrola obliczeń.
Dane:
S1-2 = 24209,534 m
B1= 53 o 42 `56 ”,5600
L1= 20 o 44 '55 ”,9379
A1-2 = 0o09'57”,7100
Błędy pomiarowe:
mS = 0,058 m
mk = 0,6”
Kierunki:
|
stopnie [º] |
minuty ['] |
sekundy ["] |
K1 - 2 |
0 |
0 |
0,0000 |
K1 - 3 |
36 |
21 |
54,3000 |
K1 - 4 |
88 |
59 |
26,5000 |
K2 - 3 |
0 |
0 |
0,0000 |
K2 - 4 |
52 |
10 |
44,8000 |
K2 - 1 |
87 |
2 |
9,7000 |
K3 - 4 |
0 |
0 |
0,0000 |
K3 - 1 |
35 |
5 |
10,6000 |
K3 - 2 |
91 |
41 |
9,7000 |
K4 - 1 |
0 |
0 |
0,0000 |
K4 - 2 |
56 |
9 |
7,9000 |
K4 - 3 |
92 |
17 |
17,0000 |
Przybliżone współrzędne punktów 2, 3, 4, oraz współrzędne stałe punktu 1
|
stopnie [º] |
minuty ['] |
sekundy ["] |
B2 |
53 |
55 |
59,4890 |
L2 |
20 |
44 |
59,7830 |
B3 |
53 |
55 |
28,0920 |
L3 |
21 |
0 |
40,5910 |
B4 |
53 |
43 |
3,4350 |
L4 |
21 |
0 |
4,2906 |
Rozwiązanie:
1. Wykonanie zadań odwrotnych dla 6 linii metodą Gaussa.
Dane: B1, B2, L1, L2
ΔB” = B2 - B1
ΔL” = L2 - L1
B = 0,5 * (B1 + B2)
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Metoda Gaussa dla linii 1 - 3 |
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Elipsoida Krasowskiego: |
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a = |
6378245 |
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ρ" = |
206264,8062 |
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e2 = |
0,006693421623 |
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ρº = |
57,29577951 |
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(e')2 = |
0,006738525415 |
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DANE |
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|
stopnie [º] |
minuty ['] |
sekundy ["] |
liczba |
radiany |
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B1 |
53 |
42 |
56,46 |
53,71568333 |
0,937515534 |
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L1 |
20 |
44 |
55,9379 |
20,74887164 |
0,362136126 |
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B3 |
53 |
55 |
28,092 |
53,92447 |
0,941159549 |
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L3 |
21 |
0 |
40,591 |
21,01127528 |
0,366715934 |
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sekundy ["] |
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ΔB = |
0 |
12 |
31,63199 |
0,208786667 |
0,003644015 |
751,6320 |
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ΔL = |
0 |
15 |
44,65309 |
0,262403639 |
0,004579807 |
944,6531 |
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B = |
53 |
49 |
12,27599 |
53,82007667 |
0,939337542 |
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C = |
0,0000073093 |
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M = |
6377222,762 |
Q = |
0,0023482 |
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S = |
0,0000136654 |
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N = |
6392198,067 |
V2 = |
1,0000055 |
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D = |
0,0000132788 |
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(1)B = |
0,032343986 |
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(2)B = |
0,032268213 |
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u = |
23238,640 |
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(3)B = |
0,317033314 |
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v = |
17281,723 |
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(4)B = |
5,99373E-07 |
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ΔA = |
762,4947 |
0,003696679 |
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(5)B = |
0,041662571 |
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s1 - 3 = |
28960,186 |
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(6)B = |
0,083333793 |
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A = |
36,63682683 |
0,639433256 |
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(7)B = |
0,12500046 |
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A1 - 3 = |
0,637584916 |
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A3 - 1 = |
3,782874249 |
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A1 - 3 = |
36 |
31 |
51,32922 |
36,53092478 |
0,637584916 |
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A3 - 1 = |
216 |
44 |
33,82396 |
216,7427289 |
3,782874249 |
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s1 - 3 = |
28960,186 |
m |
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Metoda Gaussa dla linii 1 - 4 |
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Elipsoida Krasowskiego: |
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a = |
6378245 |
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ρ" = |
206264,8062 |
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e2 = |
0,006693421623 |
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ρº = |
57,29577951 |
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(e')2 = |
0,006738525415 |
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DANE |
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|
stopnie [ş] |
minuty ['] |
sekundy ["] |
liczba |
radiany |
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B1 |
53 |
42 |
56,46 |
53,71568333 |
0,937515534 |
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L1 |
20 |
44 |
55,9379 |
20,74887164 |
0,362136126 |
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B4 |
53 |
43 |
3,435 |
53,71762083 |
0,93754935 |
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L4 |
21 |
0 |
4,2906 |
21,00119183 |
0,366539944 |
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sekundy ["] |
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ΔB = |
0 |
0 |
6,97499 |
0,0019375 |
3,38158E-05 |
6,9750 |
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ΔL = |
0 |
15 |
8,35269 |
0,252320194 |
0,004403818 |
908,3527 |
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B = |
53 |
42 |
59,9475 |
53,71665208 |
0,937532442 |
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C = |
0,0000067917 |
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M = |
6377112,076 |
Q = |
0,0023598 |
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S = |
0,0000126019 |
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N = |
6392161,085 |
V2 = |
1,0000056 |
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D = |
0,0000000011 |
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(1)B = |
0,032344548 |
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(2)B = |
0,032268399 |
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u = |
215,646 |
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(3)B = |
0,315270351 |
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v = |
16658,518 |
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(4)B = |
5,95491E-07 |
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ΔA = |
732,2238 |
0,003549921 |
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(5)B = |
0,04166256 |
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s1 - 4 = |
16659,913 |
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(6)B = |
0,083333797 |
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A = |
89,25834109 |
1,557851937 |
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(7)B = |
0,125000464 |
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A1 - 4 = |
1,556076976 |
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A4 - 1 = |
4,701219551 |
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A1 - 4 = |
89 |
9 |
23,91602 |
89,15664334 |
1,556076976 |
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A4 - 1 = |
269 |
21 |
36,13982 |
269,3600388 |
4,701219551 |
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s1 - 4 = |
16659,913 |
m |
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Metoda Gaussa dla linii 2 - 3 |
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Elipsoida Krasowskiego: |
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a = |
6378245 |
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ρ" = |
206264,8062 |
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e2 = |
0,006693421623 |
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ρº = |
57,29577951 |
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(e')2 = |
0,006738525415 |
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DANE |
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stopnie [º] |
minuty ['] |
sekundy ["] |
liczba |
radiany |
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B2 |
53 |
55 |
59,489 |
53,93319139 |
0,941311766 |
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L2 |
20 |
44 |
59,783 |
20,74993972 |
0,362154768 |
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B3 |
53 |
55 |
28,092 |
53,92447 |
0,941159549 |
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L3 |
21 |
0 |
40,591 |
21,01127528 |
0,366715934 |
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sekundy ["] |
ΔB = |
0 |
0 |
-31,39699 |
-0,008721389 |
-0,000152217 |
-31,3970 |
ΔL = |
0 |
15 |
40,80799 |
0,261335556 |
0,004561166 |
940,8080 |
B = |
53 |
55 |
43,79049 |
53,92883069 |
0,941235657 |
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C = |
0,0000072123 |
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M = |
6377339,019 |
Q = |
0,002336067 |
S = |
0,0000135920 |
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N = |
6392236,91 |
V2 = |
1,000005457 |
D = |
0,0000000232 |
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(1)B = |
0,032343397 |
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(2)B = |
0,032268017 |
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u = |
-970,737 |
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(3)B = |
0,318903788 |
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v = |
17166,774 |
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(4)B = |
6,03378E-07 |
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ΔA = |
760,4426 |
0,00368673 |
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(5)B = |
0,041662583 |
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s2 - 3 = |
17194,199 |
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(6)B = |
0,083333788 |
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A = |
93,23648203 |
1,627283594 |
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(7)B = |
0,125000455 |
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A2 - 3= |
1,625440229 |
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A3 - 2 = |
4,770719613 |
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A2 - 3 = |
93 |
7 |
51,11397 |
93,13086499 |
1,625440229 |
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A3 - 2 = |
273 |
20 |
31,55661 |
273,3420991 |
4,770719613 |
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s2 - 3 = |
17194,199 |
m |
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Metoda Gaussa dla linii 2 - 4 |
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Elipsoida Krasowskiego: |
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a = |
6378245 |
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ρ" = |
206264,8062 |
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e2 = |
0,006693421623 |
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ρº = |
57,29577951 |
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(e')2 = |
0,006738525415 |
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DANE |
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stopnie [ş] |
minuty ['] |
sekundy ["] |
liczba |
radiany |
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B2 |
53 |
55 |
59,489 |
53,93319139 |
0,941311766 |
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L2 |
20 |
44 |
59,783 |
20,74993972 |
0,362154768 |
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B4 |
53 |
43 |
3,435 |
53,71762083 |
0,93754935 |
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L4 |
21 |
0 |
4,2906 |
21,00119183 |
0,366539944 |
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sekundy ["] |
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ΔB = |
0 |
-12 |
-56,05399 |
-0,215570556 |
-0,003762416 |
-776,0540 |
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ΔL = |
0 |
15 |
4,50759 |
0,251252111 |
0,004385177 |
904,5076 |
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B = |
53 |
49 |
31,46199 |
53,82540611 |
0,939430558 |
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C = |
0,0000066995 |
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M = |
6377228,463 |
Q = |
0,0023477 |
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S = |
0,0000125303 |
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N = |
6392199,972 |
V2 = |
1,0000055 |
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D = |
0,0000141558 |
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(1)B = |
0,032343957 |
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(2)B = |
0,032268203 |
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u = |
-23993,735 |
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(3)B = |
0,317124576 |
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v = |
16545,193 |
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(4)B = |
5,99571E-07 |
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ΔA = |
730,1402 |
0,00353982 |
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(5)B = |
0,041662571 |
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s2 - 4 = |
29145,201 |
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(6)B = |
0,083333793 |
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A = |
145,4112888 |
2,53790576 |
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(7)B = |
0,125000459 |
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A2 - 4 = |
2,53613585 |
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A4 - 2 = |
5,681268323 |
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A2 - 4 = |
145 |
18 |
35,56964 |
145,3098805 |
2,53613585 |
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A4 - 2 = |
325 |
30 |
45,70988 |
325,5126972 |
5,681268323 |
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s2 - 4 = |
29145,201 |
m |
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Metoda Gaussa dla linii 3 - 4 |
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Elipsoida Krasowskiego: |
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a = |
6378245 |
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ρ" = |
206264,8062 |
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e2 = |
0,006693421623 |
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ρº = |
57,29577951 |
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(e')2 = |
0,006738525415 |
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DANE |
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|
stopnie [º] |
minuty ['] |
sekundy ["] |
liczba |
radiany |
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B3 |
53 |
55 |
28,092 |
53,92447 |
0,941159549 |
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L3 |
21 |
0 |
40,591 |
21,01127528 |
0,366715934 |
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B4 |
53 |
43 |
3,435 |
53,71762083 |
0,93754935 |
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L4 |
21 |
0 |
4,2906 |
21,00119183 |
0,366539944 |
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sekundy ["] |
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ΔB = |
0 |
-12 |
-24,65699 |
-0,206849167 |
-0,003610199 |
-744,6570 |
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ΔL = |
0 |
0 |
-36,30039 |
-0,010083444 |
-0,000175989 |
-36,3004 |
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B = |
53 |
49 |
15,76349 |
53,82104542 |
0,939354449 |
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C = |
0,0000000108 |
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M = |
6377223,799 |
Q = |
0,0023481 |
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S = |
0,0000000202 |
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N = |
6392198,414 |
V2 = |
1,0000055 |
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D = |
0,0000130335 |
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(1)B = |
0,032343981 |
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(2)B = |
0,032268211 |
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u = |
-23023,047 |
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(3)B = |
0,3170499 |
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v = |
-664,074 |
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(4)B = |
5,99409E-07 |
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ΔA = |
-29,3009 |
-0,000142055 |
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(5)B = |
0,041662571 |
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s3 - 4 = |
23032,622 |
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(6)B = |
0,083333793 |
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A = |
181,6521739 |
3,170428528 |
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(7)B = |
0,125000459 |
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A3 - 4 = |
3,170499556 |
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A4 - 3 = |
6,311950155 |
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A3 - 4 = |
181 |
39 |
22,47658 |
181,6562435 |
3,170499556 |
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A4 - 3 = |
361 |
38 |
53,17567 |
361,6481044 |
6,311950155 |
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s3 - 4 = |
23032,622 |
m |
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3. Ułożenie układu równań poprawek V=AX+L
Po oznaczeniu ogólnych symboli współczynników stojących przy parametrach:
otrzymamy równania poprawek dla długości:
dla azymutu:
dla kierunku:
gdzie
; dzi - poprawka do stałej orientacji
obliczenie współczynników przy parametrach:
|
Pik |
Qik |
Uik |
Wik |
1-2 |
0,7632997 |
-156,251 |
-30,91645264 |
-0,0531435 |
1-3 |
131,0748793 |
-104,958 |
-24,84257754 |
-10,916641 |
1-4 |
382,7338163 |
-3,34203 |
-0,455055584 |
-18,337401 |
2-3 |
370,3410001 |
11,95375 |
1,688623709 |
-18,217414 |
2-4 |
124,5325235 |
106,1679 |
25,42184623 |
-10,383717 |
2-1 |
-0,767291359 |
155,4434 |
30,91757929 |
0,05314345 |
3-4 |
-8,002550433 |
163,3523 |
30,90474864 |
0,52743271 |
3-1 |
-131,7326779 |
104,1504 |
24,77524457 |
10,9166411 |
3-2 |
-370,2632601 |
-12,762 |
-1,80242445 |
18,2174143 |
4-1 |
-382,7515295 |
2,535942 |
0,345313518 |
18,3374011 |
4-2 |
-123,8904012 |
-106,975 |
-25,48305357 |
10,3837168 |
4-3 |
7,962958736 |
-164,159 |
-30,90380294 |
-0,5274327 |
Poprawki:
vs1-2= |
30,918 |
dB2 |
0,053 |
-0,001 |
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vk1-2= |
-0,767 |
dB2 |
155,443 |
dL2 |
-1 |
dz1' |
-1,58E-06 |
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vk1-3= |
-131,733 |
dB3 |
104,15 |
dL3 |
-1 |
dz1' |
1,73E-06 |
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vk1-4= |
-382,752 |
dB4 |
2,536 |
dL4 |
-1 |
dz1' |
-1,50E-07 |
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vk2-3= |
370,341 |
dB2 |
11,954 |
dL2 |
-370,263 |
dB3 |
-12,762 |
dL3 |
-1 |
dz2' |
-5,57E-07 |
vk2-4= |
124,533 |
dB2 |
106,168 |
dL2 |
-123,89 |
dB4 |
-106,975 |
dL4 |
-1 |
dz2' |
1,11E-06 |
vk2-1= |
-0,767 |
dB2 |
155,443 |
dL2 |
-1 |
dz2' |
-5,57E-07 |
|
|
|
|
vk3-4= |
-8,003 |
dB3 |
163,352 |
dL3 |
7,963 |
dB4 |
-164,159 |
dL4 |
-1 |
dz3' |
2,06E-07 |
vk3-1= |
-131,733 |
dB3 |
104,15 |
dL3 |
-1 |
dz3' |
-3,42E-06 |
|
|
|
|
vk3-2= |
370,341 |
dB2 |
11,954 |
dL2 |
-370,263 |
dB3 |
-12,762 |
dL3 |
-1 |
dz3' |
3,21E-06 |
vk4-1= |
-382,752 |
dB4 |
2,536 |
dL4 |
-1 |
dz4' |
2,76E-06 |
|
|
|
|
vk4-2= |
124,533 |
dB2 |
106,168 |
dL2 |
-123,89 |
dB4 |
-106,975 |
dL4 |
-1 |
dz4' |
-5,34E-06 |
vk4-3= |
-8,003 |
dB3 |
163,352 |
dL3 |
7,963 |
dB4 |
-164,159 |
dL4 |
-1 |
dz4' |
2,58E-06 |
Eliminacja stałej orientacji.
|
dB2 |
dL2 |
dB3 |
dL3 |
dB4 |
dL4 |
dz1' |
dz2' |
dz3' |
dz4' |
L |
VK1 - 2 = |
-0,77 |
155,44 |
0,00 |
0,00 |
0,00 |
0,00 |
-1 |
0 |
0 |
0 |
1,57597E-06 |
VK1 - 3 = |
0,00 |
0,00 |
-131,73 |
104,15 |
0,00 |
0,00 |
-1 |
0 |
0 |
0 |
-1,72561E-06 |
VK1 - 4 = |
0,00 |
0,00 |
0,00 |
0,00 |
-382,75 |
2,54 |
-1 |
0 |
0 |
0 |
1,49646E-07 |
suma: |
-0,77 |
155,44 |
-131,73 |
104,15 |
-382,75 |
2,54 |
-3 |
0 |
0 |
0 |
-6,37511E-17 |
suma/(-3) |
0,26 |
-51,81 |
43,91 |
-34,72 |
127,58 |
-0,85 |
1 |
0 |
0 |
0 |
2,12504E-17 |
|
|
|
|
|
|
|
|
|
|
|
|
vk2-3= |
370,34 |
11,95 |
-370,26 |
-12,76 |
0,00 |
0,00 |
0 |
-1 |
0 |
0 |
5,56566E-07 |
vk2-4= |
124,53 |
106,17 |
0,00 |
0,00 |
-123,89 |
-106,98 |
0 |
-1 |
0 |
0 |
-0,000001 |
vk2-1= |
-0,77 |
155,44 |
0,00 |
0,00 |
0,00 |
0,00 |
0 |
-1 |
0 |
0 |
5,56566E-07 |
suma: |
494,11 |
273,57 |
-370,26 |
-12,76 |
-123,89 |
-106,98 |
0 |
-3 |
0 |
0 |
0,000 |
suma/(-3) |
-164,70 |
-91,19 |
123,42 |
4,25 |
41,30 |
35,66 |
0 |
1 |
0 |
0 |
3,33067E-16 |
|
|
|
|
|
|
|
|
|
|
|
|
vk3-4= |
0,00 |
0,00 |
-8,00 |
163,35 |
7,96 |
-164,16 |
0 |
0 |
-1 |
0 |
-2,05884E-07 |
vk3-1= |
0,00 |
0,00 |
-131,73 |
104,15 |
0,00 |
0,00 |
0 |
0 |
-1 |
0 |
3,41761E-06 |
vk3-2= |
370,34 |
11,95 |
-370,26 |
-12,76 |
0,00 |
0,00 |
0 |
0 |
-1 |
0 |
-3,21173E-06 |
suma: |
370,34 |
11,95 |
-510,00 |
254,74 |
7,96 |
-164,16 |
0 |
0 |
-3 |
0 |
0,000 |
suma/(-3) |
-123,45 |
-3,98 |
170,00 |
-84,91 |
-2,65 |
54,72 |
0 |
0 |
1 |
0 |
-4,44089E-16 |
|
|
|
|
|
|
|
|
|
|
|
|
vk4-1= |
0,00 |
0,00 |
0,00 |
0,00 |
-382,75 |
2,54 |
0 |
0 |
0 |
-1 |
-2,75697E-06 |
vk4-2= |
124,53 |
106,17 |
0,00 |
0,00 |
-123,89 |
-106,98 |
0 |
0 |
0 |
-1 |
5,3399E-06 |
vk4-3= |
0,00 |
0,00 |
-8,00 |
163,35 |
7,96 |
-164,16 |
0 |
0 |
0 |
-1 |
-2,58293E-06 |
suma: |
124,53 |
106,17 |
-8,00 |
163,35 |
-498,68 |
-268,60 |
0 |
0 |
0 |
-3 |
-1,77636E-15 |
suma/(-3) |
-41,51 |
-35,39 |
2,67 |
-54,45 |
166,23 |
89,53 |
0 |
0 |
0 |
1 |
5,92119E-16 |
Ułożenie układu V=AX+L po eliminacji dz'i
|
dB2 |
dL2 |
dB3 |
dL3 |
dB4 |
dL4 |
dz1' |
dz2' |
dz3' |
dz4' |
L |
vk1-2= |
-0,51 |
103,63 |
43,91 |
-34,72 |
127,58 |
-0,85 |
0 |
0 |
0 |
0 |
1,57597E-06 |
vk1-3= |
0,26 |
-51,81 |
-87,82 |
69,43 |
127,58 |
-0,85 |
0 |
0 |
0 |
0 |
-1,72561E-06 |
vk1-4= |
0,26 |
-51,81 |
43,91 |
-34,72 |
-255,17 |
1,69 |
0 |
0 |
0 |
0 |
1,49646E-07 |
vk2-3= |
205,64 |
-79,23 |
-246,84 |
-8,51 |
41,30 |
35,66 |
0 |
0 |
0 |
0 |
5,56566E-07 |
vk2-4= |
-40,17 |
14,98 |
123,42 |
4,25 |
-82,59 |
-71,32 |
0 |
0 |
0 |
0 |
-1,11313E-06 |
vk2-1= |
-165,47 |
64,26 |
123,42 |
4,25 |
41,30 |
35,66 |
0 |
0 |
0 |
0 |
5,56566E-07 |
vk3-4= |
-123,45 |
-3,98 |
162,00 |
78,44 |
5,31 |
-109,44 |
0 |
0 |
0 |
0 |
-2,05884E-07 |
vk3-1= |
-123,45 |
-3,98 |
38,27 |
19,24 |
-2,65 |
54,72 |
0 |
0 |
0 |
0 |
3,41761E-06 |
vk3-2= |
246,89 |
7,97 |
-200,26 |
-97,68 |
-2,65 |
54,72 |
0 |
0 |
0 |
0 |
-3,21173E-06 |
vk4-1= |
-41,51 |
-35,39 |
2,67 |
-54,45 |
-216,53 |
92,07 |
0 |
0 |
0 |
0 |
-2,75697E-06 |
vk4-2= |
83,02 |
70,78 |
2,67 |
-54,45 |
42,34 |
-17,44 |
0 |
0 |
0 |
0 |
5,3399E-06 |
vk4-3= |
-41,51 |
-35,39 |
-5,34 |
108,90 |
174,19 |
-74,63 |
0 |
0 |
0 |
0 |
-2,58293E-06 |
Eliminacja niewiadomej z równania warunkowego.
.VA1-2=P21dB2+Q21dL2+L=0
dL2==(-P2,1/Q2,1)*dB2 - L/Q2-1 = 0,004523*dB2-1,7294E-10
|
dB2 |
dB3 |
dL3 |
dB4 |
dL4 |
L'' |
vs1-2= |
30,918 |
0,000 |
0,000 |
0,000 |
0,000 |
0,001 |
vk1-2= |
0,000 |
43,911 |
-34,717 |
127,584 |
-0,845 |
0,327 |
vk1-3= |
0,000 |
-87,822 |
69,434 |
127,584 |
-0,845 |
-0,357 |
vk1-4= |
0,000 |
43,911 |
-34,717 |
-255,168 |
1,691 |
0,030 |
vk2-3= |
205,248 |
-246,842 |
-8,508 |
41,297 |
35,658 |
0,113 |
vk2-4= |
-40,096 |
123,421 |
4,254 |
-82,594 |
-71,317 |
-0,229 |
vk2-1= |
-165,152 |
123,421 |
4,254 |
41,297 |
35,658 |
0,116 |
vk3-4= |
-123,467 |
161,997 |
78,439 |
5,309 |
-109,440 |
-0,043 |
vk3-1= |
-123,467 |
38,267 |
19,237 |
-2,654 |
54,720 |
0,705 |
vk3-2= |
246,933 |
-200,264 |
-97,676 |
-2,654 |
54,720 |
-0,662 |
vk4-1= |
-41,686 |
2,668 |
-54,451 |
-216,525 |
92,069 |
-0,569 |
vk4-2= |
83,371 |
2,668 |
-54,451 |
42,336 |
-17,442 |
1,103 |
vk4-3= |
-41,686 |
-5,335 |
108,902 |
174,189 |
-74,627 |
-0,533 |
6. Ułożenie układu równań normalnych (ATPA)X+ATPL=0
|
ATPAX + ATPL = 0 |
|
|
X = (ATPA)-1 ATPL |
|
|
V = AX + L |
|
A= |
30,91784162 |
0 |
0 |
0 |
0 |
|
0 |
43,91089265 |
-34,7168 |
127,5838432 |
-0,845313846 |
|
0 |
-87,82178529 |
69,4336 |
127,5838432 |
-0,845313846 |
|
0 |
43,91089265 |
-34,7168 |
-255,167686 |
1,690627692 |
|
205,2478091 |
-246,8421734 |
-8,50802 |
41,2968004 |
35,65837465 |
|
-40,0956126 |
123,4210867 |
4,25401 |
-82,5936008 |
-71,31674929 |
|
-165,152196 |
123,4210867 |
4,25401 |
41,2968004 |
35,65837465 |
|
-123,466669 |
161,9969457 |
78,4387 |
5,308639157 |
-109,4396206 |
|
-123,466669 |
38,26681822 |
19,2369 |
-2,65431958 |
54,71981029 |
|
246,933337 |
-200,2637639 |
-97,6756 |
-2,65431958 |
54,71981029 |
|
-41,6855279 |
2,667516811 |
-54,4508 |
-216,525205 |
92,06881263 |
|
83,37105588 |
2,667516811 |
-54,4508 |
42,33592278 |
-17,44225284 |
|
-41,6855279 |
-5,335033622 |
108,902 |
174,1892827 |
-74,62655979 |
AT= |
30,92 |
0,00 |
0,00 |
0,00 |
205,25 |
-40,10 |
-165,15 |
-123,47 |
-123,47 |
246,93 |
-41,69 |
83,37 |
-41,69 |
|
0,00 |
43,91 |
-87,82 |
43,91 |
-246,84 |
123,42 |
123,42 |
162,00 |
38,27 |
-200,26 |
2,67 |
2,67 |
-5,34 |
|
0,00 |
-34,72 |
69,43 |
-34,72 |
-8,51 |
4,25 |
4,25 |
78,44 |
19,24 |
-97,68 |
-54,45 |
-54,45 |
108,90 |
|
0,00 |
127,58 |
127,58 |
-255,17 |
41,30 |
-82,59 |
41,30 |
5,31 |
-2,65 |
-2,65 |
-216,53 |
42,34 |
174,19 |
|
0,00 |
-0,85 |
-0,85 |
1,69 |
35,66 |
-71,32 |
35,66 |
-109,44 |
54,72 |
54,72 |
92,07 |
-17,44 |
-74,63 |
P= |
293,016 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
0 |
2,778 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
0 |
0 |
2,778 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
0 |
0 |
0 |
2,778 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
0 |
0 |
0 |
0 |
2,778 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
0 |
0 |
0 |
0 |
0 |
2,778 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
0 |
0 |
0 |
0 |
0 |
0 |
2,778 |
0 |
0 |
0 |
0 |
0 |
0 |
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
2,778 |
0 |
0 |
0 |
0 |
0 |
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
2,778 |
0 |
0 |
0 |
0 |
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
2,778 |
0 |
0 |
0 |
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
2,778 |
0 |
0 |
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
2,778 |
0 |
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
2,778 |
ATP= |
9059,41 |
0,00 |
0,00 |
0,00 |
570,13 |
-111,38 |
-458,76 |
-342,96 |
-342,96 |
685,93 |
-115,79 |
231,59 |
-115,79 |
|
0,00 |
121,97 |
-243,95 |
121,97 |
-685,67 |
342,84 |
342,84 |
449,99 |
106,30 |
-556,29 |
7,41 |
7,41 |
-14,82 |
|
0,00 |
-96,44 |
192,87 |
-96,44 |
-23,63 |
11,82 |
11,82 |
217,89 |
53,44 |
-271,32 |
-151,25 |
-151,25 |
302,50 |
|
0,00 |
354,40 |
354,40 |
-708,80 |
114,71 |
-229,43 |
114,71 |
14,75 |
-7,37 |
-7,37 |
-601,46 |
117,60 |
483,86 |
|
0,00 |
-2,35 |
-2,35 |
4,70 |
99,05 |
-198,10 |
99,05 |
-304,00 |
152,00 |
152,00 |
255,75 |
-48,45 |
-207,30 |
ATPA= |
760374,549 |
-416221,7546 |
-126688 |
25774,13173 |
62156,06281 |
|
-416221,755 |
474503,3768 |
72599,7 |
-89448,98 |
-108577,095 |
|
-126688,44 |
72599,68011 |
114424 |
116221,3871 |
-71138,84823 |
|
25774,13173 |
-89448,97998 |
116221 |
519327,9172 |
-73210,81167 |
|
62156,06281 |
-108577,095 |
-71138,8 |
-73210,8117 |
110969,3698 |
L= |
0,00100099 |
||
|
0,32699852 |
||
|
-0,3568993 |
||
|
0,02990074 |
||
|
0,11332291 |
||
|
-0,2293208 |
||
|
0,11599784 |
||
|
-0,0425409 |
||
|
0,70485905 |
||
|
-0,6623181 |
||
|
-0,5693264 |
||
|
1,10275279 |
||
|
-0,5334264 |
||
ATPL= |
-252,37439 |
||
|
450,123012 |
||
|
-141,21979 |
||
|
260,193735 |
||
|
-0,7027263 |
(ATPA)-1= |
3,57019E-06 |
3,42231E-06 |
4,3E-06 |
2,74421E-08 |
4,14186E-06 |
|
3,42231E-06 |
6,60248E-06 |
2,6E-06 |
1,38479E-06 |
7,14738E-06 |
|
4,32864E-06 |
2,63706E-06 |
2,3E-05 |
-3,0943E-06 |
1,28548E-05 |
|
2,74421E-08 |
1,38479E-06 |
-3,1E-06 |
3,04786E-06 |
1,36673E-06 |
|
4,14186E-06 |
7,14738E-06 |
1,3E-05 |
1,36673E-06 |
2,28273E-05 |
X= |
0,0000 |
dB2 |
|
-0,0021 |
dB3 |
|
0,0040 |
dL3 |
|
-0,0018 |
dB4 |
|
-0,0007 |
dL4 |
8. Obliczenie wyrównanych współrzędnych .
B1 = |
53 |
42 |
56,4600 |
L1 = |
20 |
44 |
55,9379 |
B2 = |
53 |
55 |
59,4890 |
L2 = |
20 |
44 |
59,7830 |
B3 = |
53 |
55 |
28,0899 |
L3 = |
21 |
0 |
40,5950 |
B4 = |
53 |
43 |
3,4332 |
L4 = |
21 |
0 |
4,2899 |
Do wyznaczenia błędów współrzędnych wyrównanych najpierw obliczamy macierz V ze wzoru V=AX+L, otrzymamy:
V= |
-4,0214E-11 |
|
-0,13739752 |
|
-0,13268923 |
|
0,270086758 |
|
0,488069559 |
|
-0,26716787 |
|
-0,22090169 |
|
0,000236054 |
|
0,671950496 |
|
-0,67218655 |
|
-0,45405303 |
|
0,812496497 |
|
-0,35844347 |
Obliczamy mo:
gdzie m: ilość obserwacji i n: ilość niewiadomych
m0= |
0,906375606 |
Błędy wyrównanych współrzędnych obliczamy ze wzoru:
mB2 = |
0,0017 |
mB3 = |
0,0023 |
mL3 = |
0,0043 |
mB4 = |
0,0016 |
mL4 = |
0,0043 |
mL2 = |
0,0000 |
mL2 = P21/Q21*mB2
9. Kontrola obliczeń.
Obliczenie wyrównanych obserwacji:
Obserwacje wyrównane |
|
||||
|
|
liczba |
[ º ] |
[ ' ] |
[ " ] |
S1-2 |
24209,535 |
||||
K1-2 |
-0,0000006661 |
-3,8166E-05 |
0 |
0 |
-0,1374 |
K1-3 |
0,6346897936 |
36,36504648 |
36 |
21 |
54,1673 |
K1-4 |
1,5531819311 |
88,99076947 |
88 |
59 |
26,7701 |
K2-3 |
0,0000023662 |
0,000135575 |
0 |
0 |
0,4881 |
K2-4 |
0,9106959944 |
52,1790369 |
52 |
10 |
44,5328 |
K2-1 |
1,5190641816 |
87,03596642 |
87 |
2 |
9,4791 |
K3-4 |
0,0000000011 |
6,55706E-08 |
0 |
0 |
0,0002 |
K3-1 |
0,6123743272 |
35,08646443 |
35 |
5 |
11,2720 |
K3-2 |
1,6002198039 |
91,68584106 |
91 |
41 |
9,0278 |
K4-1 |
-0,0000022013 |
-0,000126126 |
0 |
0 |
-0,4541 |
K4-2 |
0,9800446144 |
56,15242014 |
56 |
9 |
8,7125 |
K4-3 |
1,6107286919 |
92,28795599 |
92 |
17 |
16,6416 |
Kontrola kierunków polega na utworzeniu czterech trójkątów pomiędzy punktami kolejno: trójkąt 124 , 234 , 123 , 134. Suma kątów w każdym trójkącie jest równa 180o+eksces.Kąty otrzymujemy z różnicy kierunków, ich sumę w trójkącie sprawdzamy obliczając niezależnie eksces.
Obliczenie kątów z kierunków |
|
||||
|
|
liczba |
|
|
|
α = |
0,634690459755220 |
36,3650846412 |
36 |
21 |
54,3047 |
β = |
0,608368187231433 |
34,8569295184 |
34 |
51 |
24,9463 |
γ = |
0,910693628158445 |
52,1789013229 |
52 |
10 |
44,0448 |
δ = |
0,987845476745366 |
56,5993766286 |
56 |
35 |
57,7559 |
ζ = |
0,612374326055055 |
35,0864643651 |
35 |
5 |
11,2717 |
ξ = |
0,630684077555130 |
36,1355358500 |
36 |
8 |
7,9291 |
η = |
0,980046815681018 |
56,1525462638 |
56 |
9 |
9,1665 |
ε = |
0,918492137476110 |
52,6257229933 |
52 |
37 |
32,6028 |
trójkąt |
suma kątów |
eksces |
|
|
|
123 |
180,0002921111 |
1,0516 |
180 |
0 |
1,0516 |
134 |
180,0002694722 |
0,9701 |
180 |
0 |
0,9701 |
124 |
180,0002834167 |
1,0203 |
180 |
0 |
1,0203 |
234 |
180,0002781667 |
1,0014 |
180 |
0 |
1,0014 |
Obliczamy azymuty z wyrównanych współrzędnych metodą Gauss'a:
Obliczamy sumy kątów w trójkątach i porównujemy eksces:
trójkąt |
suma kątów |
eksces |
|
|
|
123 |
180,000292 |
1,0517 |
180 |
0 |
1,0517 |
134 |
180,000269 |
0,9700 |
180 |
0 |
0,9700 |
124 |
180,000283 |
1,0203 |
180 |
0 |
1,0203 |
234 |
180,000278 |
1,0015 |
180 |
0 |
1,0015 |
A1 - 2 = |
0 |
9 |
57,7133 |
0,166031465 |
0,002897796 |
A2 - 1 = |
180 |
10 |
0,8171 |
180,1668936 |
3,144505497 |
A1 - 3 = |
36 |
31 |
52,0512 |
36,53112533 |
0,6375884 |
A3 - 1 = |
216 |
44 |
34,5491 |
216,7429303 |
3,7828778 |
A1 - 4 = |
89 |
9 |
24,6215 |
89,15683931 |
1,5560804 |
A4 - 1 = |
269 |
21 |
36,8448 |
269,3602347 |
4,701223 |
A2 - 3 = |
93 |
7 |
51,8220 |
93,13106166 |
1,6254437 |
A3 - 2 = |
273 |
20 |
32,2678 |
273,3422966 |
4,7707231 |
A2 - 4 = |
145 |
18 |
35,8382 |
145,309955 |
2,5361372 |
A4 - 2 = |
325 |
30 |
45,9778 |
325,5127716 |
5,6812696 |
A3 - 4 = |
181 |
39 |
23,2461 |
181,6564572 |
3,1705033 |
A4 - 3 = |
361 |
38 |
53,9414 |
361,6483171 |
6,3119539 |
13
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