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URMARIREA COMPORTARII IN TIMP A CONSTRUCTIILOR


URMARIREA COMPORTARII IN TIMP A CONSTRUCTIILOR


UNIVERSITATEA TEHNICA DE CONSTRUCTII BUCURESTI

FACULTATEA DE GEODEZIE

URMARIREA COMPORTARII IN TIMP A CONSTRUCTIILOR




Tema lucrarii:

In reteaua de urmarire a comportarii constructiilor din reteaua din fig.1 au fost efectuate observatii azimutale in doua etape to si t1.

Se dau:

Coordonatele a doua puncte care sa fixeze coordonatele geodezice de referinta ale retelei.

Punct

X

Y

104

4887.331

6052.519

105

4950.332

6114.404

  1. Observatiile azimutale din cele doua etape de masuratori

ETAPA I

ETAPA II

Pct.statie

Pct.vizat

Hz

Pct.statie

Pct.vizat

Hz

101

102

0.0000

101

102

0.0000

101

105

267.7788

101

105

267.7790

101

104

312.1241

101

104

312.1239

101

103

357.6762

101

103

357.6655

102

101

0.0000

102

101

0.0000

102

105

40.7745

102

105

40.7745

102

104

84.1672

102

104

84.1672

102

103

131.1958

102

103

131.1712

103

102

0.0000

103

102

0.0000

103

101

26.4825

103

101

26.4961

103

105

66.7743

103

105

66.8009

103

104

107.3645

103

104

107.4094

104

103

0.0000

104

103

0.0000

104

102

45.6062

104

102

45.5860

104

101

73.5627

104

101

73.5424

104

105

116.4715

104

105

116.4514

105

104

0.0000

105

104

0.0000

105

103

42.9368

105

103

42.9389

105

102

85.7427

105

102

85.7426

105

101

112.7495

105

101

112.7492

Se cere:

1.     Calculul coordonatelor provizorii pentru etapa to. Acestea vor constitui coordonate provizorii si pentru etapa t1

2.     Formarea sistemului de ecuatii liniare (cazul retelelor libere)

3.     Normalizarea sistemului liniar

4.     Compensarea retelei ca libera in ambele etape de masuratori (inversarea lui N, calculul parametrilor, calculul corectiilor, evaluarea preciziei masuratorilor in ambele etape)

5.     Testul global de congruenta a celor doua configuratii de la etapele to si t1

6.     Localizarea punctelor deplasate

Etape de calcul si relatii utilizate:

Etapa to

1.     Calculul coordonatelor provizorii pentru etapa to. Acestea vor constitui coordonate provizorii si pentru etapa t1

Calculul distantelor si orientarilor intre punctele vechi:

Pct.

X [m]

Y [m]

G]tg

D[m]

104

4887.331

6052.519

49.4311

88.311

105

4950.332

6114.404

0.982286

88.311

63.001

61.885

 

88.311

Orientarea statiilor Unghiul de orientare al statiilor:

z101=

94.4000

z102=

294.3990

z103=

225.5944

z104=

132.9596

z105=

49.4311

= unghiul de orientare al statiei

Calculul orientarilor spre punctele noi:

Pct.statie

Pct.vizat

Hz

G]

101

102

0.0000

94.4000

101

105

267.7788

362.1788

101

104

312.1241

6.5241

101

103

357.6762

52.0762

102

101

0.0000

294.3990

102

105

40.7745

335.1735

102

104

84.1672

378.5662

102

103

131.1958

25.5948

103

102

0.0000

225.5944

103

101

26.4825

252.0769

103

105

66.7743

292.3687

103

104

107.3645

332.9589

104

103

0.0000

132.9596

104

102

45.6062

178.5658

104

101

73.5627

206.5223

104

105

116.4715

249.4311

105

104

0.0000

49.4311

105

103

42.9368

92.3679

105

102

85.7427

135.1738

105

101

112.7495

162.1806

In care: n = numarul de puncte vechi observate din statia S

Orientarea de la statia S la punctul i este:

Calculul coordonatelor provizorii ale punctelor noi prin intersectie inainte:

Pct.

X [m]

Y [m]

G]

tg

Xo [m]

Yo [m]

104

4887.331

6052.519

206.5223

0.10281

 

 

105

4950.332

6114.404

162.1806

-0.6755

 

101

5021.525

6066.316

-

-

5021.525

6066.316

104

4887.331

6052.519

178.5658

-0.35

 

105

4950.332

6114.404

135.1738

-1.6219

 

102

5016.326

6007.369

-

-

5016.325

6007.370

104

4887.331

6052.519

132.9596

-1.7558

 

105

4950.332

6114.404

92.3679

8.30137

 

103

4933.180

5972.019

-

-

4933.181

5972.016

104

4887.331

6052.519

206.5223

0.10281

 

102

5016.326

6007.369

294.3990

11.3368

101

5021.525

6066.316

-

-

105

4950.332

6114.404

135.1738

-1.6219

103

4933.180

5972.019

225.5944

0.42519

102

5016.324

6007.371

-

-

104

4887.331

6052.519

132.9596

-1.7558

101

5021.525

6066.316

52.0762

1.06745

103

4933.182

5972.014

-

-

2.     Formarea sistemului de ecuatii liniare (cazul retelelor libere).

Calculul coeficientilor de directie:

Variatia orientarilor functie de variatia coordonatelor plane

; ;

Se noteaza

Control: ;

; ;

Pct.

Xo [m]

Yo [m]

otg

D[m]

a[cc/mm]

b[cc/mm]

control

101

5021.525

6066.316

294.3982

59.175

 

 

 

102

5016.325

6007.370

11.335265

59.175

10.7167

-0.9454

-11.3352

-5.200

-58.946

 

59.175

 

 

 

101

5021.525

6066.316

252.0750

129.217

 

 

 

103

4933.181

5972.016

1.067410

129.217

3.5954

-3.3684

-1.06741

-88.344

-94.299

 

129.217

 

 

 

101

5021.525

6066.316

206.5223

134.902

 

 

 

104

4887.331

6052.519

0.102812

134.902

0.4826

-4.6944

-0.10281

-134.194

-13.797

 

134.902

 

 

 

101

5021.525

6066.316

162.1807

85.913

 

 

 

105

4950.332

6114.404

-0.675459

85.913

-4.1477

-6.1405

0.67545

-71.193

48.088

 

85.913

 

 

 

102

5016.325

6007.370

225.5952

90.348

 

 

 

103

4933.181

5972.016

0.425210

90.348

2.7572

-6.4844

-0.42521

-83.144

-35.354

 

90.348

 

 

 

102

5016.325

6007.370

178.5662

136.667

 

 

 

104

4887.331

6052.519

-0.350007

136.667

-1.5389

-4.3967

0.35001

-128.994

45.149

 

136.667

 

 

 

102

5016.325

6007.370

135.1738

125.743

 

 

 

105

4950.332

6114.404

-1.62189

125.743

-4.3096

-2.6571

1.62189

-65.993

107.034

 

125.743

 

 

 

103

4933.181

5972.016

132.9596

92.644

 

 

 

104

4887.331

6052.519

-1.755773

92.644

-5.9711

-3.4008

1.75577

-45.850

80.503

 

92.644

 

 

 

103

4933.181

5972.016

92.3686

143.417

 

 

 

105

4950.332

6114.404

8.302093

143.417

-4.4071

0.5308

-8.30209

17.151

142.388

 

143.417

 

 

 

104

4887.331

6052.519

49.4311

88.311

 

 

 

105

4950.332

6114.404

0.982286

88.311

-5.0517

5.1428

-0.98228

63.001

61.885

 

88.311

 

 

 

Formarea ecuatiilor corectiilor pentru directii masurate:

;

Pentru fiecare statie putem scrie:

; ; i = 1,2,n

valoarea din coordonate;

valoarea masurata si redusa la planul de proiectie

Intr-o statie trebuie ca

Deci

Modelului functional stochastic:

modelul functional ecuatiile de corectie

modelul stohastic

Cm = matricea de varianta-covarianta

Qm = matricea cofactorilor masuratorilor

Qx = matricea cofactorilor necunoscutelor

matricea ponderilor

conditia de prelucrare minim

Stabilirea ponderii pentru fiecare din ecuatiile corectiilor:

Se considera ponderi egale: p = 0,5


Nr.ec.

Ecuatia

pondere

dx101

dy101

dx102

dy102

dx103

dy103

dx104

dy104

dx105

dy105

l

Suma

1

101-102

0.5

-10.7167

0.9454

10.7167

-0.9454

0

0

0

0

0

0

-11

-10.5592

2

101-103

0.5

-3.5954

3.3684

0

0

3.5954

-3.3684

0

0

0

0

-5

-4.5847

3

101-104

0.5

-0.4826

4.6944

0

0

0

0

0.4826

-4.6944

0

0

-11

-10.6022

4

101-105

0.5

4.1477

6.1405

0

0

0

0

0

0

-4.1477

-6.1405

26

25.7461

5

102-101

0.5

-10.7167

0.9454

10.7167

-0.9454

0

0

0

0

0

0

-7.7

-7.6694

6

102-103

0.5

0

0

-2.7572

6.4844

2.7572

-6.4844

0

0

0

0

4.3

4.3367

7

102-104

0.5

0

0

1.5389

4.3967

0

0

-1.5389

-4.3967

0

0

0.0

0.0450

8

102-105

0.5

0

0

4.3096

2.6571

0

0

0

0

-4.3096

-2.6571

3.3

3.2877

9

103-101

0.5

-3.5954

3.3684

0

0

3.5954

-3.3684

0

0

0

0

-17.6

-17.6479

10

103-102

0.5

0

0

-2.7572

6.4844

2.7572

-6.4844

0

0

0

0

9.4

9.3837

11

103-104

0.5

0

0

0

0

5.9711

3.4008

-5.9711

-3.4008

0

0

8.3

8.3347

12

103-105

0.5

0

0

0

0

4.4071

-0.5308

0

0

-4.4071

0.5308

-0.1

-0.0705

13

104-101

0.5

-0.4826

4.6944

0

0

0

0

0.4826

-4.6944

0

0

-0.9

-0.9393

14

104-102

0.5

0

0

1.5389

4.3967

0

0

-1.5389

-4.3967

0

0

2.8

2.8180

15

104-103

0.5

0

0

0

0

5.9711

3.4008

-5.9711

-3.4008

0

0

-0.9

-0.9393

16

104-105

0.5

0

0

0

0

0

0

5.0517

-5.1428

-5.0517

5.1428

-0.9

-0.9393

17

105-101

0.5

4.1477

6.1405

0

0

0

0

0

0

-4.1477

-6.1405

-1.4

-1.3875

18

105-102

0.5

0

0

4.3096

2.6571

0

0

0

0

-4.3096

-2.6571

-1.7

-1.7358

19

105-103

0.5

0

0

0

0

4.4071

-0.5308

0

0

-4.4071

0.5308

4.9

4.8590

20

105-104

0.5

0

0

0

0

0

0

5.0517

-5.1428

-5.0517

5.1428

-1.7

-1.7358

Suma

-21.2941

30.2974

27.6157

25.1855

33.4618

-13.965

-3.9514

-35.2693

-35.8320

-6.2481

0.00

0.0000

0.0000


Transformarea ecuatiilor de corectie ale directiilor dupa regulile de echivalenta (transformarea dupa regulile de echivalenta presupune obtinerea unui sistem normal nemodificat)

Prima regula de echivalenta

Se aplica atunci cand una dintre necunoscute are acelasi coeficient in toate ecuatiile sistemului considerat (-1, de exemplu) si reduce numarul de necunoscute cu unu, marind in schimb numarul de ecuatii cu o ecuatie suma, de pondere diferita.

m ecuatii si n+1 necunoscute => m+1 ecuatii si n necunoscute

Ecuatia suma:

In fiecare statie se aplica regula 1 de echivalenta, deci din 4 ecuatii cu 15 necunoscute, reducem necunoscuta dz pentru ca are mereu coeficientul 1 si obtinem 5 ecuatii cu 10 necunoscute.

In total, pentru cele 5 statii, avem 20 de ecuatii cu 15 necunoscute (dx, dy pentru fiecare punct si cate un dz pentru fiecare statie);Dupa aplicarea primei reguli de echivalenta am ramas cu 25 de ecuatii si doar 10 necunoscute.

A doua regula de echivalenta

Se aplica atunci cand fiecare din necunoscutele implicate are acelasi coeficient in toate ecuatiile sistemului.

In cazul vizelor reciproce, in loc de doua ecuatii vom avea una singura, termenul liber se determina ca medie ponderata a termenilor liberi ale celor doua ecuatii, cu ponderea egala cu ponderea ecuatiilor respective; ponderea ecuatiei va fi suma ponderilor celor doua, deci se reduce numarul de ecuatii.

Din 20 ecuatii ( in care gasim vize reciproce), aplicand regula 2 de echivalenta raman 10 ecuatii. Impreuna cu cele 5 ecuatii suma avem 15 ecuatii cu 10 necunoscute.


Nr.ec.

Ecuatia

pondere

dx101

dy101

dx102

dy102

dx103

dy103

dx104

dy104

dx105

dy105

l[cc]

Suma

1

101-102

1

-10.7167

0.9454

10.7167

-0.9454

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

-9.11

-9.1143

2

101-103

1

-3.5954

3.3684

0.0000

0.0000

3.5954

-3.3684

0.0000

0.0000

0.0000

0.0000

-11.12

-11.1163

3

101-104

1

-0.4826

4.6944

0.0000

0.0000

0.0000

0.0000

0.4826

-4.6944

0.0000

0.0000

-5.77

-5.7708

4

101-105

1

4.1477

6.1405

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

-4.1477

-6.1405

12.18

12.1793

5

102-103

1

0.0000

0.0000

-2.7572

6.4844

2.7572

-6.4844

0.0000

0.0000

0.0000

0.0000

6.86

6.8602

6

102-104

1

0.0000

0.0000

1.5389

4.3967

0.0000

0.0000

-1.5389

-4.3967

0.0000

0.0000

1.43

1.4315

7

102-105

1

0.0000

0.0000

4.3096

2.6571

0.0000

0.0000

0.0000

0.0000

-4.3096

-2.6571

0.78

0.7759

8

103-104

1

0.0000

0.0000

0.0000

0.0000

5.9711

3.4008

-5.9711

-3.4008

0.0000

0.0000

3.70

3.6977

9

103-105

1

0.0000

0.0000

0.0000

0.0000

4.4071

-0.5308

0.0000

0.0000

-4.4071

0.5308

2.39

2.3943

10

104-105

1

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

5.0517

-5.1428

-5.0517

5.1428

-1.34

-1.3376

11

101

-0.5

-5.3235

7.5744

5.3583

-0.4727

1.7977

-1.6842

0.2413

-2.3472

-2.0738

-3.0703

0.00

0.0000

12

102

-0.5

-5.3583

0.4727

6.9039

6.2964

1.3786

-3.2422

-0.7694

-2.1983

-2.1548

-1.3286

0.00

0.0000

13

103

-0.5

-1.7977

1.6842

-1.3786

3.2422

8.3654

-3.4914

-2.9856

-1.7004

-2.2035

0.2654

0.00

0.0000

14

104

-0.5

-0.2413

2.3472

0.7694

2.1983

2.9856

1.7004

-0.9878

-8.8173

-2.5258

2.5714

0.00

0.0000

15

105

-0.5

2.0738

3.0703

2.1548

1.3286

2.2035

-0.2654

2.5258

-2.5714

-8.9580

-1.5620

0.00

0.0000

 

 

 

-21.2941

30.2974

27.6157

25.1855

33.4618

-13.9656

-3.9514

-35.2693

-35.8320

-6.2481

0.00

0.0000

0.0000


3.     Normalizarea sistemului liniar

Formarea sistemului normal de ecuatii si rezolvarea lui:


112.8895

21.0019

-85.4688

27.5447

1.1463

-3.7166

-7.0739

-9.7977

-21.4931

-35.0323

21.0019

34.2999

-14.8429

-7.9415

-8.9545

-2.8493

1.3296

3.0988

1.4659

-26.6079

-85.4688

-14.8429

101.6345

-30.3049

-14.9340

30.8085

-4.7578

12.1017

3.5262

2.2376

27.5447

-7.9415

-30.3049

40.8437

-4.3427

-28.2716

-0.0386

1.1918

7.1416

-5.8224

N=

1.1463

-8.9545

-14.9340

-4.3427

31.1651

4.0839

-24.1613

6.4260

6.7839

2.7873

-3.7166

-2.8493

30.8085

-28.2716

4.0839

50.9912

-25.3878

-12.9191

-5.7881

-6.9511

-7.0739

1.3296

-4.7578

-0.0386

-24.1613

-25.3878

55.3148

-5.3809

-19.3217

29.4777

-9.7977

3.0988

12.1017

1.1918

6.4260

-12.9191

-5.3809

30.5863

-3.3491

-21.9578

-21.4931

1.4659

3.5262

7.1416

6.7839

-5.7881

-19.3217

-3.3491

30.5048

0.5297

-35.0323

-26.6079

2.2376

-5.8224

2.7873

-6.9511

29.4777

-21.9578

0.5297

61.3392

4.        Compensarea retelei ca libera in ambele etape de masuratori (inversarea lui N, calculul parametrilor, calculul corectiilor, evaluarea preciziei masuratorilor in ambele etape).

Matricea normala in cazul retelelor libere este singulara. Inversa se construieste cu ajutorul unei matrice ajutatoare G.

In cazul de fata G are forma:

Coordonate reduse la centrul de greutate

Pct.

Xo [m]

Yo [m]

Xog [m]

Yog [m]

101

5021.525

6066.3158

59.78639587

23.790758

102

5016.325

6007.3701

54.58618869

-35.154969

103

4933.181

5972.0164

-28.55772882

-70.508631

104

4887.331

6052.519

-74.40792787

9.9939212

105

4950.332

6114.404

-11.40692787

71.878921

Centrul de greutate

4961.739

6042.5251

 

 


1

0

23.791

59.79

0

1

-59.79

23.79

1

0

-35.15

54.59

0

1

-54.59

-35.15

G=

1

0

-70.51

-28.56

0

1

28.558

-70.51

1

0

9.9939

-74.41

0

1

74.408

9.994

1

0

71.879

-11.41

0

1

11.407

71.88

Matricea N se bordeaza cu matricea auxiliara G;matricea rezultata are urmatoarea forma:

0.0051

-0.0031

0.0007

0.0022

-0.0018

0.0030

-0.0001

-0.0011

-0.0039

-0.0011

-0.0031

0.0145

-0.0037

-0.0080

-0.0020

-0.0018

0.0022

-0.0025

0.0066

-0.0022

0.0007

-0.0037

0.0064

0.0043

-0.0048

0.0019

-0.0002

0.0002

-0.0021

-0.0027

0.0022

-0.0080

0.0043

0.0134

-0.0063

-0.0014

-0.0025

-0.0022

0.0022

-0.0018

N+=

-0.0018

-0.0020

-0.0048

-0.0063

0.0120

-0.0012

-0.0023

0.0070

-0.0031

0.0025

0.0030

-0.0018

0.0019

-0.0014

-0.0012

0.0071

-0.0021

-0.0047

-0.0016

0.0007

-0.0001

0.0022

-0.0002

-0.0025

-0.0023

-0.0021

0.0065

0.0011

-0.0039

0.0013

-0.0011

-0.0025

0.0002

-0.0022

0.0070

-0.0047

0.0011

0.0125

-0.0073

-0.0031

-0.0039

0.0066

-0.0021

0.0022

-0.0031

-0.0016

-0.0039

-0.0073

0.0131

0.0000

-0.0011

-0.0022

-0.0027

-0.0018

0.0025

0.0007

0.0013

-0.0031

0.0000

0.0062

Calculul coordonatelor compensate in prima etapa

1.328

-0.990

Punct

Xo [m]

Yo [m]

dX [mm]

dY [mm]

Xt0 [m]

Yt0 [m]

-0.004

101

5021.5253

6066.3158

1.33

-0.99

5021.5267

6066.3148

X=

0.745

102

5016.3251

6007.3701

0.00

0.75

5016.3251

6007.3709

0.086

103

4933.1812

5972.0164

0.09

0.32

4933.1813

5972.0168

0.321

104

4887.331

6052.519

-0.27

0.51

4887.3307

6052.5195

-0.268

105

4950.332

6114.404

-1.14

-0.59

4950.3309

6114.4034

0.514

-1.142

-0.590

Calculul elementelor compensate si controlul compensarii:

-Determinarea valorilor cele mai probabile ale coordonatelor punctelor:

-Determinarea corectiei pentru unghiul de orientare( pentru fiecare statie): ; t = numarul de puncte vizate din statia S

-Determinarea corectiilor v pentru masuratorile care au intrat in prelucrare:

=

Pct. st.

Pct. Viz.



zi

z

lij [cc]

p

dx101

dy101

dx102

dy102

dx103

dy103

dx104

dy104

dx105

dy105

 

 

 

 

 

 

 

 

1.328

-0.99

-0.004

0.75

0.09

0.32

-0.27

0.514

-1.14

-0.59

 

102

294.39823

0.00000

294.39823

294.39928

-10.6

0.5

-10.7167

0.9454

10.7167

-0.9454

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

101

105

162.18066

267.77880

294.40186

-4.6

0.5

4.1477

6.1405

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

-4.1477

-6.1405

 

104

206.52232

312.12410

294.39822

-10.6

0.5

-0.4826

4.6944

0.0000

0.0000

0.0000

0.0000

0.4826

-4.6944

0.0000

0.0000

 

103

252.07502

357.67620

294.39882

25.7

0.5

-3.5954

3.3684

0.0000

0.0000

3.5954

-3.3684

0.0000

0.0000

0.0000

0.0000

 

101

94.39823

0.00000

94.39823

94.39899

-7.7

0.5

-10.7167

0.9454

10.7167

-0.9454

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

102

105

135.17382

40.77450

94.39932

4.3

0.5

0.0000

0.0000

4.3096

2.6571

0.0000

0.0000

0.0000

0.0000

-4.3096

-2.6571

 

104

178.56620

84.16720

94.39900

0.0

0.5

0.0000

0.0000

1.5389

4.3967

0.0000

0.0000

-1.5389

-4.3967

0.0000

0.0000

 

103

225.59523

131.19580

94.39943

3.3

0.5

0.0000

0.0000

-2.7572

6.4844

2.7572

-6.4844

0.0000

0.0000

0.0000

0.0000

 

101

52.07502

26.48250

25.59252

25.59429

-17.6

0.5

-3.5954

3.3684

0.0000

0.0000

3.5954

-3.3684

0.0000

0.0000

0.0000

0.0000

103

102

25.59523

0.00000

25.59523

9.4

0.5

0.0000

0.0000

-2.7572

6.4844

2.7572

-6.4844

0.0000

0.0000

0.0000

0.0000

 

105

92.36858

66.77430

25.59428

8.3

0.5

0.0000

0.0000

0.0000

0.0000

4.4071

-0.5308

0.0000

0.0000

-4.4071

0.5308

 

104

132.95962

107.36450

25.59512

-0.1

0.5

0.0000

0.0000

0.0000

0.0000

5.9711

3.4008

-5.9711

-3.4008

0.0000

0.0000

 

103

332.95962

0.00000

332.95962

332.95972

-0.9

0.5

0.0000

0.0000

0.0000

0.0000

5.9711

3.4008

-5.9711

-3.4008

0.0000

0.0000

104

102

378.56620

45.60620

332.96000

2.8

0.5

0.0000

0.0000

1.5389

4.3967

0.0000

0.0000

-1.5389

-4.3967

0.0000

0.0000

 

101

6.52232

73.56270

332.95962

-0.9

0.5

-0.4826

4.6944

0.0000

0.0000

0.0000

0.0000

0.4826

-4.6944

0.0000

0.0000

 

105

49.43112

116.47150

332.95962

-0.9

0.5

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

5.0517

-5.1428

-5.0517

5.1428

 

101

362.18066

112.74950

249.43116

249.43130

-1.4

0.5

4.1477

6.1405

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

-4.1477

-6.1405

105

104

249.43112

0.00000

249.43112

-1.7

0.5

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

5.0517

-5.1428

-5.0517

5.1428

 

103

292.36858

42.93680

249.43178

4.9

0.5

0.0000

0.0000

0.0000

0.0000

4.4071

-0.5308

0.0000

0.0000

-4.4071

0.5308

 

102

335.17382

85.74270

249.43112

-1.7

0.5

0.0000

0.0000

4.3096

2.6571

0.0000

0.0000

0.0000

0.0000

-4.3096

-2.6571

Pct. st.

Pct. Viz.

dcc

-dz[cc]

v[cc]

coord

Control

 

 

 

 

 

 

 

coord=0

 

102

-16

-20

294.3966

294.3966

0.000000

101

105

8

-6

9

162.1814

162.1814

0.000000

 

104

-8

-12

206.5215

206.5215

0.000000

 

103

-9

 

23

252.0741

252.0741

0.000000

 

101

-16

-23

94.3966

94.3966

0.000000

102

105

8

-0.8

14

135.1747

135.1747

0.000000

 

104

1

2

178.5663

178.5663

0.000000

 

103

3

 

7

225.5955

225.5955

0.000000

 

101

-9

-27

52.0741

52.0741

0.000000

103

102

3

0.1

12

25.5955

25.5955

0.000000

 

105

5

13

92.3691

92.3691

0.000000

 

104

1

 

1

132.9598

132.9598

0.000000

 

103

1

2

332.9598

332.9598

0.000000

104

102

1

-1.6

6

378.5663

378.5663

0.000000

 

101

-8

-7

6.5215

6.5215

0.000000

 

105

-1

 

-1

49.4310

49.4310

0.000000

 

101

8

1.4

362.1814

362.1814

0.000000

105

104

-1

5.0

-8.0

249.4310

249.4310

0.000000

 

103

5

4.8

292.3691

292.3691

0.000000

 

102

8

 

1.7

335.1747

335.1747

0.000000

Calcule de evaluare a preciziei:

n= nr. de ecuatii

u= nr. de necunoscute

d= defect de rang (d=4)

= nr. grade de libertate


Etapa t1

Calculul distantelor si orientarilor intre punctele vechi:

Pct.

X [m]

Y [m]

G]tg

D[m]

104

4887.331

6052.519

49.4311

88.311

105

4950.332

6114.404

0.982286

88.311

63.001

61.885

 

88.311

Orientarea statiilor Unghiul de orientare al statiilor:

z101=

94.3998

z102=

294.3989

z103=

225.5697

z104=





132.9797

z105=

49.4311

Calculul orientarilor spre punctele noi:

Pct.statie

Pct.vizat

Hz

G]

101

102

0.0000

94.3998

101

105

267.7790

362.1788

101

104

312.1239

6.5237

101

103

357.6655

52.0653

102

101

0.0000

294.3989

102

105

40.7745

335.1734

102

104

84.1672

378.5661

102

103

131.1712

25.5701

103

102

0.0000

225.5697

103

101

26.4961

252.0658

103

105

66.8009

292.3706

103

104

107.4094

332.9791

104

103

0.0000

132.9797

104

102

45.5860

178.5657

104

101

73.5424

206.5221

104

105

116.4514

249.4311

105

104

0.0000

49.4311

105

103

42.9389

92.3700

105

102

85.7426

135.1737

105

101

112.7492

162.1803

Calculul coeficientilor de directie:

Pct.

Xo [m]

Yo [m]

otg

D[m]

a[cc/mm]

b[cc/mm]

control

101

5021.525

6066.315

294.3982

59.174

 

 

 

102

5016.325

6007.370

11.335205

59.174

10.7167

-0.9454

-11.335205

-5.200

-58.946

 

59.174

 

 

 

101

5021.525

6066.315

252.0642

129.179

 

 

 

103

4933.191

5972.059

1.067046

129.179

3.5959

-3.3700

-1.067046

-88.334

-94.257

 

129.179

 

 

 

101

5021.525

6066.315

206.5221

134.902

 

 

 

104

4887.331

6052.519

0.102809

134.902

0.4826

-4.6944

-0.102809

-134.194

-13.796

 

134.902