memoriu

Universitatea de Stiinte Agronomice si Medicina Veterinara Bucuresti

Facultatea de Imbunatatiri Funciare si Ingineria MediuluiSpecializarea Masuratori Terestre si CadastruProiect La GeodezieMirza Beniamin Grupa 9302

Judetul Mehedinti

Numar de ordine 16Tema proiect

RETELE GEODEZICE PE ELIPSOID

Etapa 1. Proiectarea determinarilor GPS

Se va determina numarul optim, din punct de vedere economic, de sesiuni necesare pentru determinarea coordonatelor retelei de puncte. Se vor compara cel putin 2 solutii.

Date de intrare: Lista de puncte cu coordonate stereo aproximative, 2 masini, 5 echipamente GPS, 2 ore minim de stationare, viteza medie de transport intre puncte se va lua de 60 km/ora.

Distantele pe sosea dintre puncte se vor determina prin una din urmatoarele variante:

Var. 1 Se considera ca distanta pe sosea intre doua puncte este egala cu distanta directa + N km (nr. de ordine in km) iar.

Var. 2 Distantele se vor determina prin raportarea punctelor pe harta Romaniei

Date de iesire: Numarul de sesiuni necesare determinarilor GPS, totalul de km parcursi si timpul necesar determinarilor

Etapa 2. Transformarea coordonatelor geodezice (B,L,h) in coordonate geocentrice (X, Y, Z)

Date de intrare: Coordonatele geodezice din fiecare sesiune

Date de iesire: Coordonate geocentrice pentru fiecare sesiune

Etapa 3. Unificarea determinarilor GPS

Date de intrare: Coordonatele geocentrice din sesiunea unificata la etapa 2

Date de iesire: Coordonate geocentrice unificate intr-o singura sesiune

Etapa 4. Selectia si rezolvarea triunghiurilor care compun reteaua astfel incat sa nu existe triunghiuri care se intersecteaza.

Date de intrare: Vectorii 3D, schitele sesiunilor

Date de iesire: Unghiurile triunghiurilor selectate si schita unificata a retelei

Se va realiza o singura schita prin unificarea schitelor partiale pe sesiuni utilizand punctele comune.

In schita unificata se vor elimina vectorii astfel incat sa nu mai existe vectori care se intersecteaza iar reteaua sa devina doar o retea de triunghiuri. Pentru calculul unghiurilor se vor utiliza vectorii redusi la orizont (vectori 2D)

Etapa 5. Problema geodezica directa

Pornind de la N latura incepand cu cea mai scurta, singura considerata cunoscuta, inclusiv coordonatele geodezice ale unui punct de capat, sa se determine coordonatele geodezice ale tuturor punctelor din retea stiind si unghiurile triunghiurilor determinate in etapa 3

Date de intrare: Cel mai mic al N-lea vector 3D din retea, coordonatele geodezice ale punctului de capat al vectorului respectiv si orientarile laturilor

Date de iesire: Coordonate geodezice ale tuturor punctelor din retea

Etapa 6 Problema geodezica inversa

Sa se determine orientarile si lungimile vectorilor care formeaza triunghiurile retelei

Date de intrare: Coordonatele geodezice ale punctelor din retea

Date de iesire: lungimi si orientari ale laturilor triunghiurilor din retea.

ParametriElipsoidul KrasovskiElipsoidul WGS-84

a6378245.000 m6378137.000 m

f0.0033523290.003352810

b6356863.024m6356752.314 m

e20.0066934220.006694380

0.0067385250.006739497

E521825.488 m521854.012 m

c6399698.902 m6399593.626 m

MEMORIU TEHNICEtapa 1. Proiectarea determinarilor GPS

Cea de-a doua varianta este mai buna din cauza timpului mai bun cat si a distantei .Etapa 2. Transformarea coordonatelor geodezice (B,L,h) in coordonate geocentrice (X, Y, Z).Cu ajutorul datelor initiale din fiecare sesiune in parte, s-au transformat latitudinea, respectiv longitudinea in grade cu zecimale cu ajutorul formulei: grade+(minute+secunde/60)/60.

Ex: 4446'09.63288"N44+(46+9,63288/60)/60= 43.76934247 grade

Pentu formulele care folosesc functii trigonometrice a fost nesecar sa transformam gradele in radiani, utilizand urmatoarele formule:

Sin(x*180/pi())

Acos (x)*180/pi()

Formulele necesare pentru transformarea coordonatelor geodezice in coordonate geocentrice sunt:

Unde:

B latitudine;

L longitudine;

a- semiaxa mare;

e2 prima excentricitate.

N=a/W; W=(1-e 2sin 2B)1/3

Date initiale sesiunea 1

LatitudineaLongitudineaCota elips. (m)

Nr.Numegrademinutesecundegrademinutesecunde h

1DRTS443738,0529222384,29191131,08910

2MH5944299,10403223349,63598184,39100

3MH60442642,15108223832,11443131,23540

4MH61442510,1046723151,94436320,81600

5MH62441723,8793723048,03555239,92300

6MH63441340,6106322581,72162160,84700

7MH64441659,03866224152,35940153,18990

8MH65441930,2904822359,8102490,42940

Transformare coordonate sesiunea 1

Nr.NumeLatitudinea Longitudinea h W X(m) Y(m) Z(m)

1DRTS44,627222,6345131,089100,9983474196672,5771749873,9624458053,900

2MH5944,485922,5638184,391000,9983554209043,7151748935,4664446896,735

3MH6044,445022,6423131,235400,9983574209542,1561755906,7244443622,199

4MH6144,419523,0311320,816000,9983594199483,8541785265,5624441726,017

5MH6244,290023,0133239,923000,9983674209243,8121787874,9914431379,289

6MH6344,227922,9671160,847000,998374215060,2891786335,0954426388,379

7MH6444,283122,6979153,189900,9983674219460,4881764854,9104430769,838

8MH6544,325122,586190,429400,9983644219844,4991755347,1344434067,090




1DRTS443738,0528022384,29200131,07840

2MH51444349,31394223738,21625401,89310

3MH52444123,91042222118,11747293,63930

4MH53445149,36431223535,56965573,56430

5MH5444571,66981223615,67979828,34120

6MH55445256,3757922443,28429618,36030

7MH56445837,28288224826,60007638,85470

8MH57444312,63577225035,10419388,02520



1DRTS44,62722,635131,078400,998354196672,5711749873,9614458053,890

2MH5144,73022,627401,893100,998344189633,4331746317,1724466393,507

3MH5244,69022,355293,639300,998344200733,3531727561,6524463127,404

4MH5344,86422,593573,564300,998334181142,9511739860,8294477030,651

5MH5444,95022,604828,341200,998334174687,3221738126,9614484039,310

6MH5544,88222,734618,360300,998334175530,7461749595,4984478528,349

7MH5644,97722,807638,854700,998334166455,4211752048,8764485994,030

8MH5744,72022,843388,025200,998344183751,5141762390,3254465579,284




1DRTS443738,0528422384,29195131,07740

2MH51444349,31405223738,21614401,89710

3MH55445256,3756222443,28467618,36310

4MH57444312,63616225035,10409388,04720

5MH58443655,8949523522,47945363,62970

6MH5944299,10374223349,63574184,38310

7MH60442642,15106223832,11489131,22860

8MH61442510,1044323151,94436320,78890



1DRTS44,627222,6345131,077400,9984196672,5701749873,9604458053,890

2MH5144,730422,6273401,897100,9984189633,4341746317,1704466393,512

3MH5544,882322,7342618,363100,9984175530,7481749595,5074478528,347

4MH5744,720222,8431388,047200,9984183751,5221762390,3264465579,308

5MH5844,615523,0896363,629700,9984183635,7311783572,4534457290,967

6MH5944,485922,5638184,383100,9984209043,7181748935,4614446896,723

7MH6044,445022,6423131,228600,9984209542,1481755906,7324443622,193

8MH6144,419523,0311320,788900,9984199483,8411785265,5574441725,993



Nr.NumegrademinuteSecundegrademinutesecunde h

1BAIL44120,39996232026114,97720

2DJ5544144,0428223948251,05010

3DJ604419,3995423426120,58890

4DRTS443738,0524022384131,08480

5MH62441723,8786523048239,93210

6MH63441340,6103222582160,85670

7MH64441659,03789224152153,18730

8MH65441930,2904622351090,43490



1BAIL44,022323,3405114,977200,9984217904,3691820055,4004409956,227

2DJ5544,234523,1632251,050100,9984208517,2371800578,1184426969,550

3DJ6044,019323,0740120,588900,9984226546,8611800507,0084409715,975

4DRTS44,627222,6345131,084800,9984196672,5781749873,9814458053,886

5MH6244,290023,0133239,932100,9984209243,8271787875,0144431379,279

6MH6344,227922,9671160,856700,9984215060,2991786335,1074426388,379

7MH6444,283122,6979153,187300,9984219460,4981764854,9254430769,819

8MH6544,325122,586190,434900,9984219844,5041755347,1334434067,094

Etapa 3. Unificarea determinarilor GPS intr-o singura retea

Am unificat sesiunile intr-o singura retea, luand sesiunile doua cate doua, calculand diferentele de coordonate a punctelor comune dintre cele doua sesiun, am facut media pe X, Y, respectv Z , adaugand-o celei de-a doua sesiuni.

Sesiuni initiale

SesiuneNr. Crt.Nume X(m) Y(m) Z(m)

I1DRTS4196672,57681749873,96154458053,9006

2MH594209043,71481748935,46584446896,7354

3MH604209542,15571755906,72374443622,1988

4MH614199483,85371785265,56224441726,0172

5MH624209243,81251787874,99134431379,2886

6MH634215060,28921786335,09464426388,3790

7MH644219460,48841764854,90954430769,8379

8MH654219844,49881755347,13354434067,0905

II1DRTS4196672,57131749873,96134458053,8906

2MH514189633,43281746317,17184466393,5073

3MH524200733,35261727561,65214463127,4045

4MH534181142,95121739860,82864477030,6512

5MH544174687,32181738126,96084484039,3102

6MH554175530,74571749595,49754478528,3488

7MH564166455,42061752048,87624485994,0302

8MH574183751,51441762390,32474465579,2840

III1DRTS4196672,57031749873,95964458053,8908

2MH514189633,43431746317,16974466393,5124

3MH554175530,74781749595,50754478528,3471

4MH574183751,52201762390,32544465579,3078

5MH584183635,73121783572,45294457290,9676

6MH594209043,71761748935,46104446896,7234

7MH604209542,14791755906,73154443622,1935

8MH614199483,84081785265,55684441725,9929

IV1BAIL4217904,36921820055,40014409956,2276

2DJ554208517,23701800578,11754426969,5502

3DJ604226546,86121800507,00774409715,9755

4DRTS4196672,57751749873,98094458053,8862

5MH624209243,82651787875,01434431379,2792

6MH634215060,29881786335,10694426388,3790

7MH644219460,49791764854,92504430769,8191

8MH654219844,50381755347,13264434067,0940

Diferente sesiuni

I-IIDRTS0,0055000,0002000,010000

II-IIIDRTS0,00100,0017-0,0002

MH51-0,00150,0021-0,0051

MH55-0,0021-0,01000,0017

MH57-0,0076-0,0007-0,0238

media-0,00255-0,001725-0,00685

III-IVDRTS-0,0072-0,02130,0046

Sesiuni unificate

SesiuneNr. Crt.Nume X(m) Y(m) Z(m)

I1DRTS4196672,57681749873,96154458053,9006

2MH594209043,71481748935,46584446896,7354

3MH604209542,15571755906,72374443622,1988

4MH614199483,85371785265,56224441726,0172

5MH624209243,81251787874,99134431379,2886

6MH634215060,28921786335,09464426388,3790

7MH644219460,48841764854,90954430769,8379

8MH654219844,49881755347,13354434067,0905

II1DRTS4196672,5768001749873,9615004458053,900600

2MH514189633,4383001746317,1720004466393,517300

3MH524200733,3581001727561,6523004463127,414500

4MH534181142,9567001739860,8288004477030,661200

5MH544174687,3273001738126,9610004484039,320200

6MH554175530,7512001749595,4977004478528,358800

7MH564166455,4261001752048,8764004485994,040200

8MH574183751,5199001762390,3249004465579,294000

III1DRTS4196672,57031749873,95964458053,8908

2MH514189633,43431746317,16974466393,5124

3MH554175530,74781749595,50754478528,3471

4MH574183751,52201762390,32544465579,3078

5MH584183635,73121783572,45294457290,9676

6MH594209043,71761748935,46104446896,7234

7MH604209542,14791755906,73154443622,1935

8MH614199483,84081785265,55684441725,9929

IV1BAIL4217904,36201820055,37884409956,2322

2DJ554208517,22981800578,09624426969,5548

3DJ604226546,85401800506,98644409715,9801

4DRTS4196672,57031749873,95964458053,8908

5MH624209243,81931787874,99304431379,2838

6MH634215060,29161786335,08564426388,3836

7MH644219460,49071764854,90374430769,8237

8MH654219844,49661755347,11134434067,0986

COORDONATE FINALE

Nume X(m) Y(m) Z(m)

MH514189633,441746317,174466393,52

MH524200733,361727561,654463127,41

MH534181142,961739860,834477030,66

MH544174687,331738126,964484039,32

MH554175530,751749595,54478528,36

MH564166455,431752048,884485994,04

MH574183751,521762390,324465579,29

MH584183635,731783572,454457290,96

MH594209043,721748935,464446896,72

MH604209542,151755906,734443622,19

MH614199483,841785265,564441725,99

MH624209243,811787874,994431379,29

MH634215060,291786335,094426388,38

MH644219460,491764854,914430769,84

MH654219844,51755347,134434067,09

DRTS4196672,571749873,964458053,89

DJ554208517,231800578,14426969,55

DJ604226546,851800506,994409715,98

Etapa 4. Calculul Unghiurilor triunghiurilor selectate si schita retelei

Pentru calculul unghiurilor am parcurs urmatoarele etape:

am realizat schita retelei cu ajutorul programului Google Earth;

am format triunghiuri cu vectorii in existenti fisierele cu masuratori astfel incat sa avem cat mai putine triunghiuri obtuze si sa nu aibe acoperire intre ele;

se reduce distanta al orizont: d = D*cos (Elevatie);

am introdus in Excel toti vectorii care formeaza reteau de triunghiuri si am calculat unghiurile fiecarui triunghi cu ajutorul formuleler:

Cos A = (b2+c2-a2) / 2*b*c A=arccos((b2+c2-a2) / 2*b*c)*180/PI()

CosB = (a2+c2-b2) / 2*a*c B=arccos(a2+c2-b2) / 2*a*c)*180/PI()

Cos C = (a2+b2-c2) / 2*a*b C=arccos((a2+b2-c2) / 2*a*b)*180/PI()

- am ordonat vectorii in functie de distanta in ordine crescatoare, determinandu-se astfel vectorul de baza.Determinarea unghiurilor triunghiurilor

123456

LaturiC12750,31412750,31426987,11026987,11018890,52618890,526

A16289,8949682,0189682,01815063,12615063,12619973,166

B12004,87111335,89625192,40922036,87311335,89617134,901

Unghiuria82,241646,949921,024333,917852,880967,1365

b46,903758,824568,986854,720036,875552,2317

c50,854874,225689,988991,362290,243560,6319

suma180180180180180180

789101112

LaturiC22746,17219497,75723238,49619497,75722746,17220255,700

A19973,16611474,77311474,77339077,66422277,58839077,664

B40879,51317134,90122036,87336602,36436602,36431091,693

Unghiuria15,782635,777029,208382,235635,189296,8430

b146,173360,810569,579868,1359108,767252,1828

c18,044183,412581,211929,628536,043630,9742

suma180180180180180180

131415161718

LaturiC20255,70014062,29914062,29930588,24130588,24122359,677

A16685,39517954,16736990,70536990,70514460,8617816,957

B7717,9087717,90831091,69310070,45925192,40925192,409

Unghiuria52,2409107,4351103,4822122,526527,968517,6580

b21,450224,212254,821813,270054,7881102,1539

c106,308948,352621,696044,203597,243460,1881

suma180180180180180180

1920212223

LaturiC15684,63515684,63527511,77422359,67751742,447

A7816,95724954,48124954,48142006,15042006,150

B13466,32124713,26021374,96524713,26010070,459

Unghiuria29,888472,429659,8312126,270813,3025

b59,142470,757347,777128,31543,1622

c90,969236,813172,391625,4138163,5353

suma180180180180180

Etapa 5. Problema geodezica directa

Am folosit urmatoarele formule:

Rezulta:

Rezulta:

A2=arct*+arct*

= arctg -arctg *

M=a(1-e^2)/W^3

N=a/W

s = (S*180) / (PI()*RA)

=> 2=90 - 2*arctg{[sin(A2+2)/2/ sin(A2-2)/2]*tg((90- 1 +s)/2)}

sau

2=90 - 2*arctg{[cos(A2+2)/2/ cos(A2-2)/2]*tg((90- 1 +s)/2)}VECTORUL DE BAZA ESTE MH57-MH51

Etapa 6. Problema geodezica inversa

Rezulta:A1=arctg *-arctg*

A2=arctg* +arct*

Distanta: S = (2*PI()*Ra*s) / (360)

EMBED Equation.3

EMBED Equation.3

EMBED Equation.3

_1369605093.unknown

_1369606076.unknown

_1369606100.unknown

_1369605147.unknown

_1159207854.unknown

_1159207856.unknown

_1367217132.unknown

_1147934876.unknown

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