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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
Masina 2GPSOra08:00Ziua 1
SesiunePunctDistantaTimp(minute)StartStop
IMH51553,76410:3012:30
MH53419,130
72,894
Masina 1GPSOra12:45Ziua 1
SesiunePunctDistantaTimp(minute)StartStop
IIMH57169,88014:4516:45
MH60238,549
108,3129
Masina 2GPSOra12:20Ziua 1
SesiunePunctDistantaTimp(minute)StartStop
IIMH52419,13014:4516:45
MH51500
19,130
RETUR ZIUA I
MASINADISTANTATIMPTOTAL KM
118,119239,4
2103,9104195,8
Masina 1GPSOra08:00Ziua 2
SesiunePunctDistantaTimp(minute)StartStop
IIIMH591223209:2011:20
MH60211,822
33,854
Masina 2GPSOra08:00Ziua 2
SesiunePunctDistantaTimp(minute)StartStop
IIIMH6530009:2011:20
MH64414,125
MH62529,240
43,365
Masina 1GPSOra11:35Ziua 2
SesiunePunctDistantaTimp(minute)StartStop
IVMH581607013:0015:00
MH60200
6070
Masina 2GPSOra11:15Ziua 2
SesiunePunctDistantaTimp(minute)StartStop
IVMH63511,92213:0015:00
MH6146171
72,993
RETUR ZIUA II
MASINADISTANTATIMPTOTAL KM
162,463156,2
266,467182,6
Masina 1GPSOra08:00Ziua 1
SesiunePunctDistantaTimp(minute)StartStop
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
Masina 2GPSOra08:00Ziua 1
SesiunePunctDistantaTimp(minute)StartStop
IMH60518,11909:1011:10
Total18,119
ReturMH6536,237
IIMH594222213:3015:30
Total58,259
ReturMH655+429,93015:30+30'=16:00
Masina 1GPSOra08:00Ziua 1
SesiunePunctDistantaTimp(minute)StartStop
IIIMH57456,65709:5011:50
MH5552424
Total80,681
ReturMH5742424
IVMH56432,73313:0015:00
Total56,757
ReturMH654+592,79315:00+93'=16:33
Masina 2GPSOra08:00Ziua 1
SesiunePunctDistantaTimp(minute)StartStop
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
Sesiunea I 17.09.2009
NumeBLhNumeBLhNWXYZcos Bcos Lsin Bsin L
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
Sesiunea I 18.09.2009
NumeBLhNumeBLhNWXYZcos Bcos Lsin Bsin L
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
Sesiunea I 19.09.2009
NumeBLhNumeBLhNWXYZcos Bcos Lsin Bsin L
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
Sesiunea I 19.09.2009
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