Proiect Geodezie Matematica

UNIVERSITATEA DE STIINTE AGRONOMICE SI MEDICINA VETERINARA BUCURESTIFACULTATEA DE IMBUNATATIRI FUNCIARE SI INGINERIA MEDIULUIMASURATORI TERESTRE SI CADASTRU

Geodezie Matematica

Student:Simulescu Alexandru VladutAn: III Grupa:9304N=32

Tema proiect

Etapa 1. Proiectarea masuratorilor GPS.Date de intrare 2 masini, 5 GPS-uri, 5 operatori si 2 soferi, timp de stationare simultan intr-o sesiune: 2 ore. Se va considera de asemeni ca distanta intre 2 puncte este egala cu distanta din coordonate + N in km iar viteza medie de mers de la un punct la altul este de 60km / oraDate de iesire: 2 variante de proiect in care se va determina Lungimea totala parcursa de mijloacele auto, timpul total necesar masuratorilor si numarul de sesiuni necesare pentru finalizarea acestora. Intre cele 2 variante se va indica varianta optima si se va justifica alegerea

Etapa 2. Transformarea coordonatelor geodezice (B,L,h) in coordonate geocentrice (X, Y, Z)Etapa 3. Unificarea determinarilor GPS intr-o singura reteaEtapa 4. Selectia si rezolvarea triunghiurilor care compun reteaua astfel incat sa nu existe triunghiuri care se intersecteaza. Date de intrare: Vectorii 3DDate de iesire: Unghiurile triunghiurilor selectate si schita retelei

Etapa 5. Problema geodezica directaPornind 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 3Date de intrare: Cel mai mic al N-lea vector 3D din retea, coordonatele geodezice ale punctelor ce formeaza vectorul si unghiurile triunghiurilor calculate la etapa 3Date de iesire: Coordonate geocentrice ale punctelor din retea

Etapa 6 Problema geodezica inversaSa se determine orientarile si lungimile vectorilor care formeaza triunghiurile reteleiDate de intrare: Coordonatele geodezice ale punctelor din reteaDate de iesire: lungimi si orientari ale laturilor triunghiurilor din retea.

Etapa 1. Proiectarea masuratorilor GPS.Date de intrare: 2 masini, 5 GPS-uri, 5 operatori si 2 soferi, timp de stationare simultan intr-o sesiune: 2 ore. Se va considera de asemeni ca distanta intre 2 puncte este egala cu distanta din coordonate + N in km iar viteza medie de mers de la un punct la altul este de 60km / oraDate de iesire: 2 variante de proiect in care se va determina Lungimea totala parcursa de mijloacele auto, timpul total necesar masuratorilor si numarul de sesiuni necesare pentru finalizarea acestora. Intre cele 2 variante se va indica varianta optima si se va justifica alegerea

2012-2013

25

NrPctDistantaDist+Nr

1MH59-MH607718.124639.8km

2MH59-MH6137921.012870km

3MH59-MH6241917.99174km

4MH59-MH6343075.797875.1km

5MH59-MH6424940.225957km

6MH59-MH6517954.563750km

7MH60-DRTS20255.726152.3km

8MH60-MH6131091.901963.1km

9MH60-MH6234233.724366.3km

10MH60-MH6335402.542167.5km

11MH60-MH6418537.163350.6km

12MH60-MH6514062.412246.1km

13MH61-MH6430589.189762.6km

14MH62-MH6114461.005246.5km

15MH62-MH637817.406839.9km

16MH62-MH6425192.778157.2km

17MH62-MH6534317.055666.4km

18MH63-MH6121886.353453.9km

19MH63-MH6422359.725554.4km

20MH63-MH6532281.651664.3km

21MH65-MH6136990.910969km

22MH65-MH6410070.608142.1km

23MH51-DRTS11478.215343.5km

24MH51-MH5222037.358854.1km

25MH51-MH5315063.911847.1km

26MH51-MH5424532.432156.6km

27MH51-MH5518891.4750.9km

28MH51-MH5630890.988762.9km

29MH51-MH5717134.940349.2km

30MH52-DRTS23239.398455.3km

31MH52-MH5326988.030359km

32MH52-MH5435033.260367.1km

33MH52-MH5536849.02668.9km

34MH52-MH5647932.068380km

35MH53-DRTS26486.776558.5km

36MH53-MH549685.178741.7km

37MH53-MH5511335.949443.4km

38MH53-MH5621085.87753.1km

39MH54-MH5616291.250548.3km

40MH55-DRTS29432.255861.5km

41MH55-MH5412751.839744.8km

42MH55-MH5612004.874944.1km

43MH57-DRTS19499.86251.5km

44MH57-MH5238825.649870.9km

45MH57-MH5325407.019257.5km

46MH57-MH5431806.336463.9km

47MH57-MH5519974.157452km

48MH57-MH5628685.574960.7km

49MH51-DRTS11478.217343.5km

50MH51-MH5518891.465850.9km

51MH51-MH5717134.938749.2km

52MH51-MH5838817.326970.9km

53MH51-MH5927635.833759.7km

54MH51-MH6031730.89563.8km

55MH51-MH6147143.334279.2km

56MH55-DRTS29432.254661.5km

57MH55-MH6049143.122881.2km

58MH55-MH6156573.10788.6km

59MH57-DRTS19499.86651.5km

60MH57-MH5519974.135652km

61MH57-MH5822746.264354.8km

62MH57-MH5934201.864566.3km

63MH57-MH6034486.350166.5km

64MH57-MH6136602.769668.7km

65MH58-DRTS36140.415968.2km

66MH58-MH5540879.699972.9km

67MH58-MH5944196.463376.2km

68MH58-MH6040291.064372.3km

69MH58-MH6122277.737854.3km

70MH59-DRTS16685.575148.7km

71MH59-MH5546088.116678.1km

72MH59-MH607718.133139.8km

73MH59-MH6137921.018570km

74MH61-MH6031091.890363.1km

75BAIL-DJ6021374.985953.4km

76BAIL-DRTS87690.3911119.7km

77BAIL-MH6239617.300571.7km

78DJ55-BAIL27512.468459.6km

79DJ55-DJ6024955.125957km

80DJ55-DRTS60641.911492.7km

81DJ55-MH6213466.34545.5km

82DJ60-DRTS76109.9844108.2km

83DJ60-MH6230467.387362.5km

84DRTS-MH6248100.410180.2km

85MH63-BAIL37618.645469.7km

86MH63-DJ5515684.795347.7km

87MH63-DJ6024713.417956.8km

88MH63-DRTS51674.234383.7km

89MH63-MH627817.399839.9km

90MH64-BAIL59014.571291.1km

91MH64-DJ5537554.539869.6km

92MH64-DJ6042006.497474.1km

93MH64-DRTS38576.395870.6km

94MH64-MH6225192.783857.2km

95MH64-MH6322359.716954.4km

96MH65-BAIL69081.5276101.1km

97MH65-DJ5547164.860979.2km

98MH65-DJ6051742.759483.8km

99MH65-DRTS33797.33465.8km

100MH65-MH6234317.080866.4km

101MH65-MH6332281.66464.3km

102MH65-MH6410070.630542.1km

103MH52-MH5928098.084260km

104MH52-MH6544522.815576.6km

105MH56-MH5845961.389278km

Masina 1GPSOra08:00Ziua 1

SesiunePunctDistantaTimp(minute)StartStop

IMH55176,68710:3012:30

MH56216,127

MH54320,331

113145



IMH51553,76410:3012:30

MH53419,130

72,894



IIMH57169,88014:4516:45

MH60238,549

108,3129



IIMH52419,13014:4516:45

MH51500

19,130

RETUR ZIUA I

MASINADISTANTATIMPTOTAL KM

118,119239,4

2103,9104195,8



IIIMH591223209:2011:20

MH60211,822

33,854



IIIMH6530009:2011:20

MH64414,125

MH62529,240

43,365



IVMH581607013:0015:00

MH60200

6070



IVMH63511,92213:0015:00

MH6146171

72,993

RETUR ZIUA II

MASINADISTANTATIMPTOTAL KM

162,463156,2

266,467182,6



IMH64114,11509:1011:10

MH63226,427

MH62311,912

Total52,454

ReturMH643+2+138,339

IIMH61134,63513:3015:30

MH58226,327

MH57326,827

Total126126

ReturMH653+2+194,19515:30+95'=17:05



IMH60518,11909:1011:10

Total18,119

ReturMH6536,237

IIMH594222213:3015:30

Total58,259

ReturMH655+429,93015:30+30'=16:00



IIIMH57456,65709:5011:50

MH5552424

Total80,681

ReturMH5742424

IVMH56432,73313:0015:00

Total56,757

ReturMH654+592,79315:00+93'=16:33



IIIMH52148,64909:5011:50

MH51226,127

MH53319,120

Total93,896

ReturMH523+2+145,246

IVMH54339,14013:0015:00

Total39,140

ReturMH653+2+187,78815:00+88'=16:38

2. Transformarea coordonatelor geodezice in coordonate geocentrice

Descrierea procedurilor, formule folosite: formula de transformare in grade cu zecimale, formula de transformare in radiani, formule de transformare coordonate

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

Sesiunea I 16.09.2009

NumeBLhNumeBLhNWXYZcos Bcos Lsin Bsin L

gmsgmsg.decg.decm

DRTS443738.0529222384.29191131.0891DRTS44.6272369222.63452553131.08916388698.7040.9983468154196672.5771749873.9614458053.9010.7116920.9229780.7024910.384852

MH5944299.10403223349.63598184.391MH5944.4858622322.56378777184.3916388645.7720.9983550864209043.7151748935.4664446896.7350.7134230.9234530.7007330.383712

MH60442642.15108223832.11443131.2354MH6044.4450419722.64225401131.23546388630.4890.9983574744209542.1561755906.7244443622.1990.7139220.9229270.7002250.384976

MH61442510.1046723151.94436320.816MH6144.4194735223.03109566320.8166388620.9170.998358974199483.8541785265.5624441726.0170.7142350.9202930.6999060.391231

MH62441723.8793723048.03555239.923MH6244.2899664923.01334321239.9236388572.4360.9983665464209243.8121787874.9914431379.2890.7158150.9204140.698290.390945

MH63441340.6106322581.72162160.847MH6344.227947422.96714489160.8476388549.2220.9983701744215060.2891786335.0954426388.3790.716570.9207290.6975150.390203

MH64441659.03866224152.3594153.1899MH6444.2830662922.69787761153.18996388569.8530.998366954219460.4881764854.9094430769.8380.7158990.9225520.6982040.385872

MH65441930.2904822359.8102490.4294MH6544.3250806922.586058490.42946388585.5810.9983644924219844.4991755347.1344434067.0910.7153870.9233040.6987290.384071



gmsgmsg.decg.decm

DRTS443738.052822384.292131.0784DRTS44.6272368922.63452556131.07846388698.7040.9983468154196672.5711749873.9614458053.8910.7116920.9229780.7024910.384852

MH51444349.31394223738.21625401.8931MH5144.7303649822.62728229401.89316388737.3190.998340784189633.4331746317.1724466393.5070.7104270.9230270.7037710.384735

MH52444123.91042222118.11747293.6393MH5244.6899751222.35503263293.63936388722.1960.9983431444200733.3521727561.6524463127.4040.7109230.9248450.703270.380345

MH53445149.36431223535.56965573.5643MH5344.8637123122.59321379573.56436388787.2530.9983329774181142.9511739860.8294477030.6510.7087870.9232560.7054230.384186

MH5444571.66981223615.67979828.3412MH5444.9504638422.6043555828.34126388819.740.9983279014174687.3221738126.9614484039.310.7077180.9231810.7064950.384366

MH55445256.3757922443.28429618.3603MH5544.8823266122.73424564618.36036388794.2240.9983318884175530.7461749595.4984478528.3490.7085580.9223070.7056530.386457

MH56445837.28288224826.60007638.8547MH5644.9770230222.80738891638.85476388829.6860.9983263474166455.4211752048.8764485994.030.707390.9218130.7068230.387634

MH57444312.63577225035.10419388.0252MH5744.720176622.8430845388.02526388733.5040.9983413764183751.5141762390.3254465579.2840.7105520.9215710.7036450.388209



gmsgmsg.decg.decm

DRTS443738.0528422384.29195131.0774DRTS44.627236922.63452554131.07746388698.7040.9983468154196672.571749873.964458053.8910.7116920.9229780.7024910.384852

MH51444349.31405223738.21614401.8971MH5144.7303650122.62728226401.89716388737.3190.998340784189633.4341746317.174466393.5130.7104270.9230270.7037710.384735

MH55445256.3756222443.28467618.3631MH5544.8823265622.73424574618.36316388794.2240.9983318884175530.7481749595.5074478528.3470.7085580.9223070.7056530.386457

MH57444312.63616225035.10409388.0472MH5744.7201767122.84308447388.04726388733.5040.9983413764183751.5221762390.3264465579.3080.7105520.9215710.7036450.388209

MH58443655.8949523522.47945363.6297MH5844.6155263823.08957763363.62976388694.3190.99834754183635.7311783572.4534457290.9680.7118360.9198930.7023460.39217

MH5944299.10374223349.63574184.3831MH5944.4858621522.56378771184.38316388645.7720.9983550864209043.7171748935.4614446896.7230.7134230.9234530.7007330.383712

MH60442642.15106223832.11489131.2286MH6044.4450419622.64225414131.22866388630.4890.9983574744209542.1481755906.7314443622.1940.7139220.9229270.7002250.384976

MH61442510.1044323151.94436320.7889MH6144.4194734523.03109566320.78896388620.9170.998358974199483.8411785265.5574441725.9930.7142350.9202930.6999060.391231



gmsgmsg.decg.decm

BAIL44120.39996232025.93481114.9772BAIL44.0223333223.34053745114.97726388472.270.99838224217904.3691820055.44409956.2280.7190690.9181660.6949390.396195

DJ5544144.0428223947.68751251.0501DJ5544.2344563423.16324653251.05016388551.6580.9983697944208517.2371800578.1184426969.550.7164910.9193880.6975960.393352

DJ604419.3995423426.33571120.5889DJ6044.0192776523.07398214120.58896388471.1270.9983823794226546.8611800507.0084409715.9760.7191060.920.69490.391919

DRTS443738.052422384.29271131.0848DRTS44.6272367822.63452575131.08486388698.7040.9983468154196672.5781749873.9814458053.8860.7116920.9229780.7024910.384852

MH62441723.8786523048.03626239.9321MH6244.2899662923.01334341239.93216388572.4360.9983665464209243.8261787875.0144431379.2790.7158150.9204140.698290.390945

MH63441340.6103222581.72196160.8567MH6344.2279473122.96714499160.85676388549.2220.9983701744215060.2991786335.1074426388.3790.716570.9207290.6975150.390203

MH64441659.03789224152.35988153.1873MH6444.2830660822.69787774153.18736388569.8530.998366954219460.4981764854.9254430769.8190.7158990.9225520.6982040.385872

MH65441930.2904622359.8101290.4349MH6544.3250806822.5860583790.43496388585.5810.9983644924219844.5041755347.1334434067.0940.7153870.9233040.6987290.384071

3. Unificarea determinarilor GPS intr-o singura reteaSesiunea I 16.09.2009XYZII Transformat

DRTS4196672.5771749873.9614458053.901DRTS4196672.58451749873.96334458053.9178

MH594209043.7151748935.4664446896.735MH594209043.72271748935.46764446896.7524

MH604209542.1561755906.7244443622.199MH604209542.16351755906.72564443622.2158

MH614199483.8541785265.5624441726.017MH614199483.86161785265.56414441726.0343

MH624209243.8121787874.9914431379.289MH624209243.82021787874.99314431379.3058

MH634215060.2891786335.0954426388.379MH634215060.29701786335.09654426388.3961

MH644219460.4881764854.9094430769.838MH644219460.49611764854.91134430769.8551

MH654219844.4991755347.1344434067.091MH654219844.50651755347.13544434067.1077

S1-S2 transformatNume punctXYZ

DRTS0.00780.00180.0171

Sesiunea I 17.09.2009IIII Transformat

DRTS4196672.5711749873.9614458053.891DRTS4196672.56891749873.95964458053.8836

MH514189633.4331746317.1724466393.507MH514189633.43041746317.17014466393.5004

MH524200733.3521727561.6524463127.404MH524200733.35001727561.65054463127.3976

MH534181142.9511739860.8294477030.651MH534181142.94861739860.82684477030.6445

MH544174687.3221738126.9614484039.31MH544174687.31941738126.95914484039.3032

MH554175530.7461749595.4984478528.349MH554175530.74321749595.49584478528.3419

MH564166455.4211752048.8764485994.03MH564166455.41821752048.87464485994.0232

MH574183751.5141762390.3254465579.284MH574183751.51191762390.32304465579.2770

Sesiunea I 18.09.2009III

DRTS4196672.571749873.964458053.891

MH514189633.4341746317.174466393.513

MH554175530.7481749595.5074478528.347

MH574183751.5221762390.3264465579.308

MH584183635.7311783572.4534457290.968

MH594209043.7171748935.4614446896.723

MH604209542.1481755906.7314443622.194

MH614199483.8411785265.5574441725.993

S2-S3

DRTS0.0010332840.001625017-0.00017627

MH51-0.00134840.002060458-0.00522751

MH55-0.0020223-0.00989050.001742887

MH57-0.00745349-0.00075149-0.02403482

Media-0.00244773-0.00173913-0.00692393


BAIL4217904.3691820055.44409956.228

DJ554208517.2371800578.1184426969.55

DJ604226546.8611800507.0084409715.976

DRTS4196672.5781749873.9814458053.886

MH624209243.8261787875.0144431379.279

MH634215060.2991786335.1074426388.379

MH644219460.4981764854.9254430769.819

MH654219844.5041755347.1334434067.094

4. Calculul Unghiurilor triunghiurilor selectate si schita retelei

Am realizat in Autocad 2008 schita retelei cu ajutorul programului TopoLT ;

Plecand de la valorile date ale vectorilor retelei am calculat unghiurile triunghiurilor formate de acestia cu ajutorul Teoremei Cosinusului;

Mi-am ordonat vectorii dupa lungime de la cel mai scurt la cel mai lung alegand ca vector de baza al 4-lea punct.

Cos a = (B2+C2-A2) / 2*B*C rezultand a=arccos((B2+C2-A2) / 2*B*C)*180/PI()

Cos b = (A2+C2-B2) / 2*A*C rezultand b=arccos(A2+C2-B2) / 2*A*C)*180/PI()

Cos c = (A2+B2-C2) / 2*A*B rezultand c=arccos((A2+B2-C2) / 2*A*B)*180/PI()

Am inmultit cu 180/PI() deoarece valorile din excel sunt in radianiAm redus la orizont distantele date cu formula :

d = D*cos V; V-Elevation

DistantaElevationUnghiul in grade zecimaleUnghiul vertical VCos VDistanta redusa

GradeMinuteSecunde

1MH59-MH607718,133102545,22125,9689167-0,4292277780,99997197717,916524MH59-MH60

2MH62-MH637817,406803653,05208,1780361-0,6147361110,99994247816,956854MH62-MH63

3MH53-MH549685,178712749,815,2110055561,4638361110,99967369682,017924MH53-MH54

4MH65-MH6410070,63101842,63117,58073330,3118416670,999985210070,48134MH65-MH64

5MH53-MH5511335,94901032,179,434869440,1755833330,999995311335,89617MH53-MH55

6MH51-DRTS11478,21712412,93177,1286444-1,4035916670,999711474,77333MH51-DRTS

7MH55-MH5612004,8750237,8728,727069440,0438527780,999999712004,87138MH55-MH56

8MH55-MH5412751,8405310,63306,48383890,8862861110,999880412750,31411MH55-MH54

9DJ55-MH6213466,3450627,81297,3141111-0,1077250,999998213466,3212DJ55-MH62

10MH60-MH6514062,41201346,18198,5884556-0,2294944440,99999214062,2994MH60-MH65

11MH62-MH6114461,00501519,645,6108472220,2554555560,999990114460,86147MH62-MH61

12MH51-MH5315063,9120356,77349,70202780,5852138890,999947815063,12604MH51-MH53

13MH63-DJ5515684,79501532,9687,288505560,2591555560,999989815684,63486MH63-DJ55

14MH54-MH5616291,25104422,1279,48820556-0,7394777780,999916716289,89368MH54-MH56

15MH59-DRTS16685,57501529,1819,66004444-0,2581055560,999989916685,4058MH59-DRTS

16MH51-MH5717134,940723,5593,71289722-0,1232083330,999997717134,90068MH51-MH57

17MH59-MH6517954,56402250,36174,3215472-0,3806555560,999977917954,16746MH59-MH65

18MH60-MH6418537,1630055,9166,1412278-0,015527778118537,16262MH60-MH64

19MH51-MH5518891,4703417,7926,577527780,5716083330,999950218890,52988MH51-MH55

20MH57-DRTS19499,86605033,35238,0874639-0,8425972220,999891919497,75743MH57-DRTS

21MH57-MH5519974,13603415,18334,49585560,5708833330,999950419973,14412MH57-MH55

22DRTS-MH6020255,7220526,63178,2594389-0,0907305560,999998720255,6964DRTS-MH60

23MH53-MH5621085,8770457,9253,251388890,0827555560,99999921085,85501MH53-MH56

24BAIL-DJ6021374,9860450,94269,1824778-0,0808166670,99999921374,96464BAIL-DJ60

25MH63-MH6121886,35301913,1313,457030560,3203138890,999984421886,01138MH63-MH61

26MH51-MH5222037,35902249,01258,3432972-0,3802805560,99997822036,87341MH51-MH52

27MH58-MH6122277,73801237,46192,0681222-0,2104055560,999993322277,58759MH58-MH61

28MH63-MH6422359,7260711,71285,9916722-0,1199194440,999997822359,67653MH63-MH64

29MH57-MH5822746,2640948,92120,6632306-0,1635888890,999995922746,17159MH57-MH58

30MH52-DRTS23239,39803018,08107,3602972-0,5050222220,999961223238,49565MH52-DRTS

31MH51-MH5424532,4320538,42355,769550,8856722220,999880524529,50119MH51-MH54

32MH63-DJ6024713,41801216,22159,7186-0,2045055560,999993624713,26048MH63-DJ60

33MH59-MH6424940,2260111,84154,5844-0,1838444440,999994924940,09751MH59-MH64

34DJ55-DJ6024955,12602442,4196,6674944-0,4117777780,999974224954,48142DJ55-DJ60

35MH64-MH6225192,784053,5688,145750,0843222220,999998925192,75652MH64-MH62

36MH57-MH5325407,01901815,65308,98139440,3043472220,999985925406,66076MH57-MH53

37MH53-DRTS26486,7771434,92172,8886778-1,0763666670,999823526482,10279MH53-DRTS

38MH52-MH5326988,0302823,0844,233952780,4730777780,999965926987,11036MH52-MH53

39DJ55-BAIL27512,46802425,44148,8903194-0,4070666670,999974827511,77404DJ55-BAIL

40MH51-MH5927635,83403430,98190,5318083-0,5752722220,999949627634,44073MH51-MH59

41MH57-MH5628685,57502219,05354,36642780,3719583330,999978928684,97043MH57-MH56

42MH55-DRTS29432,2561451,64195,6001556-1,0810111110,99982229427,01744MH55-DRTS

43DJ60-MH6230467,3870514,19350,85941110,0872750,999998830467,35195DJ60-MH62

44MH61-MH6430589,190274,5240,4110917-0,451250,99996930588,24101MH61-MH64

45MH51-MH5630890,9890182,2927,383450,3006361110,999986230890,56346MH51-MH56

46MH60-MH6131091,90201235,8295,107155560,209950,999993331091,69316MH60-MH61

47MH51-MH6031730,89503753,46177,8472667-0,6315166670,999939331728,9676MH51-MH60

DistantaElevationUnghiul verticalCos VD. Redusa

48MH57-MH5431806,3360391,07323,67078610,6502972220,999935631804,2878MH57-MH54

49MH63-MH6532281,65201611,26289,6660972-0,2697944440,999988932281,29371MH63-MH65

50DRTS-MH6533797,34901315,56186,5685833-0,2209888890,999992633797,09741DRTS-MH65

51MH57-MH5934201,86502941,4220,5149083-0,4948333330,999962734200,58897MH57-MH59

52MH60-MH6234233,7240141,78120,09376940,0282722220,999999934233,72013MH60-MH62

53MH65-MH6234317,0810544,5696,37960,0957111110,999998634317,03292MH65-MH62

54MH57-MH6034486,3503454,25207,6200167-0,5817361110,999948534484,57256MH57-MH60

55MH52-MH5435033,260431,5334,175619440,7170916670,999921735030,51652MH52-MH54

56MH60-MH6335402,5420639,81132,8406-0,1110583330,999998135402,47559MH60-MH63

57DRTS-MH5436008,12905651,25356,20781940,9475694440,999863236003,20518DRTS-MH54

58MH58-DRTS36140,41603150,62272,2234472-0,5307277780,999957136138,86545MH58-DRTS

59MH57-MH6136602,7701611,56155,8521861-0,2698777780,999988936602,36356MH57-MH61

60MH52-MH5536849,02602022,254,405658330,33950,999982436848,37911MH52-MH55

61MH65-MH6136990,91101127,3873,371263890,1909388890,999994436990,7055MH65-MH61

62MH64-DJ5537554,54018,7898,10723333-0,0191055560,999999937554,53771MH64-DJ55

63MH63-BAIL37618,64501419,62127,2670528-0,2387833330,999991337618,31871MH63-BAIL

64MH59-MH6137921,019029,71101,05469720,0360305560,999999837921,011MH59-MH61

65DRTS-MH6438576,390826,68172,4671694-0,1407444440,99999738576,27351DRTS-MH64

66MH51-MH5838817,32701350,16109,0319111-0,23060,999991938817,01251MH51-MH58

67MH57-MH5238825,6501848,18265,2124694-0,3133833330,99998538825,06904MH57-MH52

68DRTS-MH6139077,723069,88126,07658610,1027444440,999998439077,66057DRTS-MH61

69BAIL-MH6239617,3010010,75318,76125560,002986111139617,30045BAIL-MH62

70MH58-MH6040291,06403040,65242,108425-0,5112916670,999960240289,46006MH58-MH60

71MH58-MH5540879,701024,27316,62156940,1734083330,999995440879,51267MH58-MH55

72DRTS-MH5641212,34903114,2319,323283330,5206194440,999958741210,64756DRTS-MH56

73MH59-MH6241917,9910644,08121,1288028-0,1122444440,999998141917,91056MH59-MH62

74MH64-DJ6042006,49701359,18134,1183306-0,2331055560,999991742006,14975MH64-DJ60

75MH59-MH6343075,79801329,19131,5671056-0,2247750,999992343075,46632MH59-MH63

76MH58-MH5944196,46302550,2251,1566-0,4306111110,999971844195,21511MH58-MH59

77MH59-MH5546088,11701956,0216,992472220,3322277780,999983246087,34181MH59-MH55

78MH51-MH6147143,33401837,24136,98435-0,3103444440,999985347142,64264MH51-MH61

79MH65-DJ5547164,8610059,1102,1266417-0,016416667147164,85896MH65-DJ55

80MH52-MH5647932,06801150,7248,114555560,1974222220,999994147931,78376MH52-MH56

81DRTS-MH6248100,410511,32141,0528056-0,0864777780,999998948100,35531DRTS-MH62

82MH55-MH6049143,12304720,5188,570675-0,7890277780,999905249138,46302MH55-MH60

83DRTS-MH6351674,24401157,47149,0488083-0,1992972220,99999451673,93159DRTS-MH63

84MH65-DJ6051742,75901156,33130,8790333-0,1989805560,99999451742,44737MH65-DJ60

85MH55-MH6156573,10703320,68155,2966889-0,5557444440,99995356570,44577MH55-MH61

86MH64-BAIL59014,5710187,02119,1773278-0,301950,999986159013,75169MH64-BAIL

87DJ55-DRTS60641,9110238,73316,2187028-0,3857583330,999977360640,53696DJ55-DRTS

88MH65-BAIL69081,52801722,83118,8778972-0,2896750,999987269080,64471MH65-BAIL

89DJ60-DRTS76109,9840203,57332,7280917-0,3343250,99998376108,6887DJ60-DRTS

90BAIL-DRTS87690,3910230,6320,2883389-0,38350,999977687688,42681BAIL-DRTS

TriunghiAABBCCcos(a)acos(b)bcos(c)cVerificare

IMH53-MH549682,017924MH54-MH5512750,31411MH53-MH5511335,896170,6826370546,949943270,27185028774,225600570,51766185858,82445616180

IIMH52-MH5326987,11036MH53-MH549682,017924MH52-MH5435030,516520,87357559129,123157040,98463828210,05576354-0,775176963140,8210794180

IIIMH54-MH5512750,31411MH55-MH5612004,87138MH54-MH5616289,893680,63128832350,854763210,68322697546,903672140,13499680982,24156464180

IVMH55-MH5612004,87138MH56-MH5728684,97043MH55-MH5719973,144120,94046294319,87055255-0,583430455125,69218610,82474590734,43726136180

VMH51-MH5518890,52988MH55-MH5719973,14412MH51-MH5717134,900680,49041799160,631941420,38853920667,136364980,6124698852,2316936180

VIMH51-MH5315063,12604MH53-MH5511335,89617MH51-MH5518890,529880,60347339352,880931730,79994140136,87549309-0,00425117690,24357518180

VIIMH51-MH5222036,87341MH52-MH5326987,11036MH51-MH5315063,126040,57757228554,72002936-0,02377292691,362216650,82983941933,91775399180

VIIIMH51-MH5717134,90068MH57-MH6034484,57256MH51-MH6031728,96760,86930088329,622501090,10221817384,133082890,40283589366,24441602180

IXMH57-MH5822746,17159MH58-MH6122277,58759MH57-MH6136602,363560,80856979236,043569320,81725309835,18924383-0,321723499108,7671868180

XMH57-MH6034484,57256MH60-MH6131091,69316MH57-MH6136602,363560,49086631760,602461970,61884190751,76838640,38059992667,62915162180

XIMH51-MH5927634,44073MH59-MH607717,916524MH51-MH6031728,96760,61791371951,836057260,97559278912,68481151-0,430182321115,4791312180

XIIMH59-MH607717,916524MH60-MH6514062,2994MH59-MH6517954,167460,91203234424,212265210,6645440648,35264358-0,299625167107,4350912180

XIIIMH60-MH6418537,16262MH64-MH6510070,48134MH60-MH6514062,2994-0,15698836499,032133110,84388577232,447248630,66235048948,52061826180

XIVMH60-MH6234233,72013MH62-MH6425192,75652MH60-MH6418537,16262-0,207329007101,9658710,69406280546,047418150,84817098331,98671084180

XVMH60-MH6131091,69316MH61-MH6214460,86147MH60-MH6234233,720130,41851478865,259144710,90640402324,986949770,00429514689,75390552180

XVIMH62-MH637816,956854MH63-MH6422359,67653MH62-MH6425192,756520,952886317,657583160,4971918360,18561376-0,210587835102,1568031180

5. Problema geodezica directa

Pornind de la NRO latura incepand cu cea mai scurta, singura considerata cunoscuta, inclusiv coordonatele geodezice ale punctelor 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 NRO vector 3D din retea, coordonatele geodezice ale punctelor ce formeaza vectorul si unghiurile triunghiurilor calculate la etapa 3;Date de iesire: Coordonate geocentrice ale punctelor din retea;

Formule folosite:a) Transformarea coordonatelor B L in B L cu zecimale

B transformat=(((Grade*60+Minute)*60+Secunde)/3600)L transformat=(((Grade*60+Minute)*60+Secunde)/3600)

b) Transformarea distantelor

s = (S*180) / (PI()*Ra) unde:s-distanta in gradeS-distanta in metriRa-Raza de curbura a unei laturi de azimut A Ra = (M*N) / (N*cos2A+M*sin2A)

M= (a*(1-e2)) / W3

N= a / W

c) Calcule Azimut, Latitudine si Diferenta de Longitudine

Unde

A2=azimutul invers; =Diferenta de longitudine

A1=azimutul cunoscut; =Latitudinea cunoscutas=distanta cunoscuta transformata in valori unghiulare

Rezolvnd sistemul de ecuaii constituit mai sus, rezult necunoscutele i , celelalte elemente fiind cunoscute.

Cu una din formulele de mai sus determinam latitudinea punctului nou

-latitudinea care vrem sa o determinamCelelalte elemente fiind deja cunoscute.

Date de intrareDistantaAzimutulAzimutcosAsinAVectorulBLAzimut InversLatitudineDiferenta longitudineWMNRas

Grade MinuteSecunde

MH65-MH6410070,481341173450,64117,5807333-0,22699515-0,973895889144,3250806922,5860584239,874441844,206642150,06809940,9983644926366626,2636388585,5816387450,3860,090332769

MH64-MH6322359,676532855930,02105,99167220,680407335-0,732834127244,2066421522,6541578234,108887743,950542420,1503234510,998366956366579,2446388569,8536378370,3550,200853043

MH63-MH627816,9568542081040,9328,17803611-0,9953669520,096149008343,9505424222,80448125194,355096543,878357360,0202511710,9983701746366517,5626388549,2226366720,5410,070346835

MH62-MH6114460,8614753639,055,6108472220,782367607-0,62281693443,8783573622,82473242182,86542243,747915560,0263307010,9983665466366586,9666388572,4366375097,1620,129966071

MH61-MH5822277,5875919245,2412,068122220,878420981-0,477887623543,7479155622,85106312186,180127543,546169750,0363219770,998358976366731,9086388620,9176371717,6190,200324594

MH58-MH5722746,171591203947,63300,66323060,598103141-0,801419136643,5461697522,8873851149,644547443,29773201-0,223921060,99834756366951,3636388694,3196380899,230,204243882

MH57-MH5628684,970433542159,14354,3664278-0,8059356470,592003153743,2977320122,66346404177,108651943,03931567-0,032186680,9983413766367068,5196388733,5046374644,6530,257822644

MH56-MH5512004,87138284337,45208,72706940,1877216270,982222272843,0393156722,63127736103,005653742,8937388-0,065068130,9983263476367356,0896388829,6866388070,5070,1076739

MH55-MH5412750,31411306291,82306,48383890,177607894-0,984101334942,893738822,56620924152,703513942,75877131-0,115614010,9983318886367250,0616388794,2246388112,3960,114359163

MH54-MH539682,01792451239,62185,2110056-0,9897984680,1424745341042,7587713122,4505952391,0753185842,66451409-0,009895040,9983279016367326,3516388819,746367761,2070,087116766

MH53-MH5226987,1103644142,23224,2339528-0,380116228-0,9249387291142,6645140922,44070019110,772115642,31502956-0,210494570,9983329776367229,226388787,2536385663,350,242143602

MH52-MH5122036,873412582035,8778,34329722-0,9807521840,1952566381242,3150295622,23020562220,031596142,051517820,2412796630,9983431446367034,7086388722,1966367858,8460,198280124

MH51-MH5927634,440731903154,51190,5318083-0,448827470,8936184321342,0515178222,4714852893,7450077641,76457497-0,055752830,998340786367079,9266388737,3196384362,680,24800233

MH59-MH607717,916524125588,1125,96891670,9537837130,3004939751441,7645749722,41573246244,108403941,662873560,0689954250,9983550866366806,2176388645,7726368772,1210,069433171

MH60-MH6514062,29941983518,44198,5884556-0,784988738-0,6195100341541,6628735622,4847278897,8562232941,50432386-0,0492970,9983574746366760,5276388630,4896375136,3290,126383243

41,5043238622,43543088

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;

Plecand de la coordonatele geodezice ale punctelor din retea calculate anterior s-au determinat Lungimile si Orientarile laturilor triunghiurilor din retea.Formule Folosite:-Am calculat orientarea si orientarea inversa cu formulele:

Unde A1 = Orientarea A2 = Orientarea Inversa

= Latitudinea punctului 2 in formula de mai sus

= Latitudinea punctului 1 in formula de mai sus

Ambele formule de mai sus rezolva aceiasi problema si anume:Calculul distantei dintre cele 2 puncte de coordonate cunoscute (B,L) rezultatul fiind o distanta ca unghiCu ajutorul formulei de mai jos am transformat ulterior distanta ca unghi in distanta in metri.S = (2*PI()*Ra*s) / (360) unde:s-distanta in gradeS-distanta in metriRa-Raza de curbura a Ra = (M*N) / (N*cos2A+M*sin2A)

M= (a*(1-e2)) / W3

N= a / W

Date de intrareVectorulBLDistantasA1A2

MH65-MH64144,3250806922,586058410070,481340,090332769202,3554506202,4029832

MH64-MH63244,2066421522,654157822359,676530,200853043202,811575202,916147

MH63-MH62343,9505424222,804481257816,9568540,070346835191,4184508191,4324966

MH62-MH61443,8783573622,8247324214460,861470,129966071188,2783599188,2965889

MH61-MH58543,7479155622,8510631222277,587590,200324594187,409971187,435041

MH58-MH57643,5461697522,887385122746,171590,204243882146,8666813146,7127651

MH57-MH56743,2977320122,6634640428684,970430,257822644174,820363174,7983425

MH56-MH55843,0393156722,6312773612004,871380,1076739161,9108338161,8664852

MH55-MH54942,893738822,5662092412750,314110,114359163147,900152147,8215602

MH54-MH531042,7587713122,450595239682,0179240,087116766175,592512175,5858001

MH53-MH521142,6645140922,4407001926987,110360,242143602156,1233585155,9811774

MH52-MH511242,3150295622,2302056222036,873410,198280124214,0753007214,2373216

MH51-MH591342,0515178222,4714852827634,440730,24800233171,7906113171,7533718

MH59-MH601441,7645749722,415732467717,9165240,069433171206,8356142206,8815244

MH60-MH651541,6628735622,4847278814062,29940,126383243166,9239302166,8912111

41,5043238622,43543088

Proiect Geodezie Matematica

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