of 30/30
1 Date initiale n 2 Date adaptate P1 569669,75 4 398653,56 5 627,760 P1 569671,754 398655,565 629,760 P2 572686,02 1 395381,64 7 749,710 P2 572688,021 395383,647 751,71 P3 576980,419 398163,70 3 720,860 P3 576982,419 398165,703 722,86 P4 575499,61 4 402493,15 6 672,560 P4 575501,614 402495,156 674,56 P5 572165,113 403841,83 4 474,439 P5 572167,113 403843,834 476,439 P6 571988,14 5 400620,94 2 609,000 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´n e´ i numrul observaiilor strict necesar´nsn´  e sn r n n !  Scrierea cond geometrice Intr-o reea de triangulaie independentse formeazurmtoarele condiii :       condiia de figur- Suma unghiurilor interioare ale triunghiurilor plane trebuie sfie egalcu 200 g .       condiia de tur de orizont (de staie)- Suma unghiurilor situate în jurul unui punct i care formeazun tur de orizont complet trebuie sfie egalcu 400 g .       condiia de pol sau de laturi - . Rezolvarea succesiva triunghiurilor care au vârf comun, cu începere de la o laturi finalizare pe aceeai latur, trebuie sconducctre aceeai valoare . 2( 2) 2 4 r 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 1 w =l - p + l =11-6+1=6 1 l numrul laturilor cu vizdubl;  p 1  ± numrul punctelor staionabile ; w 1 ± 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 laturi l=nr.tot de laturi

Proiect Final Geodezie Proiect

  • View
    245

  • Download
    1

Embed Size (px)

Text of Proiect Final Geodezie Proiect

  • 8/3/2019 Proiect Final Geodezie Proiect

    1/30

    1

    Date

    initiale n 2Date

    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 n funcie de natura reelei (frconstrngeri, cu constrngeri) i este dat de diferena dintre numrul observaiilor

    efectuatene i numrul observaiilor strict necesarnsn

    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 n 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 vrfcomun, cu ncepere 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 - 2p+3 ! =11-2*6+3=2

    s= numrul ecuaiilor de pol sau de laturil=nr.tot de laturi

  • 8/3/2019 Proiect Final Geodezie Proiect

    2/30

    2

    1.1.2. Scrierea conditiilor geometrice1= 02= 3= 4=

    5=

    6= Cond. Geometrice nelineare

    1.1.3.Scriereaecuatiilor de corectie()=+()=+()=+.....................

    ()=+Cond. de pol si de fig.

    = = =

  • 8/3/2019 Proiect Final Geodezie Proiect

    3/30

    3

    =* = *

    = = Tabel

    de

    calcul acoef ecde 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 P1= 0,187444

    P2= 0,199173525 P2= 0,187444

    W8= 0,935203988 W9= 1,158396

    636619,7724

  • 8/3/2019 Proiect Final Geodezie Proiect

    4/30

    4

    1.1.4. Sist de ecuatii de normale

    ........................................................

    [aa]k1+[ab]k2+...+[ai]k9+w1=0[bb]k2+...+[ah]k9+w2=0

    ...........................s[hh]k9+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]

  • 8/3/2019 Proiect Final Geodezie Proiect

    5/30

    5

    1.1.5.

    Calc coefecuatiilor

    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 0,0643665 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

  • 8/3/2019 Proiect Final Geodezie Proiect

    6/30

    6

    1.1.6.Rezolvarea sistemului normal al corelatelor prin metoda gauss doolittle

    K1 K2 K3 K4 K5 K6 K7 K8 K9 W

    K1

    K2

    K3 [dd]

    [dd3]

    K4 [ee]

  • 8/3/2019 Proiect Final Geodezie Proiect

    7/30

    7

    K5

    K6

    K7

  • 8/3/2019 Proiect Final Geodezie Proiect

    8/30

    8

    K8

    K9

    [VV]

  • 8/3/2019 Proiect Final Geodezie Proiect

    9/30

    9

    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

    K1= 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

    K2= 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

    K4= 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

    K5= 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

    K6= 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

  • 8/3/2019 Proiect Final Geodezie Proiect

    10/30

    10

    K7= 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

    K8= 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

    K9=

    -0,12227

  • 8/3/2019 Proiect Final Geodezie Proiect

    11/30

    11

    1.1.7.Calculul corectiilor elementelor masurate .................................................. =>

    (

    )=

    +

    ()=+()=+.....................

    ()=+1.1.7 Calcularea corectiilor elementelor masurate

    K1 K2 K3 K4 K5 K6 K7 K8 K9

    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=

  • 8/3/2019 Proiect Final Geodezie Proiect

    12/30

    12

    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

  • 8/3/2019 Proiect Final Geodezie Proiect

    13/30

    13

    1.1.9.Verif matriceala a corectiilor

    v=

    w=

    Sist matriceal de ecuatie *v=wF=[vv]->minim

    F=*v-2(v-w)=v-2*v-2*wF=*v-2Bk+2*w=min

    =0 => v-Bh=0 =>v=Bk=> v=B* *w

    =>*Bk=w k= *w =>=

  • 8/3/2019 Proiect Final Geodezie Proiect

    14/30

    14

    1.1.8. Verificarea matriciala a corelatelor sicorectiilor

    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

  • 8/3/2019 Proiect Final Geodezie Proiect

    15/30

    15

    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

  • 8/3/2019 Proiect Final Geodezie Proiect

    16/30

    16

    1.2

    Calculul

    orientarilor

    x y cadran Do

    P2-P3 4294,398 2782,056 1 36,59614 5116,805

    P2-P6 -697,876 5239,295 2 108,4302 5285,569

    P2-P1 -3016,267 3271,918 2 147,4132 4450,091

    P3-P4 -1480,805 4329,453 2 120,9803 4575,691

    P3-P6 -4992,274 2457,239 2 170,8813 5564,245

    P3-P1 -7310,665 489,862 2 195,7406 7327,059

    P3-P2 -4294,398 -2782,056 3 236,5961 5116,805

    P4-P5 -3334,501 1348,678 2 175,5317 3596,919

    P4-P6 -3511,469 -1872,214 3 231,1836 3979,397

    P4-P3 1480,805 -4329,453 4 320,9803 4575,691

    P5-P1 -2495,359 -5188,269 3 271,4602 5757,165

    P5-P6 -176,968 -3220,892 3 296,5057 3225,75

    P5-P4 3334,501 -1348,678 4 375,5317 3596,919

    P6-P4 3511,469 1872,214 1 31,18361 3979,397

    P6-P5 176,968 3220,892 1 96,50568 3225,75

    P6-P

    1 -2318,391 -1967,377 3 244,7976 3040,643P6-P2 697,876 -5239,295 4 308,4302 5285,569

    P6-P3 4992,274 -2457,239 4 370,8813 5564,245

    P1-P2 3016,267 -3271,918 3 347,4132 4450,091

    P1-P3 7310,665 -489,862 3 395,7406 7327,059

    P1-P4 5829,86 3839,591 1 37,0769 6980,668

    P1-P5 2495,359 5188,269 1 71,46025 5757,165

    P1-P6 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

  • 8/3/2019 Proiect Final Geodezie Proiect

    17/30

    17

    P1-P2 347,4132

    P2-P3 36,5961

    P3-P4 120,9803

    P4-P5 175,5317

    P5-P6 296,5057P6-P1 244,7976

    1.3.Calculullaturilor

    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

  • 8/3/2019 Proiect Final Geodezie Proiect

    18/30

    18

    1.4.Calcululcoordonatelor

    Puncte

    Cadran D X' Y'

    Punct

    c

    cos x' y'

    S Vsin 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

  • 8/3/2019 Proiect Final Geodezie Proiect

    19/30

    19

    2.Verificareaaltimetricaaretelei

    2.1. Calculareacotelorretelei prinnivelmentultrigonometricunilateral

    =h+-+C

    h= =D*ctgZ P2tg= 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 475,60213476,439

    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 P4P4 P5

    P5 P6

    P6 P1

  • 8/3/2019 Proiect Final Geodezie Proiect

    20/30

    20

    HB= HA + (hAB

    (hAB= D*ctg.Z+i-S+C , unde:

    unde:

    i nalimea aparatului

    S nalimea semnalului

    C corecia de sfericitate i refracie

    R

    DkC

    2)1(

    2

    !

    unde :

    k coeficientul de refracie ( k=0,14)

    R= 6378,975 km (raza medie n punctul central de proiecie) NMR *!

    D lungimea vizei

  • 8/3/2019 Proiect Final Geodezie Proiect

    21/30

    21

    P6

    P1

    P2

    P3

    P4

    P5

    IV

    III

    II

    I

  • 8/3/2019 Proiect Final Geodezie Proiect

    22/30

    22

    Indesirea retelei de triangulatie

    3.2Indesirea 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 coordonatelor1. 2. 3. 4.+=

    =

    = -( )

  • 8/3/2019 Proiect Final Geodezie Proiect

    23/30

    23

    Ecuatii:

    - - +=

    - -

    +

    =

    - -

    - - -+ -+

    - - - -

    - - -

    - - -

    -

    - - - -

  • 8/3/2019 Proiect Final Geodezie Proiect

    24/30

    24

    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=1P - P=1

    - P=1 P=-1

    - P=1P - 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

  • 8/3/2019 Proiect Final Geodezie Proiect

    25/30

    25

    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 =+

    = = == = ==

  • 8/3/2019 Proiect Final Geodezie Proiect

    26/30

    26

    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

  • 8/3/2019 Proiect Final Geodezie Proiect

    27/30

    27

    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

  • 8/3/2019 Proiect Final Geodezie Proiect

    28/30

    28

    Calculul coeficientilor ecuatiei

    echivalente

    P Nr.

    Vizei Ponderea

    P Q

    lia 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

  • 8/3/2019 Proiect Final Geodezie Proiect

    29/30

  • 8/3/2019 Proiect Final Geodezie Proiect

    30/30

    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

    dxP= 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

    Punct Coordonatele provizorii Coordonate calc din Gauss x y x y

    P 575501,614 402495,156 575501,611 402495,157

    Q 572167,113 403843,834 572167,112 403843,834