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Date
initiale n 2 Date
adaptate
P1 569669,754 398653,565 627,760 P1 569671,754 398655,565 629,760
P2 572686,021 395381,647 749,710 P2 572688,021 395383,647 751,71
P3 576980,419 398163,703 720,860 P3 576982,419 398165,703 722,86
P4 575499,614 402493,156 672,560 P4 575501,614 402495,156 674,56
P5 572165,113 403841,834 474,439 P5 572167,113 403843,834 476,439
P6 571988,145 400620,942 609,000 P6 571990,145 400622,942 611,000
1.1.1. Stabilirea numarului ecuatiilor de conditie
Numrul condiiilor geometrice ´r´ se stabilete în funcie de natura reelei (frconstrângeri, cu constrângeri) i este dat de diferena dintre numrul observaiilor
efectuate´ne´ i numrul observaiilor strict necesar´nsn´
e sn
r n n!
Scrierea cond geometrice
Intr-o reea de triangulaie independent se formeaz urmtoarele condiii : condiia de figur - Suma unghiurilor interioare ale triunghiurilor plane trebuie s fie
egal cu 200g.
condiia de tur de orizont (de staie)- Suma unghiurilor situate în jurul unui punct icare formeaz un tur de orizont complet trebuie s fie egal cu 400
g.
condiia de pol sau de laturi - . Rezolvarea succesiv a triunghiurilor care au vârf comun, cu începere de la o latur i finalizare pe aceeai latur, trebuie s conducctre aceeai valoare.
2( 2) 2 4r p p[ [! ! =17-26+4=9
= numrul unghiurilor msurate
2(p-2)-numrul strict necesar de unghiuri msurate pentru determinarea unui numr de (p-2) puncte din reea;
p ± numrul total de puncte ;r ± numrul total al condiiilor geometrice
1 1 1w = l - p + l =11-6+1=6
1l numrul laturilor cu viz dubl ;
p1 ± numrul punctelor staionabile ;w1 ± numrul condiiilor de figur .
Numrul ecuaiilor de pol sau de laturi:{1 2( 2)} s = l p l - 2 p+3 ! =11-2*6+3=2
s= numrul ecuaiilor de pol sau de laturil=nr.tot de laturi
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1.1.2 . Scrierea conditiilor geometrice1= 02= 3= 4=
5=
6 =
Cond. Geometrice nelineare
1.1.3. Scrierea ecuatiilor de corectie ()= +
()=+
()=+ .....................
()=+
Cond. de pol si de fig.
=
= =
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=* = *
= = Tabel
de
calcul acoef ec de pol
Triunghi Den. Unghi Val. Unghi Sin Ctgi=di W unghiuri din autocad
1
1 48,3276 0,6882892 1,05397 unghi valoare
2 38,9832 0,5747893 1,423655 1 48,3274
3 71,8342 0,9037151 0,473749 2 38,983
4 40,8557 0,5986061 1,338181 3 71,834
[ ] 200,0007 7 4 40,8555
2
1 48,3276 0,6882892 1,05397 5 24,8593
2 38,9832 0,5747893 1,423655 6 62,4512
7 63,6328 0,8412233 0,64274 7 63,6326
8 49,0572 0,6965577 1,030066 8 49,057
[ ] S 200,0008 8 9 26,6627
3
3 71,8342 0,9037151 0,473749 10 148,2919
4 40,8557 0,5986061 1,338181 11 25,0454
5 24,8595 0,3806435 2,429364 12 79,026
6 62,4514 0,8310452 0,669283 13 65,3221
[ ] S 200,0008 8 14 55,6519
4
9 26,6629 0,4066826 2,246394 15 89,7967
10 148,2921 0,7258201 -0,947734 16 49,9011
11 25,0456 0,3833451 2,409331 17 60,3023
[ ] S 200,0006 6
5
12 79,0262 0,9462186 0,341917
13 65,3223 0,8552745 0,605858
14 55,6521 0,7670184 0,836519
[ ] S 200,0006 6
6
15 89,7969 0,9871842 0,161656
16 49,9013 0,706010 1,003106
17 60,3025 0,8118008 0,719308
[ ] S 200,0007 7 w1 7
6 62,4514 0,8310452 0,669283 w2 8
7 63,6328 0,8412233 0,64274 w3 8
10 148,2921 0,7258201 -0,947734 w4 6
13 65,3223 0,8552745 0,605858 w5 6
17 60,3025 0,8118008 0,719308 w6 7
[ ] S 400,0011 11 w7 11
4+5 65,7152 0,8584562 0,597453 w8 0,935204
1+8 97,3848 0,9991564 0,041103 w9 1,1583957
P1= 0,199173818 P 1= 0,187444
P2= 0,199173525 P 2= 0,187444
W8= 0,935203988 W9= 1,158396
636619,7724
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1.1.4 . Sist de ecuatii de normale
........................................................
[aa]k1+[ab]k2+...+[ai]k 9+w1=0[bb]k2+...+[ah]k 9+w2=0
...........................s[hh]k 9+w9=0
1.1.5. Calculul coeficientilor ecuatiilor normale
a b c d e f g h i S
a1
...
an
b1
...
bn
c1
...
cn
d1
...
dn
e1
...
en
f1
...
fn
g1
...
gn
h1
...
gn
i1
...
in
s1
...
sn
[a] [b] [c] [d] [e] [f] [g] [h] [i] [s]
[aa] [ab] [ac] [ad] [ae] [af] [ag] [ah] [ai] [as]
[bb] [bc] [bd] [be] [bf] [bg] [bh] [bi] [bs]
[cc] [cd] [ce] [cf] [cg] [ch] [ci] [cs]
[dd] [de] [df] [dg] [dh] [di] [ds]
[ee] [ef] [eg] [eh] [ei] [es]
[ff] [fg] [fh] [fi] [fs]
[gg] [gh] [gi] [gs]
[hh] [hi] [hs]
[ii] [is]
[ss]
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1.1.5.
Calc coef ecuatiilor
normale
1 2 3 4 5 6 7 8 9
Nr crt a b c d e f g h i S
1 1 1 0 0 0 0 0 1,05397 0,041103 3,095073
2 1 1 0 0 0 0 0 -1,42365 -1,42365 -0,84731
3 1 0 1 0 0 0 0 0,473749 0,473749 2,947499
4 1 0 1 0 0 0 0 -1,33818 -0,59745 0,064366 5 0 0 1 0 0 0 0 2,429364 -0,59745 2,831912
6 0 0 1 0 0 0 1 -0,66928 0 1,330717
7 0 1 0 0 0 0 1 0,64274 0 2,64274
8 0 1 0 0 0 0 0 -1,03007 0,041103 0,011036
9 0 0 0 1 0 0 0 0 -2,24639 -1,24639
10 0 0 0 1 0 0 1 0 0 2
11 0 0 0 1 0 0 0 0 2,409331 3,409331
12 0 0 0 0 1 0 0 0 -0,34192 0,658083
13 0 0 0 0 1 0 1 0 0 2
14 0 0 0 0 1 0 0 0 0,836519 1,836519
15 0 0 0 0 0 1 0 0 -0,16166 0,838344
16 0 0 0 0 0 1 0 0 1,003106 2,003106
17 0 0 0 0 0 1 1 0 0 2
[ ] 4 4 4 3 3 3 5 0,138638 -0,56362 25,57502
4 2 2 0 0 0 0 -1,23412 -1,50626 5,259628
4 0 0 0 0 1 -0,75701 -1,34145 4,90154
4 0 0 0 1 0,895649 -0,72116 7,174493
3 0 0 1 0 0,162936 4,162936
3 0 1 0 0,494602 4,494602
3 1 0 0,841449 4,841449
5 -0,02654 0 9,973457
12,97672 1,600283 13,45498
15,6687 15,19911
69,46219
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1.1.6.Rezolvarea sistemului normal al corelatelor prin metoda gauss doolittle
K 1 K 2 K 3 K 4 K 5 K6 K7 K8 K9 W
K 1
K 2
K 3 [dd]
[dd 3 ]
K4 [ee]
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K5
K 6
K 7
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K8
K 9
[VV]
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a b c d e f g h i W S
4 2 2 0 0 0 0 -1,23412 -1,50626 7 12,25963
-1 -0,5 -0,5 0 0 0 0 0,308529 0,376564 -1,75 -3,06491
K 1= 4 0 0 0 0 1 -0,75701 -1,34145 8 12,90154
0,444926 -1 -1 0 0 0 0 0,617058 0,753128 -3,5 -6,12981
3 -1 0 0 0 1 -0,13995 -0,58832 4,5 6,771726
-1 0,333333 0 0 0 -0,33333 0,046651 0,196107 -1,5 -2,25724
K 2= 4 0 0 0 1 0,895649 -0,72116 8 15,17449
-
2,24627 -1 0 0 0 0 0,617058 0,753128 -3,5 -6,12981
-0,33333 0 0 0 0,333333 -0,04665 -0,19611 1,5 2,257242
2,666667 0 0 0 1,333333 1,466056 -0,16414 6 11,30192
-1 0 0 0 -0,5 -0,54977 0,061551 -2,25 -4,23822
k3= 3 0 0 1 0 0,162936 6 10,16294
-2,23066 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
3 0 0 1 0 0,162936 6 10,16294
-1 0 0 -0,33333 0 -0,05431 -2 -3,38765
K 4= 3 0 1 0 0,494602 6 10,4946
-
1,97247 0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
3 0 1 0 0,494602 6 10,4946
-1 0 -0,33333 0 -0,16487 -2 -3,4982
K 5= 3 1 0 0,841449 7 11,84145
-
1,95896 0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
3 1 0 0,841449 7 11,84145
-1 -0,33333 0 -0,28048 -2,33333 -3,94715
K 6= 5 -0,02654 0 11 20,97346
-
2,27815 0 0 0 0 0
-0,33333 0,046651 0,196107 -1,5 -2,25724
-0,66667 -0,73303 0,082068 -3 -5,65096
-0,33333 0 -0,05431 -2 -3,38765
-0,33333 0 -0,16487 -2 -3,4982
-0,33333 0 -0,28048 -2,33333 -3,94715
3 -0,71292 -0,22149 0,166667 2,232259
-1 0,23764 0,073829 -0,05556 -0,74409
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K 7= 12,97672 1,600283 0,935204 14,39018
-0,06265 -0,38076 -0,46472 2,159704 3,782452
-0,00653 -0,02745 0,209929 0,315906
-0,806 0,090237 -3,29863 -6,21347
0 0 0 0
0 0 0 0
0 0 0 0
-0,16942 -0,05263 0,039607 0,530474
11,61401 1,145716 0,045817 12,80555
-1 -0,09865 -0,00394 -1,10259
K 8= 15,6687 1,158396 16,3575
0,008117 -0,5672 2,635947 4,616533
-0,11537 0,882482 1,327984
-0,0101 0,369305 0,695643
-0,00885 -0,32587 -0,55197
-0,08154 -0,9892 -1,73022 -0,23601 -1,96338 -3,32133
-0,01635 0,012305 0,164806
-0,11302 -0,00452 -1,26326
14,52024 1,775458 16,29569
-1 -0,12227 -1,12227
K 9=
-0,12227
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1.1.7. Calculul corectiilor elementelor masurate .................................................. =>
(
)=
+
()=+
()=+ .....................
()=+
1.1.7 Calcularea corectiilor elementelor masurate
K 1 K 2 K 3 K 4 K 5 K 6 K 7 K 8 K 9
0,444926 -2,24627 -2,23066 -1,97247 -1,95896 -2,27815 -0,06265 0,008117 -0,12227
a b c d e f g h i v v v w kw
1 1 1 0 0 0 0 0 1,05397 0,041103 -1,79781 3,232135 7 3,114481
2 1 1 0 0 0 0 0 -1,42365 -1,42365 -1,63882 2,685741 8 -17,9702
3 1 0 1 0 0 0 0 0,473749 0,473749 -1,83982 3,38493 8 -17,8453
4 1 0 1 0 0 0 0 -1,33818 -0,59745 -1,72355 2,970608 6 -11,8348
5 0 0 1 0 0 0 0 2,429364 -0,59745 -2,13789 4,570567 6 -11,7537
6 0 0 1 0 0 0 1 -0,66928 0 -2,29875 5,284245 7 -15,9471
7 0 1 0 0 0 0 1 0,64274 0 -2,30371 5,307062 11 -0,68919
8 0 1 0 0 0 0 0 -1,03007 0,041103 -2,25966 5,106049 0,935204 0,007591
9 0 0 0 1 0 0 0 0 -2,24639 -1,6978 2,882515 1,158396 -0,14164
10 0 0 0 1 0 0 1 0 0 -2,03513 4,141747
11 0 0 0 1 0 0 0 0 2,409331 -2,26707 5,139627
12 0 0 0 0 1 0 0 0 -0,34192 -1,91715 3,675458
13 0 0 0 0 1 0 1 0 0 -2,02161 4,086908
14 0 0 0 0 1 0 0 0 0,836519 -2,06124 4,248716
15 0 0 0 0 0 1 0 0 -0,16166 -2,25839 5,100308
16 0 0 0 0 0 1 0 0 1,003106 -2,40081 5,763875
17 0 0 0 0 0 1 1 0 0 -2,34081 5,479376
1.1.8. Verificarea cond geometrice:
1=
0
2= 3= 4= 5= 6 =
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1.1.8 Verificarea conditiilor geometrice
v v^2 v/10^4 Unghiuri compensate
v1 -1,797813953 3,232135 -0,00018 1= 48,3274
v2 -1,638823075 2,685741 -0,00016 2= 38,9830
v3 -1,839817856 3,38493 -0,00018 3= 71,8340
v4 -1,723545115 2,970608 -0,00017 4= 40,8555
v5 -2,137888383 4,570567 -0,00021 5= 24,8593v6 -2,298748646 5,284245 -0,00023 6= 62,4511701
v7 -2,303706155 5,307062 -0,00023 7= 63,6325696
v8 -2,259656817 5,106049 -0,00023 8= 49,056974
v9 -1,697797139 2,882515 -0,00017 9= 26,6627302
v10 -2,035128313 4,141747 -0,0002 10= 148,291896
v11 -2,267074548 5,139627 -0,00023 11= 25,0453733
v12 -1,917148473 3,675458 -0,00019 12= 79,0260083
v13 -2,021610218 4,086908 -0,0002 13= 65,3220978
v14 -2,061241308 4,248716 -0,00021 14= 55,6518939
v15 -2,258386206 5,100308 -0,00023 15= 89,7966742
v16 -2,400807125 5,763875 -0,00024 16= 49,9010599
v17 -2,340806669 5,479376 -0,00023 17= 60,3022659
Triunghi Den. Unghi Val. Unghi
1
1 48,3274
2 38,9830
3 71,8340
4 40,8555
[ ] 200,0000
2
1 48,3274
2 38,9830
7 63,63257
8 49,056974
[ ] S 200,0000
3
3 71,8340
4 40,8555
5 24,8593
6 62,45117
[ ] S 200,0000
4
9 26,66273
10 148,2919
11 25,045373
[ ] S 200,0000
5
12 79,026008
13 65,322098
14 55,651894
[ ] S 200,0000
6
15 89,796674
16 49,90106
17 60,302266
[ ] S 200,0000
6 62,45117
7 63,63257
10 148,2919
13 65,322098
17 60,302266
[ ] S 400,0000
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1.1.9 .Verif matriceala a corectiilor
v= w=
Sist matriceal de ecuatie *v=w
F=[vv]->minim
F=*v-2(v-w)=v-2*v-2*w
F=*v-2Bk+2*w=min
=0 => v-Bh=0 =>v=Bk => v=B* *w
=>*Bk =w k = *w =>=
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1.1.8. Verificarea matriciala a corelatelor si corectiilor
B 1 1 0 0 0 0 0 1,05
1 1 0 0 0 0 0 -1,4
1 0 1 0 0 0 0 0,47
1 0 1 0 0 0 0 -1,30 0 1 0 0 0 0 2,43
0 0 1 0 0 0 1 -0,7
0 1 0 0 0 0 1 0,64
0 1 0 0 0 0 0 -1
0 0 0 1 0 0 0 0
0 0 0 1 0 0 1 0
0 0 0 1 0 0 0 0
0 0 0 0 1 0 0 0
0 0 0 0 1 0 1 0
0 0 0 0 1 0 0 0
0 0 0 0 0 1 0 0
0 0 0 0 0 1 0 0
0 0 0 0 0 1 1 0
BT
1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0
0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1
0 0 0 0 0 1 1 0 0 1 0 0 1 0 0 0
1,05397
-
1,4 0,5
-
1,3 2,43
-
0,7 0,64 -1 0 0 0 0 0 0 0 0
0,041103
-
1,4 0,5
-
0,6 -0,6 0 0 0,04
-
2,2 0 2,409331 -0,34192 0 0,836519 -0,16166 1,003106
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B*Bt
4,00 2,00 2,00 0,00 0,00 0,00
2,00 4,00 0,00 0,00 0,00 0,00
2,00 0,00 4,00 0,00 0,00 0,00
0,00 0,00 0,00 3,00 0,00 0,00
0,00 0,00 0,00 0,00 3,00 0,00
0,00 0,00 0,00 0,00 0,00 3,00
0,00 1,00 1,00 1,00 1,00 1,00
-1,23 -0,76 0,90 0,00 0,00 0,00
-1,51 -1,34 -0,72 0,16 0,49 0,84
(B*BT)-1
0,637165 -0,34748 -0,376453687 -0,061782493 -0,063292915 -0,064872475
-0,34748 0,466843 0,22431605 0,056294234 0,054734097 0,053102546
-0,37645 0,224316 0,497387756 0,059672041 0,058982282 0,058260949
-0,06178 0,056294 0,059672041 0,371258868 0,038466938 0,039033124
-0,06329 0,054734 0,058982282 0,038466938 0,373183426 0,041296561
-0,06487 0,053103 0,058260949 0,039033124 0,041296561 0,376996941 0,183121 -0,17118 -0,180032691 -0,112978684 -0,113362317 -0,11376351
0,064998 -0,02339 -0,058183109 -0,006337404 -0,0055863 -0,004800814
0,013662 0,014112 0,00623905 -0,004897131 -0,012510997 -0,020473386
W (-w) K =(B*B)-1W
w1 7 -7 0,44
w2 8 -8 -2,25
w3 8 -8 -2,23
w4 6 -6 -1,97
w5 6 -6 -1,96
w6 7 -7 -2,28
w7 11 -11 -0,06
w8 0,935204 -0,935203988 0,01
w9 1,158396 -1,158395714 -0,12
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1.2
Calculul
orientarilor
x y cadran Do
P 2- P 3 4294,398 2782,056 1 36,59614 5116,805
P 2- P 6 -697,876 5239,295 2 108,4302 5285,569
P 2- P 1 -3016,267 3271,918 2 147,4132 4450,091
P 3- P 4 -1480,805 4329,453 2 120,9803 4575,691
P 3- P 6 -4992,274 2457,239 2 170,8813 5564,245
P 3- P 1 -7310,665 489,862 2 195,7406 7327,059
P 3- P 2 -4294,398 -2782,056 3 236,5961 5116,805
P 4- P 5 -3334,501 1348,678 2 175,5317 3596,919
P 4- P 6 -3511,469 -1872,214 3 231,1836 3979,397
P 4- P 3 1480,805 -4329,453 4 320,9803 4575,691
P 5- P 1 -2495,359 -5188,269 3 271,4602 5757,165
P 5- P 6 -176,968 -3220,892 3 296,5057 3225,75
P 5- P 4 3334,501 -1348,678 4 375,5317 3596,919
P 6- P 4 3511,469 1872,214 1 31,18361 3979,397
P 6- P 5 176,968 3220,892 1 96,50568 3225,75
P 6- P
1 -2318,391 -1967,377 3 244,7976 3040,643P 6- P 2 697,876 -5239,295 4 308,4302 5285,569
P 6- P 3 4992,274 -2457,239 4 370,8813 5564,245
P 1- P 2 3016,267 -3271,918 3 347,4132 4450,091
P 1- P 3 7310,665 -489,862 3 395,7406 7327,059
P 1- P 4 5829,86 3839,591 1 37,0769 6980,668
P 1- P 5 2495,359 5188,269 1 71,46025 5757,165
P 1- P 6 2318,391 1967,377 1 44,79755 3040,643
V V(gauss)
-1,7978 -1,7978
-1,6388 -1,6388
-1,8398 -1,8398
-1,7235 -1,7235
-2,1379 -2,1379
-2,2987 -2,2987
-2,3037 -2,3037
-2,2597 -2,2597
-1,6978 -1,6978
-2,035128313 -2,035128313
-2,267074548 -2,267074548
-1,917148473 -1,917148473
-2,021610218 -2,021610218
-2,061241308 -2,061241308
-2,258386206 -2,258386206
-2,400807125 -2,400807125
-2,340806669 -2,340806669
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P1-P2 347,4132
P2-P3 36,5961
P3-P4 120,9803
P4-P5 175,5317
P5-P6 296,5057 P6-P1 244,7976
1.3.Calculul laturilor
Denutr.
DenumUnghi ValoarUnghi sin Modul ValoareLatura
Denumlatura
1 1 48,3274 0,688287198
6465,457262
4450,091 P1-P2
2+3 110,8170521 0,985599337 5116,804644 P2-P34 40,85552765 0,598603903 7327,058586 P3-P1
2 1+8 97,38439425 0,999156096
4453,850085
4450,091461 P1-P2
2 38,98303612 0,574787221 5285,569317 P2-P6
7 63,63256963 0,841221311 3040,642874 P6-P1
3 3 71,83401602 0,903713857
5661,974315
5116,804644 P2-P3
4+5 65,71481386 0,858453049 5564,24507 P3-P6
6 62,45117013 0,831043235 5285,569317 P6-P2
4 9 26,66273022 0,406680155
7931,909011
3225,749982 P5-P6
10 148,2918965 0,725822259 3040,642874 P6-P1
11 25,04537329 0,383341804 5757,165253 P1-P5
5 12 79,02600829 0,946217612
3801,365951
3596,919413 P4-P5
13 65,32209784 0,855272822 3225,749982 P5-P614 55,65189388 0,767016282 3979,396914 P6-P4
6 15 89,79667416 0,987183678
4635,095726
4575,691 P3-P4
16 49,90105992 0,70600698 3979,396914 P4-P6
17 60,30226592 0,811798659 5564,24507 P6-P3
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1.4.Calculul coordonatelor
Puncte
Cadran D X' Y'
Punct
c
cos x' y'
S V sin Cx Cy
[D] x y
569671,754 398655,565 P1
P1 0,677798878
347,4132
-0,73524736
P2 4450,091461 572688,021 395383,647 P2
5116,804644 4294,398 2782,056
P2 P1 0,839273371 576982,419 398165,703
36,59610,543709673
P3 9566,896106 576982,419 398165,703 P3
4575,690847 -1480,804 4329,453
P3 P2 -0,323624224 575501,615 402495,156
120,9803
0,946185691
P4 14142,58695 50869745,566 402495,156 P4
3596,919413 -3334,501 1348,679
P4 P3 -0,92704344 572167,114 403843,836
175,5317
0,374953945
P5 17739,50637 572167,114 403843,836 P5
3225,749982 -176,970 -3220,892
P5 P4 -0,054860847 571990,144 400622,943
296,5057-0,99849401
P6 20965,25635 571990,144 400622,943 P6
3040,642874 -2318,390 -1967,378
P6 P5 -0,762466983 569671,754 398655,565
244,7976
-0,647027124
P1 24005,89922 569671,754 398655,565 P1
Punct x y z
P1 569671,754 398655,565 629,760
P2 572688,021 395383,647 751,710
P3 576982,419 398165,703 722,860P4 575501,614 402495,156 674,560
P5 572167,113 403843,834 476,439
P6 571990,145 400622,942 611,000
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2.Verificarea altimetrica a retelei
2.1. Calcularea cotelor retelei prin nivelmentul trigonometric unilateral
=h+-+C
h= =D*ctgZ P2
tg=
Z=100-
Calculul unghiului zenital
Puncte Z D [D] i S C h' Z' Z
Statie Viza
629,760
P1 P2 98,24833 4449,3563 4449,356 1,55 3,6 1,334484 121,74017 751,500 751,710
P2 P3 100,3512 5116,261 9565,617 1,47 4,1 1,764511 -29,09111 722,40906 722,860
P3 P4 100,6491 4572,4644 14138,08 1,7 5 1,409352 -48,51549 673,89357 674,560
P4 P5 103,4723 3606,1918 17744,27 1,62 3,9 0,87663 -
198,29144 475,60213 476,439
P5 P6 97,30595 3226,6486 20970,92 1,58 4,5 0,701814 134,40867 610,01080 611,000
P6 P1 99,54991 3040,0606 24010,98 1,5 5 0,622993 18,61673 628,62753 629,760
Wh= 1,13247
Ch= 0,00005
T=0,2sqrt([D]km) 0,9800201
Puncte Z D [D] i S C h' Z' Z
Statie Viza
P1 P2
P2 P3
P3 P4 P4 P5
P5 P6
P6 P1
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HB = HA + (hAB
(hAB = D*ctg.Z+i-S+C , unde:
unde:
i ± înalimea aparatului
S ± înalimea semnalului
C ± corecia de sfericitate i refracie
R
Dk C
2)1(
2
!
unde :
k ± coeficientul de refracie ( k =0,14)
R = 6378,975 km (raza medie în punctul central de proiecie) N M R *!
D ± lungimea vizei
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P6
P1
P2
P3
P4
P5
IV
III
II
I
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Indesirea retelei de triangulatie
3.2I ndesirea simultana a 2 puncte3.1.1.Indesirea provizorie a punctelor Psi Q3.1.2.Calculul corectiilor
3.1.1. Indesirea provizorie a punctelor Psi Q
=
P= =
=
Q = =
3.1.2 .Calculul corectiilor
()=+ Unde:(xP), (yP), (xQ), (yQ) - valoarea cea mai probabil acoordonatelor, ()=
xP , yP , xQ ,yQ - valoarea provizorie a coordonatelor punctului,
()=+dxP dyP , dxQ ,dyQ - coreciile coordonatelor
()=+ dxP , dyP , dxQ ,dyQ - coreciile coordonatelor
1.
2.
3.
4.+=
=
= -( )
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Ecuatii:
-
- +=
-
-
+
=
-
-
-
-
-+
-+
- -
-
-
-
-
- -
-
-
-
-
-
-
-
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Regula 1-3 Schreiber
P=1
` P=-1
P=1
` P=-1
P=1
` P=-1
P=1
` P=-1
P=1
` P=-1
- P=1
P - P=1
- P=1
P=-1
- P=1
P - P=1
- P=1
P=-1
[pvv]-minim
[paa]+[pab]+[pac]+[pad]+[pal]=0
[pbb]+[pbc]+[pbd]+[pbl]=0
[pcc]+[pcd]+[pcl]=0
[pdd]+[pdl]=0
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Nr.crt Nr.viza P a b c d l S
1 2 1
2 [] -1 ... ... ... ... ... ...
... ... ... ... ... ... ... ... ...
... 25 1 ... ... ... ... ... ...
18 [] -1
[] [a] [b] [c] [d] [l] [s]
[paa] [pab] [pac] [pad] [pal] [pas]
[pbb] [pbc] [pbd] [pbl] [pbs]
[pcc] [pcd] [pcl] [pcs]
[pdd] [pdl] [pds]
[pll] [pls]
[pss]
=±
( )=+ P =+
( )=+
Q =+
= =
=
= =
=
= ±
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Calculul coeficientilor de directie
tg sin D=x/cos a Control
Punct X Y Nr.viza ctg cos D=y/sin b a/b= - tg
D=sqrt(x2+y2)
b/a= -
ctg
P1 569671,754 398655,565
1
-1,084757 -0,73525 4450,091 105,1828 1,084757
P2 572688,021 395383,647 -0,921865 0,677799 4450,091 96,96434 0,921865
3016,267 -3271,918 347,413198 4450,091
P1 569671,754 398655,565
2
-0,262484 -0,25388 2477,319 65,24287 0,262484
P 572067,903 398026,614 -3,809755 0,967235 2477,319 248,5593 3,809755
2396,149 -628,951 383,658387 2477,319
P1 569671,754 398655,565
3
0,848596 0,647027 3040,643 -135,468
-
0,848596
P6 571990,145 400622,942 1,17841725 0,762467 3040,643 159,6379
-
1,178417
2318,391 1967,377 44,7975533 3040,643
P1 569671,754 398655,565
4
2,07916737 0,901185 5757,165 -99,6518
-
2,079167
P5 572167,113 403843,834 0,48096176 0,433435 5757,165 47,92871
-
0,480962
2495,359 5188,269 71,4602498 5757,165
P2 572688,021 395383,647
5
0,64783376 0,54371 5116,805 -67,647
-
0,647834
P3 576982,419 398165,703 1,54360588 0,839273 5116,805 104,4203
-
1,543606
4294,398 2782,056 36,5961431 5116,805
P2 572688,021 395383,647
6
-7,507487 0,991245 5285,569 -119,39 7,50749
P6 571990,145 400622,942 -0,13320 -0,13203 5285,569 -15,9028 0,13320
-697,876 5239,295 108,430175 5285,569
P2 572688,021 395383,647
7
-4,262039 0,973561 2714,741 -228,305 4,262039
P 572067,903 398026,614 -0,234629 -0,22843 2714,741 -53,567 0,234629
-620,118 2642,967 114,671591 2714,741
P2 572688,021 395383,647
8
-1,084757 0,735247 4450,091 -105,183 1,084757
P1 569671,754 398655,565 -0,921865 -0,6778 4450,091 -96,9643 0,921865
-3016,267 3271,918 147,413198 4450,091
P3 576982,419 398165,7039
-
119,756424 0,999965 177342,1 -3,58966 119,7564
P4 575501,614 575501,614 -0,008350 -0,00835 177342,1 -0,02997 0,00835
-1480,805 177335,911 100,531583 177342,1P3 576982,419 398165,703
10
-1,216434 0,772481 3732,267 -131,764 1,216434
Q 574612,289 401048,809 -0,822075 -0,63504 3732,267 -108,32 0,822075
-2370,13 2883,106 143,803085 3732,267
P3 576982,419 398165,703
11
-0,492208 0,441612 5564,245 -50,526 0,492208
P6 571990,145 400622,942 -2,0316599 -0,89721 5564,245 -102,652 2,03166
-4992,274 2457,239 170,881337 5564,245
P3 576982,419 398165,703 12 0,64783376 -0,54371 5116,805 67,64697 -0,64783
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P2 572688,021 395383,647 1,54360588 -0,83927 5116,805 -104,42 -1,54361
-4294,398 -2782,056 236,596143 5116,805
P4 575501,614 575501,614
13
-51,479301 0,999811 171690,2 -3,70726 51,4793
P5 572167,113 403843,834 -0,019425 -0,01942 -171690 -0,07201 0,019425
-3334,501 -171657,78 101,236496 171690,2
P4 575501,614 575501,61414
49,8021404 -0,9998 174913,9 3,638884 -49,8021
P6 571990,145 400622,942 0,02007946 -0,02008 174913,9 -0,07307 -0,02008
-3511,469 -174878,67 298,721874 174913,9
P4 575501,614 575501,614
15
196,163163 -0,99999 174455,1 3,649143 -196,163
Q 574612,289 401048,809 0,0050978 -0,0051 174455,1 -0,0186 -0,0051
-889,325 -174452,81 299,675467 174455,1
P4 575501,614 575501,61416
-
119,756424 -0,99997 177342,1 3,589659 119,7564
P3 576982,419 398165,703 -0,008350 0,00835 177342,1 0,029975 0,00835
1480,805 -177335,91 300,531583 177342,1
P5 572167,113 403843,83417
2,07916737 -0,90118 5757,165 99,65182 -2,07917P1 569671,754 398655,565 0,48096176 -0,43344 5757,165 -47,9287 -0,48096
-2495,359 -5188,269 271,46025 5757,165
P5 572167,113 403843,834
18
-1,143077 -0,75264 3713,63 129,0234 1,143077
Q 574612,289 401048,809 -0,874832 0,658433 3713,63 112,8737 0,874832
2445,176 -2795,025 345,756064 3713,63
P5 572167,113 403843,834
19
-51,479301 -0,99981 171690,2 3,707258 51,4793
P4 575501,614 575501,614 -0,019425 0,019422 -171690 0,072015 0,019425
3334,501 171657,78 301,236496 171690,2
P 572067,903 398026,614
20
-0,262484 0,253884 2477,319 -65,2429 0,262484
P1 569671,754 398655,565 -3,809755 -0,96723 2477,319 -248,559 3,809755 -2396,149 628,951 183,658387 2477,319
P 572067,903 398655,565
21
-5,276283 -0,98251 3330,164 187,8241 -5,27628
P2 572688,021 395383,647 -0,189527 0,186212 3330,164 -35,5978 -0,18953
620,118 -3271,918 311,924254 3330,164
P 572067,903 398026,614
22
1,18778951 0,764989 3950,641 -123,273 1,18779
Q 574612,289 401048,809 0,84190001 0,644044 3950,641 -103,783 0,8419
2544,386 3022,195 55,4510821 3950,641
Q 574612,289 401048,809
23
-1,216434 -0,77248 3732,267 131,7636 -1,21643
P3 576982,419 398165,703 -0,822075 0,635038 3732,267 -108,32 -0,82208
2370,13 -2883,106 343,803085 3732,267Q 574612,289 401048,809
24
-1,1430772 0,75264 3713,63 -129,023 -1,14308
P5 572167,113 403843,834 -0,8748315 -0,65843 3713,63 112,8737 -0,87483
-2445,176 2795,025 145,756064 3713,63
Q 574612,289 401048,809
25
1,18778951 -0,76499 3950,641 123,2729 1,18779
P 572067,903 398026,614 0,84190001 -0,64404 3950,641 103,7834 0,8419
-2544,386 -3022,195 255,451082 3950,641
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Calculul coeficientilor ecuatiei
echivalente
P Nr .
V izei Ponderea
P Q
li a b c d
P.S P.V
P1
P2 1 1 0,00000080845
P 2 1 65,242872 248,5593 0 0 -0,00000969570
P6 3 1 -0,00004377869
P5 4 1 0,00005266594
-1 32,621436 124,2797 0 0 0,00000000000
P2
P1 5 1 0,00004131910
P6 6 1 -0,00002658244
P 7 1 -228,3047408 -53,56702 0 0 -0,00001084297
P3 8 1 -0,00000389369
-1 -114,1523704 -26,78351 0 0 0,00000000000
P3
P4 9 1 -15,33655390494
Q 10 1 0 0 -131,76357 -108,31956 5,11214801591
P6 11 1 5,11219980331
P2 12 1 5,11220608571
-1 0 0 -65,881783 -54,159781 0,00000000000
P4
P5 13 1 -76,18665864421
P6 14 1 65,64681866539
Q 15 1 0 0 3,64914298 -0,0186026 32,88001189628
P3 16 1 -22,34017191746
-1 0 0 1,82457149 -0,0093013 0,00000000000
P5
P1 17 1 24,76511298743
Q 18 1 0 0 129,023397 112,87374 24,76502738724
P4 19 1 -49,53014037467-1 0 0 74,4916932 65,167682 0,00000000000
P
P1 20 1 -65,242872 -248,5593 0 0 0,91577965742
P2 21 1 187,824064 -35,5978 0 0 -1,83155398275
Q 22 1 0 0 -123,27287 -103,78343 0,91577432533
-1 70,77228418 -164,0582 -71,171626 -59,919393 0,00000000000
Q
P3 23 1 0 0 131,763566 -108,31956 0,00000795497
P5 24 1 0 0 -129,0234 112,87374 -0,00001293072
P 25 1 123,2728726 103,7834 0 0 0,00000497575
-1 71,17162619 59,91939 1,58203706 2,6293535 0,00000000000
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Rezolvarea sistemului normal de ecuatii prin Gauss-Dolittle
a] b] c] d] l] s]
86941,36 38775,64 4924,382404 4053,496933-
403,7519577 134291,1269
-1 -0,446-
0,056640273-
0,046623343 0,004643957-
1,544617258
dx P = 88933,47 -11771,08349 -9987,816906 -162,428184 105787,7819
-0,29989 -17293,8 -2196,26273-
1807,849901 180,0724038 -59893,5202
71639,63-
13967,34622-
11795,66681 17,64421988 45894,2617
-1 0,194966754 0,164652815-
0,000246291-
0,640626723
0,136353 68266,2122 102,3166684 2528,769567 64050,59735
dy P=-
278,9183622-
229,5911716 22,86862098-
7606,286047
-2723,168154
-2299,762869 3,440036276 8947,85523
65264,12568-
2427,037372 2555,078225 65392,16654
-1 0,037187924-
0,039149812-
1,001961887
-0,05039285 48940,86128 2145,919356 45254,77733
dx Q=-
188,9875793 18,82426615-
6261,101319-
1942,189741 2,905170466 7556,619367-
90,25648229 95,01805585 2431,798945
46719,42747 2262,666849 48982,09432
-1
-
0,048430963
-
1,048430963- 0,048430963 1725,567706 5834,076488
dy Q= -1,875007 623,642242
-0,004346 -11,303359
-100,030831-
2560,091000
-109,583134-
2372,249983
[ v v ]= 1514,074389 1514,074389
P unct Coordonatele provizorii Coordonate calc din Gauss x y x y
P 575501,6 14 402495 ,156 575501,6 11 402495 ,157
Q 57 2167 ,113 403843 ,834 57 2167 ,112 403843 ,834
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