gg excell 2014 2015 examen
DESCRIPTION
Examen geodesia geométricaTRANSCRIPT
Datos del ElipsoideNos lo dan Calculado Calculado Calculado
a 6378137b 6586.0000 6356752.31 0.0033528107Excentricidad E 521854.0097002 521854.01e 0.081819191 0.08181919e' 0.0820944382 0 0.0820944382
0.00669438 0.00669438
0.0067394968
Caso 1 Caso 2
a 6378137 b 6356752.31 a
0.00335281 Excentricidad E 521854.01e 0.08181919e' 0.08209444
0.00669438
0.0067395
e2
e'2
e2
e2
e'2
6378137 0.00335281
0.00669438 b 6356752.31Excentricidad E 521854.01e 0.08181919
e' 0.08209444
0.0067395e'2
Geodésicas -> Cartesianas 3Da (m) 6378137.000 521854.008
b (m) 6356752.314 0.08181919
α 0.00335 0.08209444
N/S ° ´ ´´ rad
N 41 33 50.97797 0.72543
E/W ° ´ ´´ radE 0 37 53.62065 0.01102° ´ ´´ rad
h (m) 280.658 280.658H (m)
° ´ ´´ N/S
0.7220986445 41 22 23.53700 N
0.0033328079 0 11 27.44097X (m) 4779172.9281
Y (m) 52682.11559
Z (m) 4209692.8321
ε excent lineal e2
e1º excent e'2
e'2º excent N1º vert(m)
φ lat geodésica
λ long geodésica
α (acimut)
N ondul (m)
φ' lat geocént
νang de la vertical
Geodésicas -> Cartesianas 3DCartesianas 3D -> Geodésicas
0.00669438 ###
0.00673950 R (m) #VALUE!
6387555.08 C 1
S 0.99477236
###
### X
6369048.83 YZ
1º iteración
3º iteración
5º iteración
ρ R curv merid(m)
x elip merid(m)
y elip merid(m)
r (D origen) (m)
Cartesianas 3D -> Geodésicasa (m) 6378137.000 521854.01 0.00669438
b (m) 6356752.31414 0.08181919 0.00673950
α 0.00335 0.08209444
° ´
4887959.725 0.6959695 39 52
-370869.749 -0.075729 4 204067832.670 h (m) 614.1860
02º iteración
0.6969696
6378137 6386951.64h (m) -1476127.75468 h (m) 5937.3009
0.6959668
4º iteración
0.6959695
6386930.477546 6386930.54
h (m) 599.5117 h (m) 614.2265
0.69596956º iteración
0.6959695
6386930.535786 -0.075729h (m) 614.1859 h (m) 614.1860
ε excent lineal e2
e1º excent e'2
e'2º excent
φ lat geodésica
λ long geodésica
φ lat geodésica φ lat geodésica
N1º vert(m) N1º vert(m)
φ lat geodésica φ lat geodésica
N1º vert(m) N1º vert(m)
φ lat geodésica φ lat geodésica
N1º vert(m) λ long geodésica
Cartesianas 3D -> Geodésicas
´´
34.01850 N
20.23640 W
Geodésicas -> UTM PROBLEMA DIRECTO
a (m) 6378137 521854.008
b (m) 6356752.314 0.08181919
α 0.003352811 0.08209444
nombreN/S ° ´ ´´
N 36 42 33.36103
E/W ° ´ ´´
W 2 52 1.44982
UTM -> Geodésicas PROBLEMA INVERSOa (m) 6378137 521854.01
b (m) 6356752.314 0.08181919
ε excent lineal e2
e1º excent e'2
e'2º excent
φ lat geod
λ long geod
ε excent lineal e2
e1º excent e'2
α 0.00335 0.08209444
NombreX
Huso-0.052360
394006.153 -0.016653
30 0.638506 Q
4064025.574 -0.016645
e'2º excent
0 '
' Q'0
Geodésicas -> UTM PROBLEMA DIRECTO
0.00669438 C1 1.00505250 C3 0.00001063
0.00673950 C2 0.00506311 C4 0.00000002
radHuso
β
0.64070 -0.0523598776 4064246.9
rad30
0.0023200767
-0.05004 0.0043024056 6385778.88
UTM -> Geodésicas PROBLEMA INVERSO0.00669438 n 0.00167922 h1 0.00083773
0.00673950 A 6367449.1458 h2 0.00000006
0 x1
Δ N1º vert(m) x2
x3
0.63770327 0.689793 ° ´
0.63760064 0.689793 0.6408152651 36 42
0.68578782 0.689793 ° ´
0.68977594 0.689793 -0.0730741196 4 11
Q'1 φ lat geodésica
Q'2Q'3 λ long geodésica
Q'4
Geodésicas -> UTM PROBLEMA DIRECTO
X Y
5119344.67 3060112.94
511872.525 4062629.4321475105.72 8816395.42
-10100586 37205931.2
UTM -> Geodésicas PROBLEMA INVERSOh3 0.00000000
h4 0.00000000
y1
y2
y3
´´ N/S
57.63650 N
´´ E/W
12.61913 W
Sistema Geodésico Local4779172.93 4741135.35 0.7254315
52682.1156 80331.4421 0.011023
4209692.83 4253130.05
1º iteración 0 2º iteración 0.7265521
6378137 6387578.95h (m) -1598673.716 h (m) 6614.51
4º iteración 0.7254315 5º iteración 0.7254315
6387555.0852 6387555.09h (m) 280.71 h (m) 280.66
Xi Xj φi
Yi Yj λi
Zi Zj
φ lat geodésica φ lat geodésica
N1º vert(m) N1º vert(m)
φ lat geodésica φ lat geodésica
N1º vert(m) N1º vert(m)
Sistema Geodésico LocalE 28066.9198
N 57532.9122 a 6378137
U 588.3207 0.00335281
3º iteración 0.7254281
6387555.01h (m) 261.96
6º iteración 0.7254315
0.011023h (m) 280.66
φ lat geodésica
N1º vert(m)
φ lat geodésica
λ long geodésica
b 6356752.31
Excentricidad 521854.01e 0.08181919e' 0.08209444
0.00669438
0.0067395
e2
e'2
Inc K 0.0000028 (1+IncK) 1.0000028Seg Grad Rad
ω 1.2 0.00033333 0.00000582 Matriz R (ω)Ψ -1.5 -0.00041667 -0.00000727 1ε 0.6 0.00016667 0.00000291 -5.818E-006
Inc X 169.5 0
Inc Y 79
Inc Z 12.9 Matriz R (ε)10
Nombre Firenze 0X 4702884.28Y 1192253.16 Matriz R (Ψ )Z 4127302.19 1
0-0.0000073
Metodo 2
Inc K 4.08E-06 (1+IncK) 1.00000408
Seg Grad Rad Matriz 3ω 0.00000906 4.08E-06Ψ -0.00000174 -0.00000906
ε 0.00000198 -0.00000174
Inc X 593.032 3903453.15
Inc Y 26 368135.313
Inc Z 478.741 5012970.31 Suma590.179093
Nombre DUT 10.0741125
X 5112979.27 472.890887
Y -256066.228Z 3791608.6
X0
Y0
Z0
Metodo 3
Si lo da en ppm Aquí multiplica por 10^-6Inc K(m) 2.00E-06 (1+IncK) 1.000002
Seg Grad Radω -2.9 -0.00080556 -0.00001406Ψ -1.2 -0.00033333 -0.00000582ε 2.1 0.00058333 0.00001018Inc X 106.5Inc Y 104.9Inc Z 134.5 Matriz 2
1.000002 -0.00001406 0.00000582Nombre V2 0.00001406 1.000002 0.00001018X 5113004.23 -0.00000582 -0.00001018 1.000002Y -256015.621Z 3791576.39
Matriz R (ω) MatriG*Coor Factor Escala0.00000582 0 4702921.23018 4702934.4
1 0 1192237.80036 1192241.14
0 1 4127264.52341 4127276.08
Matriz R (ε) Coord0 0 4703103.8981 0.0000029 1192320.139
-0.0000029 1 4127288.980
Matriz R (Ψ )0 0.00000731 00 1
Matriz 3
x =0.00000906 0.00000174 1209526.1193 -2.85290729
4.08E-06 0.00000198 -624201.54159 -15.9258875
-0.00000198 4.08E-06 -1221361.7036 -5.85011332
Coord ###
-256056.154
###
X-X0
Mmult 2;3 Coord5113040.12 5113146.617
-255905.644 -255800.7443791556.83 3791691.335
Factor Escala Transformación Helmert de 7 parámetros sistema B -> sistema A
### ΔX
900718.814 ΔY
### ΔZ
Transformación Helmert de 7 parámetros sistema B -> sistema A
3924689.340 ΔX 593.032000
301145.338 ΔY 26.000000
5001908.687 ΔZ 478.741000
3903453.1482
368135.3134
5012970.3051
X SISTEMA B
Y SISTEMA B
Z SISTEMA B
X SISTEMA B
Y SISTEMA B
Z SISTEMA B
X0 SISTEMA A
Y0 SISTEMA A
Z0 SISTEMA A
Transformación Helmert de 7 parámetros sistema B -> sistema A ´´ rad
169.500000 ω 1.200000 0.000006 4524367.05
79.000000 ψ -1.500000 -0.000007 900639.814
12.900000 ε 0.600000 0.000003 4390807.450.000003
1 -5.818E-006 -7.272E-0065.8178E-006 1 -2.909E-0067.2722E-006 2.9089E-006 1
Transformación Helmert de 7 parámetros sistema B -> sistema A ´´ ppm rad
ω 0.0000091 3924096.3076
ψ -0.0000017 301119.3376
ε 0.00000198 5001429.9463
0.000004
0.000004 0.000009 0.000002
-0.000009 0.000004 0.000002
-0.000002 -0.000002 0.000004
∆k
X SISTEMA A
Y SISTEMA A
Z SISTEMA A
∆k
Transformación Helmert de 7 parámetros sistema B -> sistema A
4524329.88 ###
900653.363 900653.363
4390842.97 ###
Transformación Helmert de 7 parámetros sistema B -> sistema A
###
301135.263
###
X SISTEMA A
Y SISTEMA A
Z SISTEMA A
Cambio de epoca
Km Km/a
-1248.5973 Vx -1.8 -0.000018
-4819.43324 Vy 0.1 0.000001
3976.50018 Vz -0.4 -0.000004
Epoca i 2001Epoca j 1997 Estacion
-1248.59722
-4819.43325
3976.50019
m m/a
### Vx 0 0
-319058.410 Vy 0 0
### Vz 0 0
Epoca i 0Epoca j 0
X 5077906.3100Y -319058.3590
m Z 3834733.4080T1(cm) 0.054T2(cm) 0.051T3(cm) -0.048
maa rad
3.9270E-010
2.3756E-009
-3.840E-009
ITRFy1y1(XX) ITRFy1y1(YY)
Xi Xj
Yi Yj
Zi Zj
X0
Y0
Z0
ITRFy1y1(XX) VI ITRFy1y1(YY)
Xi Xj
Yi Yj
Zi Zj
ETRFy1y1(YY)
R1yy
R2yy
R3yy
Velocidades
0 3.8397E-009 2.37559E-009 Vx-3.840E-009 0 -3.9270E-010 Vy-2.376E-009 3.9270E-010 0 Vz
Transformación ITRF --> ETRF en una epoca tc
tc 2000.25Epoca base 1989
m
5077906.26 5077906.399
-319058.41 -319058.5953
3834733.46 3834733.271
VE
ITRFy1y1(XX) ETRFy1y1(XX)
Xi
Yi
Zi
Cambio de época de marcoestación Época i X [m] 4433469.953 -0.9
SJDV 1997.00Y [m] 362672.672 1.86
Z [m] 4556211.610 1.45
coordenadas ITFRxx traslaciones xx
estación Época X [m] 4433470.025 5.4
Colorado 2000.00Y [m] 362672.523 5.1
Z [m] 4556211.494 -4.8
0
coordenadas ITFRxx traslaciones xx
estación Época X [m] 4848724.786 5.4
P2 1997.00Y [m] -261632.373 5.1
Z [m] 4123094.050 -4.80.00E+00 3.84E-09 2.38E-09-3.84E-09 0.00E+00 -3.93E-10-2.38E-09 3.93E-10 0.00E+00
VX [cm/a]
VY [cm/a]
VZ [cm/a]
ITRFXX -> ETRFXX (posición - misma época -con velocidades)
TX [cm]
TY [cm]
TZ [cm]
y1y1
ITRFXX -> ETRFXX (posición - misma época -sin velocidades)
TX [cm]
TY [cm]
TZ [cm]
-1248.59722 Δx -0.000002
-4819.43324 Δy 0.000003
3976.50019 Δz -0.000002
m
### T1(cm) T2(cm) T3(cm)
-319058.410 89 0 0 0
### 90 1.9 2.8 -2.391 2.1 2.5 -3.792 3.8 4 -3.793 1.9 5.3 -2.1
94 4.1 4.1 -4.996 4.1 4.1 -4.997 4.1 4.1 -4.9
0 5.4 5.1 -4.85 5.6 4.8 -3.7
y1y1
0.00788465-0.02100366
-0.0121883
Cambio de época de marco Discrepancias (marcos distintos - misma época)Época j X [km] ### Sistema X [m] ###
1989.00Y [km] 362672.523 Y [m] 362672.523
Z [km] ### Z [m] ###
ITRFXX -> ETRFXX (velocidades - misma época -con velocidades)coordenadas ETFRxx velocidades ITRFxx milseg
X [m] ### -0.9 0.081
Y [m] 362672.574 1.86 0.49
Z [m] ### 1.45 -0.792
0.00E+00 3.84E-09 2.38E-09-3.84E-09 0.00E+00 -3.93E-10-2.38E-09 3.93E-10 0.00E+00
milseg rad coordenadas ETFRxx
0.081 3.93E-10 X [m] ###
0.49 2.38E-09 Y [m] -261632.484
-0.792 -3.84E-09 Z [m] ###7.03E-02-1.62E-01-9.30E-02
WGS84 (G1150) época
1997,00
(posición - misma época -con velocidades)
VX [cm/a] R1
VY [cm/a] R2
VZ [cm/a] R3
(posición - misma época -sin velocidades)
R1
R2
R3
89 0.11 0.57 -0.71
90 0.11 0.57 -0.7191 0.21 0.52 -0.6892 0.21 0.52 -0.6893 0.32 0.78 -0.67
94 0.2 0.5 -0.6596 0.2 0.5 -0.6597 0.2 0.5 -0.65
0 0.081 0.49 -0.7925 0.054 0.518 -0.781
y1y1 R1yy R2yy R3yy
Discrepancias (marcos distintos - misma época)Sistema X [m] discrep. X [cm]
Y [m] discrep. Y [cm]
Z [m] discrep. Z [cm]
ITRFXX -> ETRFXX (velocidades - misma época -con velocidades)rad coordenadas ITFRxx veloc. ETRFxx
3.93E-10 X [m] ### 0.32
2.38E-09 Y [m] 362672.672 -0.02
-3.84E-09 Z [m] ### 0.41
1.22E-02-1.88E-02-1.04E-02
WGS84 (G873) época
1997,00
VX [cm/a]
VY [cm/a]
VZ [cm/a]
Distancia Geodesica sobre el Elipsoide
N/S ° ´ ´´ radN 40 26 36.92524 0.70587
E/W ° ´ ´´ rad
W 3 57 7.13606 -0.06898
N/S ° ´ ´´ radN 40 31 29.63143 0.70729
ha 1423.636hb 828.228 Distancia esp 7250.125
6335682.93 6335682.93 Rmedio
7224.3512
7224.35159
φ lat A geodésica
λ long geodésica
φ lat B geodésica
Ri() Ri()
lij0
SijE
Distancia Geodesica sobre el Elipsoidea 6378137 b 6356752.31 0.00335281 Excentricidad 521854.01
N 6387139.84 e 0.08181919 ρ 6335439.33 e' 0.08209444
C 1.00141152 0.00669438
S 0.99470769 0.0067395
6335682.93
e2
e'2
Datosa 0
0ε 0b 0
#DIV/0!Dirección Grados Minutos Segundos Grados Deci.
N 0 0 0 0
E 0 0 0 0
0 0 0 0
635250.500
0.000
Iteraciones para calcular senz12, cosz12, n121ª Iteracion 2ª Iteracion 3ª iteración
1 #DIV/0! #DIV/0!
#DIV/0! #DIV/0! #DIV/0!
#DIV/0! #DIV/0! #DIV/0!
Obtenemos λ2
#DIV/0! #DIV/0!
#DIV/0! #DIV/0!
Iteraciones para calcular sen(φ2-φ1) definitivo y N2 1ª Iterración 2ª Iteracion
#DIV/0! #DIV/0!
#DIV/0! #DIV/0! #DIV/0! #DIV/0!
Obtenemos φ2
#DIV/0! #DIV/0!
#DIV/0!
Calculamos el Acimut Reciproco
#DIV/0! #DIV/0!
#DIV/0!
Grados Minutos Segundos
#DIV/0! #DIV/0! #DIV/0! #DIV/0!
#DIV/0! #DIV/0! #DIV/0!
e2
e'2
φ1
λ1
A12
S12
N1
senz12 cosz12 cosz12
cosz12 senz12 senz12
n12 n12 n12
cot(λ2-λ1) λ2-λ1
tan(λ2-λ1) λ2
sen(φ2-φ1) φ2-φ1 φ2 sen(φ2-φ1)
N2 N2
sen(φ2-φ1) φ2
φ2-φ1
cotA21 A21
tanA21
λ2
φ2
#DIV/0! #DIV/0! #DIV/0!A21
Datos
Radianes
0
0
0
Iteraciones para calcular senz12, cosz12, n124ª Iteración
#DIV/0!
#DIV/0!
#DIV/0!
#DIV/0!
Iteraciones para calcular sen(φ2-φ1) definitivo y N2 2ª Iteracion 3ª iteración
#DIV/0!
#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
cosz12
senz12
n12
cotz12
φ2-φ1 φ2 sen(φ2-φ1) φ2-φ1 φ2
N2
Iteraciones para calcular sen(φ2-φ1) definitivo y N2 4ª Iteración
#DIV/0!
#DIV/0! #DIV/0! #DIV/0!
sen(φ2-φ1) φ2-φ1 φ2
N2
Datosa 6378137
0.00669438ε 521854.01b 6356752.31
0.0067395Dirección Grados Minutos Segundos Grados Deci.
N 40 26 36.92524 40.4435903
W 3 57 7.13606 3.95198224
N 40 31 29.63143 40.5248976
W 3 5 19.06552 3.08862931
6387139.84
6387169.89
###
0.00003334
0.12830654 7.79383501 1.443187
0.11837457 8.44776067 1.45297007
Grados Minutos Segundos
82.6885241 41.3114434 18.6866032 82 º 41 ' 18,68660 ''
263.249053 14.9431591 56.589548 263 º 14 ' 56,58955 ''
73755.5937
e2
e'2
φ1
λ1
φ2
λ2
N1
N2
K0
sen2(ψ/2)
cot A12 tan A12 A12
cot A21 tan A21 A21
A12
A21
S12
Datos
Radianes
0.70587381
-0.0689751
0.70729289
-0.05390675
Datos
a 6378137 Coordenadas Punto A
0.00335281 X (m) 4887959.725ε 369316.201 Y (m) -370869.749b 6367435.68
0.00336409
Huso 30
Parametros para el Cálculo Posterior de Coordenadas Geodésicas
n 0.00084 h1 4.1934E-04 h3
A ### h2 1.4726E-08 h4
Cálculos para punto A Cálculos para punto B
0.688822 -0.046799
-0.058219 -0.046800
0.688048 -0.046800
-0.05811637 -0.046800
-0.0466258 -0.046800
Q -0.0466427 -0.046782 Q
-0.04679898 0.587865
4389715.61 1.003357
-371018.157 6367482.46863043
### 4.6076680264
Rad ° ´
convergencia merid -0.03406335 -1 57
ang. Reducc. Cuerda -1.596E-005 -0 0
aci. Geodésico direct 4.57358872 262 2
Factor Escala K ### Distancia Geodésica
e2
e'2
Q'1Q'2
' Q'3 '
' Q'4 '
Q'5φ lat geodésica
Q'0 λ long geodésica Q'0xA V2 xB
yA RA yB
kA tAB kB
A
dTA
αEAB
SEij
Datos
Punto B Incrementos
4885155.753 -2803.972-371164.462 -294.713
Parametros para el Cálculo Posterior de Coordenadas Geodésicas
2.0941E-11 -0.052360
1.3548E-14 2819.4171
Cálculos para punto B Cálculos para punto medio
0.688382 -0.046849 0.688382
-0.058265 -0.046849 -0.058265
0.687609 -0.046849 0.687609
-0.0581626315 -0.046849 -0.05816263
-0.0466751442 -0.046849 -0.04667514
-0.0466921009 -0.046832 Q -0.0466921
-0.0468485374 0.587514 -0.04684854 Rm
4386910.5172 1.003357
-371312.98719 6367482.47
1.236986467 1.46607537
´´ Rad ° ´
6.07036 -0.0340761 -1 57
3.2914 1.5954E-005 0 0
50.39099 1.43201522 82 2
2279.2627
l0l0ij
Q'1 Q'1Q'2 Q'2Q'3 ' Q'3Q'4 ' Q'4Q'5 Q'5
φ lat geodésica φ lat geodésica
λ long geodésica Q'0
V2 km
RB
tBA
b
dTB
αEBA
Cálculos para punto medio
-0.046849
-0.046849
-0.046849
-0.046849
-0.046849
-0.046832
6367482.47
###
´´
8.70064
3.2907
54.34274
Vértices X YP1 90296.116 80834.826P2 97156.749 81102.868
P3 98050.171 75960.756
a b 6865.86715 5219.14923 86.447441358 94.3408889
Lectura dcha 86.447441358 180.78833Lectura izda 0 86.4474414
B
97.5140181 189.048307 297.514018 389.048307 108.465710747
59.19902051/2(A+C) 55.37297951/2(A-C) -10.8689776
A 44.5040019
C 66.2419571
142.01802 6210.46204 4906.15007 -3807.82487 95202.266 77027.001
322.80635 3040.96056 -2847.90493 1066.24513 95202.266 77027.001
DESORIENTACIÓN
Vértice P1
X 90296.116
Y 80834.826 Xp 95202.292342.01802 Yp 77026.979
0 342.01802005342.01802
307.816218048 48.955596
A
B B
C B
A C
B
AP DA
P xAP yA
P XP YP
C
P DC
P xC
P yC
P XP
YP
P
V
HP
V
P
X Y Radianes HP P1 90296.116 80834.826 0 0
P2 97156.749 81102.868 1.3579132335 86.4474414P3 98050.171 75960.756 2.8398164508 180.78833P4 94491.189 73608.3 4.2574575662 271.038167P5 88148.558 76244.855 5.5127463608 350.952333P 95202.2661 77027.0011
N/S ° ´ ´´N 37 20 30.00000
θc θo DcP P1 342.01802 342.018020053 6210.46204
P2 28.4654614 28.4654614114 4520.25378P3 122.80635 122.8063503 3040.96056P4 213.055309 213.05618672 3491.86884P5 292.9696 292.970353387 7096.93949
Matriz A
Dx Dy
-9.87254547E-005 -0.0001272017
-0.0001994777 9.565468E-005
0.0001153016 0.0003079668
0.0002803789 -5.83178E-005
1.552907886E-005 -0.0001400475
Matriz P
1.00000000 00 1.00000000
57.33576 0 00 00 0
Dx 0.02628879Dy -0.02175684 -4.867E-006
φ lat A geodésica
195.5482.27
3013
52.5
328.31 49.2465 10.341765
387.898265rad
0.65174
Δx Δy θc θo-4906.15007 3807.82487 5.3724065 5.37240651954.48293 4075.86687 0.44713442 0.447134422847.90493 -1066.24513 1.92903764 1.92903764
-711.077071 -3418.70113 3.34666498 3.34667876-7053.70807 -782.146129 4.60195572 4.60196755
720
Matriz t
-1 0
-1 0
-1 0
-1 1.377961E-005
-1 1.183031E-005
0 0 00 0 0
1.00000000 0 00 1.00000000 00 0 1.00000000
P
coordenadas conocidas
Vértice X [m] Y [m]
C 588981.283 4095406.502
D 591987.540 4091740.150
coordenadas calculadas
A 586868.645 4092401.165
B 589969.029 4090274.904
ángulos observados ángulos calculados
α1 96.2508 α1 96.2508
α2 49.6247 α2 49.6247
α3 72.1324 α3 72.1324
α4 69.1688 α4 69.1692α5 30.0943 α5 30.0939
586868.645 96.25081 l
4092401.165 49.62470589969.029 72.13240
4090274.904 69.1691730.09392
4.73E-05 -3.87E-05 1.43E-05 5.63E-06
-3.87E-05 8.91E-05 -6.81E-06 4.80E-061.43E-05 -6.81E-06 4.13E-05 1.03E-055.63E-06 4.80E-06 1.03E-05 1.16E-05
7.41E+00 3.50E-04 -2.87E-04
-2.87E-04 6.60E-04
1.06E-04 -5.05E-05
4.17E-05 3.55E-05
1.56E+00 7.74E-02 2.38E+00 -8.02E-01
7.74E-02 3.83E-03 1.18E-01 -3.97E-02
X0 L0
N-1
σ^o2 ΣXX^^
ΣVV^^
2.38E+00 1.18E-01 3.64E+00 -1.22E+00-8.02E-01 -3.97E-02 -1.22E+00 4.12E-011.67E+00 8.28E-02 2.55E+00 -8.58E-01
coordenadas conocidas
Vértice X [m] Y [m]
P 455511.829 4094989.214
Q 460963.661 4092712.794
coordenadas calculadas
R 457373.383 4091620.647
S 459934.419 4089420.313
ángulos observados ángulos calculados
α 357.3213 α 357.3213
β 113.3432 β 113.3407
177.3272 177.3260
74.1003 74.1024
ε 105.8929 ε 105.8929
43.9802 43.9806
457373.383 357.3213 l
4091620.647 113.3407459934.428 177.3260
4089420.341 74.1024105.892943.9806
4.08E-03 -1.18E-03 1.91E-03 2.92E-03
-1.18E-03 1.44E-03 -4.84E-05 2.08E-041.91E-03 -4.84E-05 3.59E-03 2.02E-032.92E-03 2.08E-04 2.02E-03 4.83E-03
X0 L0
N-1
1.0127212389 0.0041305987 -0.001199562
-0.001199562 0.0014567392
0.0019327742 -4.902449E-005
0.0029570798 0.0002101787
Vértice X [m] Y [m] tipo
9826.121 10242.342 fija
10654.162 1323.995 fija
876.254 324.568 fija
988.443 10144.245 fija
P 5595.872 5124.105 aprox
COOR. EST
ESTACION VISADO LECTURA(g) σ [m] X
9826.121
9826.121
9826.121
10654.162
10654.162
10654.162
876.254
876.254
876.254
988.443
988.443
988.443
P 6640.132 0.013 5595.872
P 6326.700 0.011 5595.872
P 6731.310 0.014 5595.872
P 6813.950 0.015 5595.872
σ^o2 ΣXX^^
P1
P2
P3
P4
P1 P2
P1 P3
P1 P4
P2 P3
P2 P4
P2 P1
P3 P4
P3 P1
P3 P2
P4 P1
P4 P2
P4 P3
P1
P2
P3
P4
5595.872 6640.132
5124.105 6326.7006731.2976813.972
8.21E-05 5.19E-06 d -16.5355.19E-06 8.73E-05 119.399
0.868 0.00007 0.00000
0.00000 0.00008
X0 L0
PX
PY
N-1
σ^o2 ΣXX^^
Vértice X [m] Y [m] tipoA 5640.914 4912.480 fija
B 6079.721 5308.740 fija
C 6804.102 5308.740 fija
6133.001 4473.847 aprox
6777.299 4452.923 aprox
COOR. EST
ESTACION VISADO LECTURA(g) X
A B A-B 5640.914A C A-C 5640.914
P1
P2
B A B-A 6079.721B C B-C 6079.721C A C-A 6804.102C B C-B 6804.102
A P1-A 659.200 6133.001
B P1-B 836.593 6133.001
C P1-C 1071.176 6133.001
P1-P2 644.600 6133.001
A P2-A 1225.742 6777.299
B P2-B 1104.134 6777.299
C P2-C 856.170 6777.299
DISTANCIAS
P1-A 659.200 P1-B 836.593
P1-A 659.200 P1-C 1071.176
P1-B 836.593 P1-C 1071.176
P2-A 1225.742 P2-B 1104.134
P2-A 1225.742 P2-C 856.170
P2-B 1104.134 P2-C 856.170
6133.001 659.203
6777.299 836.591
4473.847 1071.178
4452.923 644.6381225.7911104.100856.236
0.700710 0.370954 0.029940 0.1655660.370954 0.735648 0.007439 0.3472820.029940 0.007439 0.489873 0.0033200.165566 0.347282 0.003320 0.738356
0.002 0.00153 0.00081
0.00081 0.00160
0.00007 0.00002
0.00036 0.00076
P1
P1
P1
P1 P2
P2
P2
P2
TRIANGULOS
A-P1-B
A-P1-C
B-P1-C
A-P2-B
A-P2-C
B-P2-C
X0 L0
P1X
P2X
P1Y
P2Y
N-1
σ^o2 ΣXX^^
Vértice X [m] Y [m] Z [m] tipoA 1177425.8873 -4674386.5584 4162989.7864 fijaD 1178680.6937 -4673056.1532 4164169.6566 fija
linea base increm. Coordenadas Elementos matriz covarianza
ABΔX -825.5585 0.00002199 -0.00000030ΔY 492.7369 0.00002806ΔZ 788.9732
BCΔX 606.2113 0.00003096 -0.00000029ΔY 558.8905 0.00002709ΔZ 546.7241
CDΔX 1474.1569 0.00004127 -0.00000045ΔY 278.7786 0.00004315ΔZ -155.8336
ACΔX -219.351 0.00002440 -0.00000020ΔY 1051.6348 0.00001700ΔZ 1335.6877
CBΔX -2080.3644 0.00003589 -0.00000034ΔY -837.6605 0.00002658ΔZ -390.9075
0.00002199 -0.00000030 0.00000030 0-0.00000030 0.00002806 -0.00000030 00.00000030 -0.00000030 0.00003640 0
0 0 0 0.000030960 0 0 -0.000000290 0 0 0.000000400 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 0
45486.8567674 482.3514667 -370.9162525 0.0000000
482.3514667 35646.1742323 289.8117261 0.0000000
ΔXAB
ΔYAB
-370.9162525 289.8117261 27477.9730328 0.0000000
0.0000000 0.0000000 0.0000000 32309.3268434
0.0000000 0.0000000 0.0000000 340.5743899
0.0000000 0.0000000 0.0000000 -494.9812491
0.0000000 0.0000000 0.0000000 0.0000000
0.0000000 0.0000000 0.0000000 0.0000000
0.0000000 0.0000000 0.0000000 0.0000000
0.0000000 0.0000000 0.0000000 0.0000000
0.0000000 0.0000000 0.0000000 0.0000000
0.0000000 0.0000000 0.0000000 0.0000000
0.0000000 0.0000000 0.0000000 0.0000000
0.0000000 0.0000000 0.0000000 0.0000000
0.0000000 0.0000000 0.0000000 0.0000000
X Y Z XB B B C
AB 1 0 0 0
AB 0 1 0 0AB 0 0 1 0BC -1 0 0 1BC 0 -1 0 0BC 0 0 -1 0CD 0 0 0 -1CD 0 0 0 0CD 0 0 0 0AC 0 0 0 1AC 0 0 0 0AC 0 0 0 0CB 1 0 0 -1CB 0 1 0 0CB 0 0 1 0
ΔZAB
ΔXBC
ΔYBC
ΔZBC
ΔXCD
ΔYCD
ΔZCD
ΔXAC
ΔYAC
ΔZAC
ΔXCB
ΔYCB
ΔZCB
calculado
2494.260 ESTACION
3759.370 A
por coordenadas A
356.2774 4741.278 A
260.0266 2494.260 B
60.0266 5225.796 B
387.8942 3759.437 B
338.2695 5161.398 D
138.2695 3673.594 D
108.1756
39.0064
96.25080 t -0.1 A 0
49.62470 0.0 -95.7747972.13240 0.0 069.16880 -3.7 157.5686130.09430 3.8 79.97844
d -2.88E+02 x^ -0.021 X
-2.09E+01 0.009-3.73E+02 -0.025-5.03E+02 -0.011
1.06E-04 4.17E-05 1.87E-02
-5.05E-05 3.55E-05 2.57E-02
3.06E-04 7.61E-05 1.75E-02
7.61E-05 8.63E-05 9.29E-03
1.67E+00 1.25E+00 5.84E+00
8.28E-02 6.19E-02 -7.74E-02
DDB
[m]
DBA
[m]
ϴDC [g] DD
C [m]
ϴDB [g] DD
B [g]
ϴBD [g] DB
C [g]
ϴBC [g] DB
A [g]
ϴBA [g] DA
D [g]
ϴAB [g] DA
C [g]
ϴAD [g]
ϴAC [g]
σxA
σyA
σxB
σyB
σV^ ΣLL^^
2.55E+00 1.91E+00 -2.38E+00-8.58E-01 6.42E-01 8.02E-011.79E+00 1.34E+00 -1.67E+00
calculado
3848.718
3449.575
por coordenadas
125.1812 5908.008
325.1812 3449.575
167.8599 3376.433
367.8599 3848.718
81.2005 3752.717
281.2005
145.1859
345.1859
19.2883
219.2883
357.3213 t 0.0 A 144.77493
113.3432 25.5 95.40415177.3272 11.5 267.6452874.1003 -20.5 -122.87035
105.8929 0.0 0.0000043.9802 -4.5 49.37078
d 7.29E+01 x^ -0.005 X
1.20E+02 0.075-7.77E-01 0.021-5.43E+01 -0.026
DPR [m]
DQS [m]
ϴPQ [g] DP
Q [m]
ϴQP [g] DQ
S [g]
ϴPR [g] DS
R [g]
ϴRP [g] DR
P [g]
ϴRQ [g] DR
Q [g]
ϴQR [g]
ϴRS [g]
ϴSR [g]
ϴSQ [g]
ϴQS [g]
0.0019327742 0.0029570798 0.064269734
-4.902449E-005 0.0002101787 3.82E-02 a
0.0036307429 0.0020494578 6.03E-02 b
0.0020494578 0.0048866068 6.99E-02
observ. m 4 SOLUCIÓN
incog. n 2 Vértice X [m]
redund 2 P 5595.871
COOR. EST COOR. PTO VIS calculado
Y X Y
10242.342 10654.162 1323.995 194.1061 8956.705
10242.342 876.254 324.568 246.7370 13358.981
10242.342 988.443 10144.245 299.2934 8838.222
1323.995 876.254 324.568 293.5155 9828.852
1323.995 988.443 10144.245 347.0904 13085.218
1323.995 9826.121 10242.342 394.1061 8956.705
324.568 988.443 10144.245 0.7273 9820.318
324.568 9826.121 10242.342 46.7370 13358.981
324.568 10654.162 1323.995 93.5155 9828.852
10144.245 9826.121 10242.342 99.2934 8838.222
10144.245 10654.162 1323.995 147.0904 13085.218
10144.245 876.254 324.568 200.7273 9820.318
5124.105 9826.121 10242.342 43.9710 6640.132
5124.105 10654.162 1323.995 141.0180 6326.700
5124.105 876.254 324.568 249.4655 6731.297
5124.105 988.443 10144.245 352.7274 6813.972
σxA
σyA
σxB
σyB ϴa
ϴ [g] D [m]
l t
6640.132 0.000 -0.63707
6326.700 0.000 -0.799516731.310 0.013 0.701156813.950 -0.022 0.67617
x^ -0.001 X 5595.871 Ax^0.010 5124.116
0.008 probabilidad 97 % 6.078
0.009
PX
σpx
σpy
observ. m 7 SOLUCIÓNincog. n 4 Vértice X [m]
redund 3 6133.015
6777.290
COOR. EST COOR. PTO VIS calculado
Y X Y
4912.480 6079.721 5308.740 53.241 591.2474912.480 6804.102 5308.740 79.097 1228.832
P1
P2
ϴ [g] D [m]
5308.740 5640.914 4912.480 253.241 591.2475308.740 6804.102 5308.740 100.000 724.3815308.740 5640.914 4912.480 279.097 1228.8325308.740 6079.721 5308.740 300.000 724.381
4473.847 5640.914 4912.480 659.203
4473.847 6079.721 5308.740 836.591
4473.847 6804.102 5308.740 1071.178
4473.847 6777.299 4452.923 644.638
4452.923 5640.914 4912.480 1225.791
4452.923 6079.721 5308.740 1104.100
4452.923 6804.102 5308.740 856.236
DISTANCIAS ACIMUT
A-B 591.247 A-B 53.241 B-A
A-C 1228.832 A-C 79.097 C-A
B-C 724.381 B-C 100.000 C-B
A-B 591.247 A-B 53.241 B-A
A-C 1228.832 A-C 79.097 C-A
B-C 724.381 B-C 100.000 C-B
l t
659.200 -0.003 P1-A 0.74649
836.593 0.002 P1-B 0.06369
1071.176 -0.002 P1-C -0.62651
644.600 -0.038 P1-P2 -0.999471225.742 -0.049 P2-A 0.000001104.134 0.034 P2-B 0.00000856.170 -0.066 P2-C 0.00000
d 0.038 x^ 0.014 X-0.059 -0.0090.001 0.0010.059 0.029
0.00007 0.00036 0.039
0.00002 0.00076 0.040
0.00107 0.00001 0.033
0.00001 0.00161 0.040 probabilidad 97 %
P1
σp1x
σp2x
σp1y
σp2y
SOLUCIÓNB C
X [m] 1176322.292 X [m]Y [m] -4673967.796 Y [m]
Elementos matriz covarianza Z [m] 4163818.065 Z [m]0.00000030-0.000000300.000036400.00000040-0.000000290.000025910.00000053-0.000000450.000058110.00000019-0.000000190.000023520.00000036-0.000000330.00002982
0 0 0 0 00 0 0 0 00 0 0 0 0
-0.00000029 0.00000040 0 0 00.00002709 -0.00000029 0 0 0-0.00000029 0.00002591 0 0 0
0 0 0.00004127 -0.00000045 0.000000530 0 -0.00000045 0.00004315 -0.000000450 0 0.00000053 -0.00000045 0.000058110 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 0
0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
340.5743899 -494.9812491 0.0000000 0.0000000 0.0000000
36922.0038809 407.9950355 0.0000000 0.0000000 0.0000000
407.9950355 38607.3450814 0.0000000 0.0000000 0.0000000
0.0000000 0.0000000 24236.2209595 250.4681321 -219.1100748
0.0000000 0.0000000 250.4681321 23179.4312320 177.2155557
0.0000000 0.0000000 -219.1100748 177.2155557 17212.1128092
0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
Y ZC C t
0 0 1176600.3288
0 0 -4673893.82150 0 4163778.75960 0 606.21131 0 558.89050 1 546.72410 0 -1177206.5368-1 0 4673334.93180 -1 -4164325.49020 0 1177206.5363 d1 0 -4673334.92360 1 4164325.47410 0 -2080.3644-1 0 -837.66050 -1 -390.9075
N-1
COOR. EST COOR. PTO VIS
P.VIS X [m] Y [m] X [m] Y [m]
B 586868.645 4092401.165 589969.029 4090274.904
C 586868.645 4092401.165 588981.283 4095406.502
D 586868.645 4092401.165 591987.540 4091740.150
A 589969.029 4090274.904 586868.645 4092401.165
C 589969.029 4090274.904 588981.283 4095406.502
D 589969.029 4090274.904 591987.540 4091740.150
B 591987.540 4091740.150 589969.029 4090274.904
C 591987.540 4091740.150 588981.283 4095406.502
0 149.93651 -206.55133 P 1
-139.65296 -23.85189 116.62684 00 -30.30983 229.57744 0
22.66634 0 0 017.32609 -95.77479 -139.65296 0
586868.6240 v^ -1.2501 Ax^ -1.3239
4092401.1744 -0.0619 -0.0501589969.0044 -1.9072 -1.8777
4090274.8926 0.6415 -3.0915-1.3380 2.4333
A B
a 2.88E-02 1.82E-02
b 1.34E-02 7.90E-03
1.66E+02 1.81E+02
-7.74E-02 -2.38E+00 8.02E-01 -1.67E+00
7.40E+00 -1.18E-01 3.97E-02 -8.28E-02
ϴa
σL^
-1.18E-01 3.77E+00 1.22E+00 -2.55E+003.97E-02 1.22E+00 6.99E+00 8.58E-01-8.28E-02 -2.55E+00 8.58E-01 5.62E+00
80.00621 0.00000 0.00000 P 0.006944
242.30557 0.00000 0.00000 0223.02112 -122.87035 -143.01490 0-143.01490 -53.27398 198.07826 0
0.00000 176.14433 -55.06335 0-162.29935 0.00000 0.00000 0
457373.3781 v^ 5.2920 Ax^ 5.2920
4091620.7211 -7.8540 17.6268459934.4487 5.0565 16.5985
4089420.3145 4.1790 -16.36305.0565 5.0565-7.8540 -12.3347
A B
0.068 0.080
0.032 0.046
223.2778 240.5364
SOLUCIÓN
precisión 97 % Y [m] precisión 97 %
± 0.051 5124.116 ± 0.053
TRIANGULOS Est
49.8649 53.0881 I
D
I [g] D [g]
P1-P-P2
-0.77080 P 5917.1598 0 0
0.60065 0 8264.4628 00.71302 0 0 5102.0408-0.73674 0 0 0
-0.00749 v^ -0.007 L^ 6640.1250.00680 0.007 6326.7070.00685 -0.007 6731.303-0.00811 0.013 6813.963
PY
SOLUCIÓNprecisión 97 % Y [m] precisión 97 %
± 0.160 4473.848 ± 0.134
± 0.164 4452.953 ± 0.164
COORDENADAS POR LA IZQUIERDA
ACIMUT
253.241 A 93.1074 146.3482 6132.995
279.097 A 67.2501 146.3475 6133.000
300.000 B 95.9424 195.9424 6133.006
253.241 A 71.2325 124.4733 6777.194
279.097 A 45.3648 124.4623 6777.273
300.000 B 56.4546 156.4546 6777.429
0.00000 -0.66540 0.00000 P 1
0.00000 -0.99797 0.00000 0
0.00000 -0.77942 0.00000 0
0.99947 0.03246 -0.03246 00.92706 0.00000 -0.37491 00.63181 0.00000 -0.77513 0-0.03130 0.00000 -0.99951 0
6133.015 Ax^ 0.00976 v^ 0.0126777.290 -0.00031 -0.0024473.848 -0.00981 -0.0074452.953 -0.02421 0.014
-0.01950 0.029
-0.02855 -0.063
-0.02907 0.037
probabilidad 97 % 4.088
I [g] Ѳ [g] X [m]
P2 P1 P2
SOLUCIÓNC
1177400.692-4673302.8614164307.459
0 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 0
0.00002440 -0.00000020 0.00000019 0 0-0.00000020 0.00001700 -0.00000019 0 00.00000019 -0.00000019 0.00002352 0 0
0 0 0 0.00003589 -0.000000340 0 0 -0.00000034 0.000026580 0 0 0.00000036 -0.00000033
0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
40990.0776785 478.5785821 -327.2612597 0.0000000 0.0000000
478.5785821 58834.4284710 471.4120527 0.0000000 0.0000000
-327.2612597 471.4120527 42523.4586705 0.0000000 0.0000000
0.0000000 0.0000000 0.0000000 27869.5883080 352.3670839
0.0000000 0.0000000 0.0000000 352.3670839 37631.8972675
0.0000000 0.0000000 0.0000000 -332.5543479 412.1956388
1.3026054E-005 -1.474691E-007 1.5519020E-007 6.2505785E-006 -6.916586E-008
-1.474691E-007 0.00001339 -1.471713E-007 -6.884972E-008 6.3758331E-0061.5519020E-007 -1.471713E-007 1.6626523E-005 6.4361917E-008 -6.820490E-0086.2505785E-006 -6.884972E-008 6.4361917E-008 1.0975259E-005 -1.055056E-007-6.916586E-008 6.3758331E-006 -6.820490E-008 -1.055056E-007 9.4242971E-0066.8133626E-008 -0.000000068 9.0953589E-006 1.1107051E-007 -1.032855E-007
49643327805.2 x^ 1176322.29156-164885668515 -4673967.79615112587429821 4163818.0648971180127635.7 1177400.6925-379665418111 -4673302.86093245117717565 4164307.4587
Dist. [m]
138.26950 3759.4370
39.00641 3673.5936
108.17558 5161.3978
338.26950 3759.4370
387.89420 5225.7957
60.02660 2494.2599
260.02660 2494.2599
356.27740 4741.2781
0 0 0 0
1 0 0 00 1 0 00 0 1 00 0 0 1
L^ 96.2507 96.2507
49.6247 49.624772.1322 72.132269.1689 69.168930.0942 30.0942
2.42E+00
2.72E+00
Ѳ [g]
1.94E+002.64E+002.37E+00
0 0 0 0 0
0.010000 0 0 0 00 0.008264 0 0 00 0 0.010000 0 00 0 0 0.008264 00 0 0 0 0.010000
L^ 357.3218 357.3218
113.3424 113.3399177.3277 177.326674.1007 74.1028
105.8934 105.893443.9794 43.9799
6640.132 243.9710 -4230.249 -5118.237 5595.872 5124.105
6326.700 341.0180 -5058.290 3800.110 5595.872 5124.105
Dr [m] Ѳ [g] ΔX'V [m] ΔY'
V [m] X'
V [m] Y'
V [m]
0
00
4444.4444
6640.1256326.7076731.3036813.963
COORDENADAS POR LA IZQUIERDA COORDENADAS POR LA DERECHA
4473.845 B 57.2975 195.9433 6132.995 4473.845
4473.851 C 35.9941 243.1034 6133.000 4473.851
4473.846 C 56.8971 243.1029 6133.006 4473.846
4452.794 B 96.7687 156.4721 6777.194 4452.794
4452.990 C 77.1022 201.9952 6777.273 4452.990
4452.986 C 98.0164 201.9836 6777.429 4452.986
0 0 0 0 0 0
1 0 0 0 0 0
0 1 0 0 0 0
0 0 1 0 0 00 0 0 1 0 00 0 0 0 1 00 0 0 0 0 1
L^ 659.212 659.212836.591 836.591
1071.169 1071.169644.614 644.614
1225.771 1225.771
1104.071 1104.071
856.207 856.207
Y [m] D [g] Ѳ [g] X [m] Y [m]
000000000000
0.00000036-0.000000330.00002982
0.0000000
0.0000000
0.0000000
0.0000000
0.0000000
0.0000000
0.0000000
0.0000000
0.0000000
0.0000000
0.0000000
0.0000000
-332.5543479
412.1956388
33543.1168386
6.8133626E-008
-0.0000000689.0953589E-0061.1107051E-007-1.032855E-0071.2559529E-005
COORDENADAS APROXIMADAS
6133.001 4473.847
6777.299 4452.923
X [m] Y [m]
P1
P2
DISTANCIASD
I-P 6640.132 I DD-P 6326.7 0.78327643 0.83390537I-D 8956.70504 49.864926 53.0880645
Xi Yi Xd YdI-D 9826.121 10242.342 10654.162 1323.995 194.1061
ANGULOS
I 49.864926D 53.0880645 PI 6640.132P 97.0470096 PD 6326.7
Xi Yi Xd YdI-D 9826.121 10242.342 10654.162 1323.995 194.1061
ϴ [g]
ϴ [g]
Dr X
I 6640.132 243.9710 -4230.249 -5118.237 5595.872D 6326.700 341.0180 -5058.290 3800.110 5595.872
8956.705 394.1061
X Y
I 243.9710 -4230.249 -5118.237 5595.872 5124.105D 341.0180 -5308.883 3800.110 5345.279 5124.105
8956.705 394.1061
ϴ [g] ΔX'V [m] ΔY'
V [m]
D [m] ϴr [g]
ϴ [g] ΔX'V [m] ΔY'
V [m]
D [m] ϴr [g]
Y
5124.1055124.105
1a)
Cartesianas 3D -> Geodésicasa (m) ### 521854.00842
b (m) 6356752.31 0.0818191908
α 0.00335 0.0820944379V1
X 5113681.077 0.6405277
Y -254961.108 -0.049817Z 3790742.991 h (m) 53.6288
1º iteración0
2º iteración6378137h (m) ###
3º iteración0.6405258
4º iteración6385775.36h (m) 44.6014
5º iteración0.6405277
6º iteración6385775.39h (m) 53.6288
Δh 1.6714 m
b)
Geodésicas -> UTM PROBLEMA DIRECTOa (m) 6378137 521854.00842
b (m) 6356752.314 0.0818191908
α 0.003352811 0.0820944379
nombreN/S ° ´ ´´
N 36 42 33.36103
E/W ° ´ ´´
W 2 52 1.44982
ε excent lineal
e1º excent
e'2º excent
φ lat geodésica
λ long geodésica
φ lat geodésica
N1º vert(m)
φ lat geodésica
N1º vert(m)
φ lat geodésica
N1º vert(m)
ε excent lineal e2
e1º excent e'2
e'2º excent
φ lat geod
λ long geod
Datos
a 6378137 Coordenadas Punto A Punto B
0.00335281 X (m) 511872.525 513012.398ε 369316.2 Y (m) 4062629.432 4061551.566b 6367435.68
0.00336409
Huso 30
Parametros para el Cálculo Posterior de Coordenadas Geodésicas
n 0.00084 h1 4.1934E-04 h3 2.0941E-11
A ### h2 1.4726E-08 h4 1.3548E-14
Cálculos para punto A Cálculos para punto B
0.001864 0.687475 0.002043
0.637752 0.687475 0.637582
0.001863 0.687475 0.002042
0.63735036 0.687475 0.6371811989
0.63734908 0.687475 0.6371796555
Q 0.68547478 0.638956 Q 0.6852639842
0.68747072 -0.050041 0.6872594644
11877.2756 1.002168 13017.604892
4064255.13 6375033.81 4063176.8363
### 2.32824226 0.999601907
Rad ° ´ ´´
convergencia merid 0.001382635 0 4 45.18887
ang. Reducc. Cuerda -1.6261E-007 -0 0 0.0335
aci. Geodésico direct 2.329624734 133 28 39.59442
Factor Escala K 0.999601907Distancia Geodésica 1569.4162
e2
e'2
Q'1Q'2
' Q'3 '
' Q'4 '
Q'5φ lat geodésica
Q'0 λ long geodésica Q'0xA V2 xB
yA RA yB
kA tAB kB
A
dTA
αEAB
SEij
c)
Metodo 3
Si lo da en ppm Aquí multiplica por 10^-6Inc K(m) 2.00E-06 (1+IncK) 1.000002
Seg Grad Radω -2.9 -0.000805556 -0.00001406Ψ -1.2 -0.000333333 -0.00000582ε 2.1 0.000583333 0.00001018Inc X 106.5Inc Y 104.9Inc Z 134.5 Matriz 2
1.000002 -0.00001406 0.00000582Nombre V2 0.00001406 1.000002 0.00001018X 5113004.23 -0.00000582 -0.00001018 1.000002Y -256015.621Z 3791576.39
Cartesianas 3D -> Geodésicas0.00669438
0.00673950
° ´ ´´
36 41 58.32677 N
2 51 15.57069 W
0.6413221
6385791.71h (m) 3822.6357
0.6405277
6385775.39h (m) 53.6504
0.6405277
-0.049817h (m) 53.6288
Geodésicas -> UTM PROBLEMA DIRECTO0.00669438 C1 1.00505250 C3 0.00001063
0.00673950 C2 0.00506311 C4 0.00000002
radHuso
β
0.64070 -0.05235988 4064246.9
rad30
0.00232008
-0.05004 0.00430241 6385778.88
e2
e'2
φ lat geodésica
N1º vert(m)
φ lat geodésica
N1º vert(m)
φ lat geodésica
λ long geodésica
0 x1
Δ N1º vert(m) x2
x3
Datos
Incrementos
1139.873-1077.866
Parametros para el Cálculo Posterior de Coordenadas Geodésicas
-0.052360
1568.7914
Cálculos para punto B Cálculos para punto medio
0.687264 0.002043 0.687264
0.687264 0.637582 0.687264
0.687264 0.002042 0.687264
0.687264 0.6371812 0.687264
0.687264 0.63717966 0.687264
0.638786 Q 0.68526398 0.638786
-0.049819 0.68725946 Rm 6375033.81
1.002168 ###
6375033.81
5.46983492
Rad ° ´ ´´
0.00151484 0 5 12.45909
1.6765E-007 0 0 0.0346
5.47134993 313 29 6.93276
l0l0ij
Q'1 Q'1Q'2 Q'2Q'3 ' Q'3Q'4 ' Q'4Q'5 Q'5
φ lat geodésica φ lat geodésica
λ long geodésica Q'0
V2 km
RB
tBA
b
dTB
αEBA
Mmult 2;3 Coord5113040.12 ###
-255905.644 -255800.7443791556.83 ###
Cartesianas 3D -> Geodésicasa (m) ### 521854.008
b (m) 6356752.31 0.08181919
α 0.00335 0.08209444V2
X 5113004.233 0.6406914
Y -256015.621 -0.050030Z 3791576.392 h (m) 51.9574
1º iteración0
2º iteración6378137h (m) ###
3º iteración0.6406895
4º iteración6385778.72h (m) 42.9165
5º iteración0.6406914
6º iteración6385778.76h (m) 51.9574
Geodésicas -> UTM PROBLEMA DIRECTO
V3X Y
5119344.67 3060112.936
511872.525 ###1475105.72 8816395.42
-10100586 37205931.23
ε excent lineal
e1º excent
e'2º excent
φ lat geodésica
λ long geodésica
φ lat geodésica
N1º vert(m)
φ lat geodésica
N1º vert(m)
φ lat geodésica
N1º vert(m)
y1
y2
y3
Cartesianas 3D -> Geodésicas0.00669438
0.00673950
° ´ ´´
36 42 32.08892 N
2 51 59.36305 W
0.6414864
6385795.08h (m) 3824.9529
0.6406914
6385778.76h (m) 51.9791
0.6406914
-0.050030h (m) 51.9574
Geodésicas -> UTM PROBLEMA DIRECTOa (m) 6378137 521854.008
b (m) 6356752.31 0.08181919
α 0.00335281 0.08209444
nombreN/S ° ´
N 36 41
E/W ° ´
W 2 51
e2
e'2
φ lat geodésica
N1º vert(m)
φ lat geodésica
N1º vert(m)
φ lat geodésica
λ long geodésica
ε excent lineal
e1º excent
e'2º excent
φ lat geod
λ long geod
Geodésicas -> UTM PROBLEMA DIRECTO0.00669438 C1 1.00505250 C3
0.00673950 C2 0.00506311 C4
´´ radHuso
β
58.32677 0.64053 -0.05235988 4063166.95
´´ rad30
0.00254251
15.57069 -0.04982 0.0043035 6385775.39
e2
e'2
0
Δ N1º vert(m)
Geodésicas -> UTM PROBLEMA DIRECTO0.00001063
0.00000002
V1X Y
5119990.14 3059801.56
513012.398 4061551.5661476965.73 8818525.44
-10092732 37250161.3
x1 y1
x2 y2
x3 y3
2a)V1
Cartesianas 3D -> Geodésicasa (m) 6378137.000 521854.01
b (m) 6356752.3141 0.08181919
α 0.00335 0.08209444
X 4887959.725 0.6959695
Y -370869.749 -0.075729Z 4067832.670 h (m) 614.1860
1º iteración0
2º iteración6378137h (m) ###
3º iteración0.6959668
4º iteración6386930.4775h (m) 599.5117
5º iteración0.6959695
6º iteración6386930.5358h (m) 614.1859
b) N/S ° ´ ´´ radφ2-φ1 N 0 2 20.98506 0.00068λ2-λ1 E/W ° ´ ´´ rad
W 0 0 21.30364 -0.00010h2-h1 20.382
V2 ° ´ ´´ rad
39 54 55.00356
-4 -20 -41.54004h (m) 634.5680
ε excent lineal
e1º excent
e'2º excent
φ lat geodésica
λ long geodésica
φ lat geodésica
N1º vert(m)
φ lat geodésica
N1º vert(m)
φ lat geodésica
N1º vert(m)
φ lat geodésica
λ long geodésica
Geodésicas -> Cartesianas 3Da (m) 6378137.000 521854.01
b (m) 6356752.3141 0.08181919
α 0.00335 0.08209444
N/S ° ´ ´´ rad
N 39 54 55.00356 0.69665
E/W ° ´ ´´ radW 4 20 41.54004 -0.07583° ´ ´´ rad
h (m) 634.568 634.568H (m)
° ´ ´´ N/S
0.6933496664 39 43 33.63460 N
0.00330337 0 11 21.36896X (m) 4885155.753Y (m) -371164.462Z (m) 4071182.157
Sistema Geodésico Local4887959.7247 4885155.753 0.6959695
-370869.7493 -371164.462 -0.075729
4067832.67 4071182.157
1º iteración 0 2º iteración 0.6969696
6378137 6386951.64h (m) -1476127.755 h (m) 5937.30
4º iteración 0.6959695 5º iteración 0.6959695
ε excent lineal e2
e1º excent e'2
e'2º excent N1º vert(m)
φ lat geodésica
λ long geodésica
α (acimut)
N ondul (m)
φ' lat geocént
νang de la vertical
Xi Xj φi
Yi Yj λi
Zi Zj
φ lat geodésica φ lat geodésica
N1º vert(m) N1º vert(m)
φ lat geodésica φ lat geodésica
6386930.5359 6386930.54h (m) 614.23 h (m) 614.19
d)Datos
a 6378137
0.00669438ε 521854.0097002b 6356752.31414
0.0067394968Dirección Grados Minutos Segundos Grados Deci.
N 39 52 34.01850 39.8761162
W 4 20 20.23640 4.33895456
N 39 54 55.00356 39.9152788
W 4 20 41.54004 4.34487223
6386930.535786
6386944.956552
0.013343945
1.1836788E-007
-8.5942699888 -0.1163565959 -0.11583571
-8.5893136217 -0.1164237382 -0.11590195
Grados Minutos Segundos
353.3631027618 21.786165708 47.169942455 353 º 21 ' 47.16994 ''
173.3593072103 21.558432616 33.505956932 173 º 21 ' 33.50596 ''
4377.6706216
N1º vert(m) N1º vert(m)
e2
e'2
φ1
λ1
φ2
λ2
N1
N2
K0
sen2(ψ/2)
cot A12 tan A12 A12
cot A21 tan A21 A21
A12
A21
S12
Cartesianas 3D -> Geodésicas0.00669438
0.00673950
° ´ ´´
39 52 34.01850 N
4 20 20.23640 W
0.6969696
6386951.64h (m) 5937.3009
0.6959695
6386930.54h (m) 614.2265
0.6959695
-0.075729h (m) 614.1860
e2
e'2
φ lat geodésica
N1º vert(m)
φ lat geodésica
N1º vert(m)
φ lat geodésica
λ long geodésica
Geodésicas -> Cartesianas 3D0.00669438 ###
0.00673950 R (m) #VALUE!
6386944.96 C 1S 0.99467734
###
###
6370010.51
Sistema Geodésico LocalE -506.0076
N 4348.7674 a 6378137
U 18.8757 0.00335281
3º iteración 0.6959668
6386930.48h (m) 599.51
6º iteración 0.6959695
ρ R curv merid(m)
x elip merid(m)
y elip merid(m)
r (D origen) (m)
φ lat geodésica
N1º vert(m)
φ lat geodésica
-0.075729h (m) 614.19
Datos
Radianes
0.69596952
-0.07572904
0.69665304
-0.07583233
λ long geodésica
b 6356752.31
Excentricidad 521854.01e 0.08181919e' 0.08209444
0.00669438
0.0067395
e2
e'2