GG Excell 2014 2015 Examen

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)




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


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


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





Sistema Geodésico LocalE 28066.9198

N 57532.9122 a 6378137

U 588.3207 0.00335281

3º iteración 0.7254281

6387555.01h (m) 261.96


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


4524329.88 ###

900653.363 900653.363

4390842.97 ###


###

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


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


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


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 ° ´ ´Ń 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

σô2 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

σô2 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

σô2 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

σô2 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


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


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


-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


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



4º iteración6385778.72h (m) 42.9165


6º iteración6385778.76h (m) 51.9574


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


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



4º iteración6386930.4775h (m) 599.5117


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




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


353.3631027618 21.786165708 47.169942455 353 º 21 ' 47.16994 ''

173.3593072103 21.558432616 33.505956932 173 º 21 ' 33.50596 ''

4377.6706216


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


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


6386930.48h (m) 599.51


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

Documents

GG Excell 2014 2015 Examen