Problemas Resueltos Cartografía Matemática

81
1. Dadas las coordenadas UTM de dos bases de replanteo: X Y H(m) Huso B1 537874.93 4751640.93 161.79 29 B2 46545.21 4729813.85 294.11 30 φ λ Y las coord. geodésicas del punt P 42.59682222 -8.5284806 a) Calcula la distancia UTM en el huso 29 desde las dos bases. 1. Primero calcularemos las coordenadas geodésicas del p x -453636.244 y 4731706.533 = Sm A 1.005073987 m 6367654.49 B 0.005084684 n 16107.0277 C 1.0717E-05 p 16.9744555 D 2.07694E-08 q 0.02193076 Obtenemos n y N N n B2 6388278.663 0.003653123 Obtenemos las coordenadas geodésicas φ λ B2 0.743276452 -0.09643657 2. Ahora obtenemos las coordenadas UTM de B2 y P en el h φ λ φ B2 42.5866037 0.474591358 B2 0.74327645 P 42.5968222 0.471519444 P 0.7434548 A 1.00507399 m 6367654.491 B 0.00508468 n 16107.02766

description

Cartografia

Transcript of Problemas Resueltos Cartografía Matemática

Ejercicio 1

1. Dadas las coordenadas UTM de dos bases de replanteo:XYH(m)HusoElipsoide de HayforfdB1537874.934751640.93161.7929a6378388B246545.214729813.85294.1130e^20.00672267e'^20.0067681702Ko0.9996hY las coord. geodsicas del puntoP42.5968222222-8.5284805556W209.49a) Calcula la distancia UTM en el huso 29 desde las dos bases.1. Primero calcularemos las coordenadas geodsicas del punto B2.x-453636.244497799y4731706.53261304 = SmA1.0050739874m6367654.49129146'0.7430846851B0.0050846837n16107.0276636486' 10.7456046875C0.000010717p16.9744554954' 20.7456057596D0.0000000208q0.0219307596' 30.7456057642.7200632303sexa

Obtenemos n y NNnTanCosB26388278.662656410.00365312260.92342199320.7346770793Obtenemos las coordenadas geodsicas

B20.7432764516-0.0964365733B242.5866036862-5.5254086423B242.58660368620.4745913577Huso 29-8.5254086423Huso 300.74327645160.00828318182. Ahora obtenemos las coordenadas UTM de B2 y P en el huso 29

B242.58660368620.4745913577B20.74327645160.0082831818P42.59682222220.4715194444P0.74345479870.0082295668A1.0050739874m6367654.49129146B0.0050846837n16107.0276636486Sm B24716880.5967474C0.000010717p16.9744554954Sm P4718015.75510313D0.0000000208q0.0219307596

Nn^2pXYB26388228.658704720.00366883496364876.97576413B2538943.3018781324715102.98950294P6388232.486611450.00366763216364888.4175133P538684.9110389954716236.288714723. Calculamos las distancias UTM entre los puntosXYHNn^2pAxAyDB1537874.934751640.93161.790.7490362946388352.342605090.00362997156365246.67827181D utm B2 a P-258.39083913711133.29921178051162.382mB2538943.3018781324715102.98950294294.11D utm B1 a P809.9810389947-35404.641285280735413.905mP538684.9110389954716236.28871472209.49b) Acimut UTM y acimut geodsico.AxAyAcimutB1 a P809.9810389947-35404.64128528073.1187188229178.6894260407B2 a P-258.39083913711133.29921178056.0590184212347.1561835289

Calculamos la reduccion angular dTxyreducidas de translacion y escalaNmnmpmdTsegundosB137890.08603441384753542.34693877dT B1 a P6388292.414608270.00364880186365067.54789256-0.0000166805-3.4405950321B238958.88543230484716989.78541711dT B2 a P6388230.572658090.00366823356364882.696638710.00000054390.1121960601P38700.3911954734718123.53812997Calculamos la convergencia de meridianos.B10.0055146234B20.0056051386P0.0055699399Obtenemos el acimut geodsico.

B1 a P3.1242167658179.004434966sexa179016B2 a P6.0646241037347.477365477sexa3472939c) Distancia reducida al horizonte medio de B1 y B21. Calculamos el modulo de deformacion lineal puntual.B10.9996176459B20.9996186569K1 B1 y B20.9996181514P0.99961841012. Clculo de la distancia sobre el elipsoide. (d2)3. Clculo de la distancia sobre el eliposide (cuerda). D1R6376665.58677967D 2 B1 a P35427.4332904223D1 B1 a P35427.3877265589D 2 B2 a P1162.8264603938D1 B2 a P1162.82645878264. Distancia reducida al horizonte medio.

H medio227.95Dr B1 a P35428.6541679163 mDr B2 a P1162.8680269481 mKh = R0.9999642538

Ejercicio 22. Dadas las coordenadas geodsicas de los verticas y las alturas ortomtricas.HElip. HayfordV141.93229263890.025414505.3a6378388V241.9071101389-0.32318675337.1e^20.00672267e'^20.0067681702Ko0.9996a) Calcular las coordenadas UTM de los vrtices. (en los husos 31 y 30)Huso 30HV10.73185656950.0528034355505.3A1.0050739874m6367654.49129146V20.73141705190.0467192047337.1B0.0050846837n16107.0276636486C0.000010717p16.9744554954Sm V14644198.63216349D0.0000000208q0.0219307596Sm V24641401.48491338

Nn^2pXYHusoV16387983.826666350.00374577166335686.17161378V1750847.1399982794646768.8312574430V26387974.415547210.00374872916335647.54911531V2722028.4126954494643010.4516531330

Huso 31HV10.7318565695-0.0519163196505.3A1.0050739874m6367654.49129146V20.7314170519-0.0580005504337.1B0.0050846837n16107.0276636486C0.000010717p16.9744554954Sm V14644198.63216349D0.0000000208q0.0219307596Sm V24641401.48491338

Nn^2pXYHusoV16387983.826666350.00374577166335680.24714516V1253367.5917230264646621.2237536631V26387974.415547210.00374872916335722.8883144V2224352.1850288334644887.4029195431b) Acimut de V1 a V2Huso 30AxAyAcimutAcimut UTM-28818.7273028301-3758.37960431174.5827063971262.5697353004xyV1-246731.1007172614648480.61600006Huso 31AxAyAcimutV2-275758.1182184554646746.10136009Acimut UTM-29015.4066941935-1733.82083411334.6527047712266.5803467088Calculamos el acimut geodsico.dT0.000005515-0.0347106329

Acimut geodsico4.6179996533264.5918899251c) Distancia UTM.AxAyDD UTM-29015.4066941935-1733.820834113329067.1629216588md) Distancia sobre el elipsoide.1. Calculamos el coeficiente de demormacion lineal puntual K1K1 V11.000348338D229054.3340672704R6361786.64623558K1 V21.000534756Km1.000441547D129054.3088171569e) Distancia terreno reducida al horizonte medio.Hm421.2

kh = R V10.9999205789kh = R V20.9999470145Dr29056.2324344038kh = R Vm0.9999337967

Ejercicio 33. Desde el vrtice V1 se ha realizado una observacion a una base, obtenidose:HElipsoideV140.40833333334.0252777778508a6378388e0.00672267DgAcimutVime'0.00676817022890.25108.3631591.08361.561.3ko0.9996

a) Calcular las coordenadas UTM del vrtice.

Huso 31HV10.70525846190.017894473508A1.0050739874m6367654.49129146B0.0050846837n16107.0276636486C0.000010717p16.9744554954Sm V14474947.00099086D0.0000000208q0.0219307596

Nn^2pXYHusoV16387416.241790430.00392416496362448.94301452V1586998.5705639034473661.6321427730

b) Coordenadas UTM de la base (obtener la convergencia de meridianos y el acimut a la base).1. Hallamos K1 y la convergencia de meridianos2. Hallamos la distancia sobre la cuerda del elipsoide D1K1 V10.999693156AH-53.8479122037mH454.1520877963R6374920.36939861 V10.0116004723radD12889.53028430463. Hallamos D24. Hallamos la distancia UTMD22889.5303090401D utm2888.64367408165. Hallamos el acimut cartogrfico.Acimut1.879693283107.6984918962sexa6 Obtenemos las coordenadas UTM del punto.

XYHBase589750.4932408844472783.46139871454.1520877963

Ejercicio 44. Dadas las coordenadas UTM y alturas ortomtricas de los vrtices.XYHHusoElipsoideV1733480.094739868.923299.130a6378388V2257091.744729254.093348.231e0.00672267e'0.0067681702ko0.9996a) Calcular las coordenadas geodsicas de los vrtices.

xy = SmV1233573.5194077634741765.6262505V2-243005.4621848744731146.54861945A1.0050739874m6367654.49129146B0.0050846837n16107.0276636486'0.74466440240.7429967432C0.000010717p16.9744554954' 10.74718508430.745516707D0.0000000208q0.0219307596' 20.74718611650.7455177813' 30.74718611690.7455177817Nn^2pV16388312.599959670.0036424596365127.88230328TanCosV26388276.773634340.00365371626365020.79399482V10.92635421490.7336040214V20.92325900830.7347367624

HusoV10.74656519760.0498095685V142.7750349534-0.1461219476300.0498095685V20.7448479788-0.0517388921V242.67664556380.035579843731b) Acimut UTM de V1 a V21. Calculamos las coordenadas UTM de V2 en el huso 30.husoA1.0050739874m6367654.49129146V20.74484797880.05298086330B0.0050846837n16107.0276636486C0.000010717p16.9744554954Sm4726883.25344349D0.0000000208q0.0219307596

Nn^2pXYHusoV26388262.392922420.00365823496364977.80901109V2748739.6162452944729461.25882117302. Calculamos el acimut UTMAXAYAcimutV1 a V215259.5262452944-10407.66117882912.1693690399124.2956901919c) Calculamos el acimut geodsico.dT -0.0000306671xyNnpV1233573.5194077634741765.62625056388312.599959670.0036424596365127.88230328 V10.033841993V2248839.1519060574731353.800341316388276.773634340.00365371626365020.793994826388294.686797010.00364808766365074.33814905

Acimut geodsico2.2031803657126.2329364628d) Coeficiente de anamorfosis en V2K V21.0003610628K1 V11.0002705382Km1.0003158005e) Distancia UTM entre V1 y V2.AXAYDD UTM15259.5262452944-10407.661178829118470.857mf) Distancia reducida al horizonteD218465.0255769003R6376673.94301022

D118465.0191255582H V13299.1Kh0.9994828976D r18474.6434599583mH V23348.20.9994752057Hm3323.650.9994790517

Ejercicio 55. Dadas las coordenadas geodsicas del punto inicial y final de un tramo de obra lineal.ElipsoideI40.40.1Ea6378388F40.4-0.2We0.00672267e'0.0067681702ko0.9996a) Calcular las coordenadas UTM de ambos puntos.

Huso 30V10.70511301780.0541052068A1.0050739874m6367654.49129146V20.70511301780.0488692191B0.0050846837n16107.0276636486C0.000010717p16.9744554954Sm V14474021.62097493D0.0000000208q0.0219307596Sm V24474021.62097493

Nn^2pXYHusoV16387413.150436550.00392513666335695.04634317V1763097.2751347624476847.4337483530V26387413.150436550.00392513666335660.65951525V2737632.8005399254475996.9280092530

Huso 31V10.7051130178-0.0506145483A1.0050739874m6367654.49129146V20.7051130178-0.0558505361B0.0050846837n16107.0276636486C0.000010717p16.9744554954Sm V14474021.62097493D0.0000000208q0.0219307596Sm V24474021.62097493

Nn^2pXYHusoV16387413.150436550.00392513666335671.73455582V1253879.1633740744476270.7988373231V26387413.150436550.00392513666335707.28281305V2228414.3142403934477150.2022231431b) Distancia UTM entre ambos puntos.Huso 31AxAyDV1 a V2-25464.8491336813879.403385820825480.0292722779c) Acimut Utm y geodsico.Huso 31AxAyAcimutxxNn^2pV1 a V2-25464.8491336813879.40338582084.746909273271.977867076V1-246219.3243556684478062.023646786387413.150436550.00392513666335671.73455582V2-271694.3635050094478941.778934726387413.150436550.00392513666335707.28281305dT-0.00000277956387413.150436550.00392513666335689.50868443

-0.0328207399

Acimut g4.7140857537270.0972179473d) Coeficiente de anamorfosisHuso 31K V11.0005789039K V21.0007919115Km1.0006854077e) Distancia geodsicaHuso 31D225462.5770251515D125462.5600279693R6361498.76089384

Ejercicio 66. Desde el vrtice de Llatas, de coordenadas geodsicas en el sistema Geodsico de Referencia ED50.HElipsoideV43.4883333333-3.801666666772.2a6378388e0.00672267Se ha observado una base de replanteo.e'0.0067681702ko0.9996DgAcimutVinstmira3980103.849291.93951.651.55a) Calcular las coordenadas UTM de ambos puntos

1. Calculamos las coordenadas UTM del punto V.HV10.7590146029-0.013991722872.2A1.0050739874m6367654.49129146B0.0050846837n16107.0276636486C0.000010717p16.9744554954Sm V14817059.94573831D0.0000000208q0.0219307596

Nn^2pXYHusoV16388566.86501050.00356257076365887.93933999V435174.217504314815445.242479930

2. Calculamos las coordenadas UTM a partir de las observaciones.Hallamos la distancia UTM a partir de la distancia geodsica.

K1 V0.9996516863AH-133.5566620436mH-61.3566620436R6377217.32071579 V-0.0096295339radD13977.7551101475

3. Hallamos D24. Hallamos la distancia UTM

D23977.7551746298D utm3976.3696679444

5. Hallamos el acimut cartogrfico.

Acimut1.8221399995104.4009316532sexa

6 Obtenemos las coordenadas UTM del punto.

XYHBase439025.6461269474814456.2969299-61.3566620436b) coeficiente anamorfosis en ambos puntos.

Ejercicio 77. Dadas las coordenadas UTM y las alturas elipsoidales de las estaciones permanentes.XYhHusoElipsoideV212922.1214375456.56577.55531a6378388M1121661.2234441731.97997.93530e0.00672267e'0.0067681702ko0.9996a) Coordenadas geodsicas de ambas estaciones.

Huso 31xy = SmV-287192.7561024414377207.44797919M621909.9869947984443509.3827531A1.0050739874m6367654.49129146B0.0050846837n16107.0276636486'0.68741283840.6978251394C0.000010717p16.9744554954' 10.68989290750.7003150301D0.0000000208q0.0219307596' 20.68989534450.7003172191' 30.68989534690.700317221Nn^2pV6387090.584516350.00402654136361475.83961971TanCosM6387311.303417710.00395715256362135.36360569V0.82516017970.7713126264M0.84283079870.7646377894

V0.6890588194-0.0582497584V39.4801621856-0.3374653121-0.0582497584M0.69632870950.1268524232M39.89669620764.268108473b) Calcular la distancia UTM entre ambos puntos en el huso 31.1. Hallamos las coordenadas UTM en el huso 31 del punto MhusoA1.0050739874m6367654.49129146M0.69632870950.022132668131B0.0050846837n16107.0276636486C0.000010717p16.9744554954Sm4418134.43692832D0.0000000208q0.0219307596

Nn^2pXYHusoM6387226.731540770.0039837396361882.65135513M608414.7868798764417136.7809164631V6387072.906388910.00403209916361423.01807232c) Calcular el acimut geodsico.1. Obtenemos el acimut UTM2. Obtenemos la reduccion angularAXAYacimutNmn^2pmdTV a M395492.66587987641680.21591646221.465795828683.9839146044dT6387149.818964840.00400791916361652.83471372-0.00008000753. Obtenemos la convergencia de meridianosxyV-287192.7561024414377207.44797919-0.0370611087M108458.1701479354418904.342653524. Obtenemos el acimut geodsicoAcimut g1.428654712381.8558853987825121d) Distancia UTM y reducida al horizonte medio entre ambas estaciones.AXAYD utmCalculamos el modulo de deformacion para grandes distanciasV a M395492.66587987641680.2159164622397682.900265544K V1.0006143598K M0.9997446805K1.0001794572km1.0001795202D2397611.546028615D1397547.086273507R6374388.57864493

Hm87.745Kh0.9999862349Dr397552.558605268

Junio 2005Dadas las coordenadas UTM, obtener los datos para replantear por polares los puntos P1, P2, y P3.XYHElipsoideDebemos obtener el acimut geodsico y el acimut utm desde ambas bases.BR1423233.7714865331.822627.252a6378388BR2424733.2134865144.783727.141e0.00672267P1423525.9214865531.823650.325e'0.0067681702P2423945.0284865006.153675.85ko0.9996P3424425.0974865402.31695.631. Calcularemos la distancias geomtricas a partir de las distancia UTMAXAYD UTMB1 P1292.15200.0010000002354.0508755829B1 P2711.257-325.6689999998782.2702970264B1 P31191.32670.48799999991193.409483966B2 P1-1207.292387.041267.8146295354B2 P2-788.185-138.6299999999800.2836191782B2 P3-308.116257.5269999998401.56646421842. Calculamos K1 de los puntos B1 y B2. Para ello debemos hallar las coordenadas geodsicas.

xy = SmB1-76796.94777911164867278.7334934B2-75296.90576230494867091.61964786A1.0050739874m6367654.49129146B0.0050846837n16107.0276636486'0.76437544470.7643460597C0.000010717p16.9744554954' 10.7669024890.7668730974D0.0000000208q0.0219307596' 20.7669030210.7668736301' 30.76690302110.7668736302Nn^2pB16388736.636788040.00350923486366395.46012876TanCosB26388736.004012710.00350943366366393.56844133V0.96367736590.7200631395M0.96362068210.7200835338

Nn^2pB10.7668331592-0.0166927725B143.936303612-0.956425415rad-0.0690526501B16388735.132687960.00350970736366390.96360892B20.7668064745-0.0163663015B243.9347746927-0.9377200029radB26388734.558179320.00350988786366389.24611107

K1 B10.9996724727K1 B20.99966966923. Hallamos las distancias.R6377552.68912323

D2D1AHDgB1 P1354.1668749049354.166874859423.073354.9530494488B1 P2782.5265958532782.526595362348.598784.1139988773B1 P31193.80048622161193.800484478768.3781195.880755216B2 P11268.23356611451268.2335640248-76.8161270.6944895916B2 P2800.5480648423800.5480643167-51.291802.2773607654B2 P3401.6991578132401.6991577468-31.511402.97786146214. Suponemos un i y un m constantes para todas las estaciones, de manera que:i1.5m1.55. Hallamos la correccion por refracion de cada punto y el ngulo cenital.R6377552.68912323

DgCimAHCosVVB1 P1354.95304944880.00829730511.51.523.0730.06497958741.505770924686.2743188919B1 P2784.11399887730.04049054761.51.548.5980.06192659421.508830083786.4495957968B1 P31195.8807552160.09418266811.51.568.3780.05709918571.513666068686.726677321B2 P11270.69448959160.10633531661.51.5-76.816-0.06053566451.631369025293.4705599745B2 P2802.27736076540.04238813511.51.5-51.291-0.06398459021.634824656793.6685530737B2 P3402.97786146210.01069442921.51.5-31.511-0.07822190111.649098217394.48636785336. Por ultimo hallamos el acimut UTM y conseguimos el acimut geodsico.7. Hallamos la reduccion angular y la convergencia de meridianos.AXAYAcimut UTMxyB1 P1292.15200.00100000020.970492275255.6051114217sexaBR1-76796.94777911164867278.7334934-0.0115829816B1 P2711.257-325.6689999998-1.1414103212114.6020058998BR2-75296.90576230494867091.61964786-0.0113561101B1 P31191.32670.48799999991.511697543486.6138891384P1-76504.6808723494867478.81452581B2 P1-1207.292387.04-1.2605625911287.7750837201P2-76085.4061624654866952.93417367B2 P2-788.185-138.62999999991.3966919873260.0245561525P3-75605.14505802324867349.24969988B2 P3-308.116257.5269999998-0.8745971089309.88927688578. Hallamos el acimut geodsico.Acimut GeodsicoB1 P10.958909293654.9414554617sexaB1 P2-1.1529933028113.9383499399B1 P31.500114561885.9502331784B2 P1-1.2719187011287.1244265417B2 P21.3853358772259.373898974B2 P3-0.885953219309.2386197073

DgAcimutVi mB1 P1354.95354.941586.27431.51.5B1 P2784.114113.938386.44961.51.5B1 P31195.88185.950286.72671.51.5B2 P11270.694287.124493.47061.51.5B2 P2802.277259.373993.66861.51.5B2 P3402.978309.238694.48641.51.5

Sept 2005Dadas las coordenadas ED50-UTM de los puntos A y R y las observaciones, determinar:XYHElipsoideA674032.34364853.5701.9a6378388R670496.784361317.99e0.00672267e'0.0067681702HzVDgimko0.9996A a R01.3A a B275102.8937451.32B a A3592.6011.4B a C18099.4527501.42

Dic 2006Dadas las coordenadas geodsicas y las alturas ortomtricas de los vrticesHElipsoideV141.93229263890.025414505.3a6378388V241.9071101389-0.27318675337.1e0.00672267e'0.0067681702ko0.99961. Coordenadas UTM de los vrtices en los husos 31 y 30.

Huso 30V10.73185656950.0528034355A1.0050739874m6367654.49129146V20.73141705190.0475918693B0.0050846837n16107.0276636486C0.000010717p16.9744554954Sm V14644198.63216349D0.0000000208q0.0219307596Sm V24641401.48491338

Nn^2pXYHusoV16387983.826666350.00374577166335686.17161378V1750847.1399982794646768.8312574430V26387974.415547210.00374872916335652.79956784V2726176.0040931614643141.1832053630

Huso 31V10.7318565695-0.0519163196A1.0050739874m6367654.49129146V20.7314170519-0.0571278858B0.0050846837n16107.0276636486C0.000010717p16.9744554954Sm V14644198.63216349D0.0000000208q0.0219307596Sm V24641401.48491338

Nn^2pXYHusoV16387983.826666350.00374577166335680.24714516V1253367.5917230264646621.2237536631V26387974.415547210.00374872916335716.48346718V2228500.02178564644727.74700713312. Acimut de V1 a V2. UTM y Geodsico.AXAYAcimutV1 a V2-24867.5699374261-1893.47674652934.6363932084265.6457630062xyNmnmpmV1-246731.1007172614648480.616000066387979.121106780.00374725036335698.36530617Hallamos la reduccion angular y la convergencia de meridianos.V2-271608.6216630654646586.38155975

dT0.0000059903

-0.0347106329

Acimut G4.6016885659263.65733345813. Distancia UTM.AXAYDV1 a V2-24867.5699374261-1893.476746529324939.55269812244. Distancia sobre el elipsoide. Aproximar a la esfera.Obtenemos el coeficiente de anarmofosis de ambos puntos.K1 V11.000348338K1 V21.0005068393D224928.8933859152R6361785.03843113D124928.8774366831Km1.00042758875. Distancia reducida al horizonte medio.Hm421.2Dr24930.5279236245Kh0.9999337966

Junio 2007Desde el vrtice V, se realiza una observacion a una base.HElipsoideV41.40833333334.0252777778508a6378388e0.00672267DgAzVime'0.0067681702Base2890.25108.3631591.08361.561.3ko0.99961. Calcular las coordenadas UTM del vrtice.

HV10.72271175440.017894473508A1.0050739874m6367654.49129146B0.0050846837n16107.0276636486C0.000010717p16.9744554954Sm V14586002.37571973D0.0000000208q0.0219307596

Nn^2pXYHusoV16387788.217041970.00380724686363560.5715434V585697.567293954584675.15248538312. Coordenadas UTM de la Base.Debemos obtener el acimut UTM y la distancia UTM.Dg2890.25AH-53.847976299D12889.5303085178D22889.5303332476R6375662.88611136Hb454.152023701Calculamos K10.99969037D UTM2888.6356478966Ahora hallamos el acimut UTM a partir del acimut geodsico.Calculamos la convergencia y la reduccion angular.dT0.0118364983Acimut g1.8912937553Az UTM1.8794572571107.6849686054Calculamos las coordenadas UTM de la base.

XYBase588449.6895184834583797.63372915

Setp 2007Dados los vrtices de coordenadadasHElipsoideV140.3416666667-9.0252777778120a6378388V240.4236111111-8.9897222222330e0.00672267e'0.0067681702ko0.99961. Calcular las coordenadas UTM de los vrtices en los huso 29 y 30.

Huso 30V10.7040949091-0.1051609356A1.0050739874m6367654.49129146V20.7055251094-0.1045403741B0.0050846837n16107.0276636486C0.000010717p16.9744554954Sm V14467543.99847905D0.0000000208q0.0219307596Sm V24476643.5345098

Nn^2pXYHusoV16387391.515177620.00393193766336212.18506423V1-11920.07937356944483216.5906973330V26387421.90966160.00392238326336203.9305267V2-8278.5433883074492114.5385469930

Huso 29V10.7040949091-0.0004411804A1.0050739874m6367654.49129146V20.70552510940.0001793811B0.0050846837n16107.0276636486C0.000010717p16.9744554954Sm V14467543.99847905D0.0000000208q0.0219307596Sm V24476643.5345098

Nn^2pXYHusoV16387391.515177620.00393193766335508.21463662V1497852.9917197914465757.2874677629V26387421.90966160.00392238326335508.20425733V2500871.9022905184474852.9278044129

2. Acimut UTM de V1 a V2AXAYAzV1 a V23018.91057072629095.64033665230.320466689218.36138876443. Acimut geodsico.Calculamos la convergencia de meridianos y la reduccion angular.xyHusoV1-2147.86742717944467544.3051898329dT-0.0000001288V2872.2511909944476643.585238529

-0.0002855956Az G0.320180964718.34501796034. Coeficiente de anamorfosis en K2.K1 V10.9996000567K1 V20.99960000945. Distancia UTMAXAYDV1 a V23018.91057072629095.64033665239583.5533163738m

Junio 2010Dadas las coordenadas de los puntos en el sistema SGR ED50.

X utmY utmHusoElipsoide de Hayforfd1720781.6054393632.52130a63783884732804.3524413105.40230e0.00672267e'0.0067681702540.02750.3472222167wko0.9996R6367640.91900784639.88513284170.2655899806wb6356911.946

Y las observaciones de la poligonal sobre el elipsoide de Hayford

EstVisHzHz radDist Elip155.973910.093837958812104.41321.64011871038765.84521273.07644.289474060523383.59226.025452187511234.34232274.357754.30960145933458.21780.91448306399649.27543158.238852.485610043446368.28455.7849993982Determinar las coordenadas UTM de los puntos 2 y 3, haciendo que los errores de cierren angular sea mnimo.

1. Obtenemos las coordenadas UTM de los puntos 5 y 6.

ElipsoideHuso 30540.02750.3472222167a6378388639.88513284170.265589980650.69861166630.0462997066e0.00672267A1.0050739874m6367654.4912914660.69612689070.0477244579e'0.0067681702B0.0050846837n16107.0276636486ko0.9996C0.000010717p16.9744554954Sm 54432658.50554984D0.0000000208q0.0219307596Sm 64416850.49064237

Nn^2pXYHuso56387275.124139390.00396852596335645.059656275726373.8200572784434257.228910483066387222.455471360.00398508336335653.605775436733825.5571240054418663.16197048302. Ahora obtenemos las coordenadas Geodsicas de los puntos 1 y 2, para poder obtener una latitud correcta.

XYHElipsoide1720781.6054393632.521a63783884732804.3524413105.402xy = Sme0.006722671220869.9529811924395390.67727091e'0.00676817024232897.5110044024414871.35054022ko0.9996A1.0050739874m6367654.49129146B0.0050846837n16107.0276636486'0.69026840.6933277169C0.000010717p16.9744554954' 10.69275126970.6958134974D0.0000000208q0.0219307596' 20.69275363910.695815794' 30.69275364130.6958157961Nn^2p16387151.032111760.00400753736361656.45685942TanCos46387215.864730810.00398715536361850.1803367610.82997602790.769490298140.83516077260.7675310223

HusoNn^2p10.69225575950.0449179875139.6633333641-0.4263888913016387140.498000170.0040108496361624.9807185840.6952588230.0474817391439.8353962282-0.27949674673046387204.066801640.00399086426361814.927174483. Realizamos la transicin de la poligonalCalculamos la desorientacion del primer punto a partir de la observacion a la referencia.

estVisadoLHAXAYAcimutdTAcimut CorregidoDesorientacion155.973910.09383795885592.215057278140624.70791047630.13679578798.70869033340.00011206240.00713411320.13690785038.71582444650.04306989142.7419144465X utmY utmxyNmn^2mpm1720781.6054393632.521220869.9529811924395390.677270916387207.811069780.00398968756348635.020187425726373.8200572784434257.22891048226464.4058196064436031.6415671Calculamos una primeras coordenadas del punto 2.estVisadoLHDistanciaAcimutK1D UTM12104.41321.64011871038765.8451.6831886017107.15511444661.00019998488767.5980361453

XY2729493.8850524164392649.18402231Son coordenadas aproximadas del punto 2.Nn^2p26387136.383238260.00401214266361612.685754050.69206125430.0466827603Con estas coordenadas calculamos unas segundas coordenadas aproximadas.estVisadoLHDistanciaAcimutdT 1 a 2Acimut corregidoK1 1K1 2K1 mD UTM12104.41321.64011871038765.8451.6831886017107.1551144466-0.00000271971.6831913214107.15528758871.00019998481.00024826621.00022412558767.8096494946xy229585.7193401524394406.94680103

XYDifAXAY2729494.092656134392649.136593190.2076037137-0.0474291202Nn^2p26387136.383060010.00401214276361612.685221430.69206124590.0466828022Con estas coordenadas calculamos unas segundas coordenadas aproximadas.

estVisadoLHDistanciaAcimutdT 1 a 2Acimut corregidoK1 1K1 2K1 mD UTM12104.41321.64011871038765.8451.6831886017107.1551144466-0.00000271981.6831913215107.15528759721.00019998481.00024826741.00022412618767.8096546347

xy229585.9270269414394406.89935293

XYDifAXAY2729494.0926611084392649.136591470.0000049779-0.0000017267Calculamos una primeras coordenadas del punto 3

estVisadoLHAXAYAcimutdTAcimut CorregidoDesorientacion21273.07644.2894740605-8712.4876611079983.3844085345-1.458401332307.15528759720.00000275520.0001753987-1.4583985769307.1554629958-5.747872637434.0790629958

X utmY utmxyNmn^2mpm2729494.0926611084392649.13659147229585.9270319214394406.899351216387138.440530090.00401149596361618.832973720781.6054393632.521220869.9529811924395390.67727091

estVisadoLHDistanciaAcimutK1D UTM23383.59226.025452187511234.3420.2775795517.67126299581.000248267411237.1311203371

XY3732573.3885848114403456.12749689Son coordenadas aproximadas del punto 3Nn^2p36387171.997647440.00400094616361719.102617720.69374426830.04737503Con estas coordenadas calculamos unas segundas coordenadas aproximadas.

estVisadoLHDistanciaAcimutdT 1 a 2Acimut corregidoK1 2K1 3K1 mD UTM23383.59226.025452187511234.3420.2775795517.67126299580.00003080280.277548747217.66930202871.00024826741.00026576471.000257016111237.2294062077

xy232666.4551668784405218.2147828

XYDifAXAY3732573.0826280154403456.31686716-0.30595679560.1893702736Nn^2p36387171.998307930.00400094596361719.10459130.69374429950.0473749689Con estas coordenadas calculamos unas segundas coordenadas aproximadas.

estVisadoLHDistanciaAcimutdT 1 a 2Acimut corregidoK1 1K1 2K1 mD UTM23383.59226.025452187511234.3420.2775795517.67126299580.00003080330.277548746717.66930199521.00024826741.0002657631.000257015211237.2293963683

xy232666.149087654405218.40422885

XYDifAXAY3732573.0826196344403456.31685932-0.0000083818-0.0000078427

Calculamos una primeras coordenadas del punto 4

estVisadoLHAXAYAcimutdTAcimut CorregidoDesorientacion32274.357754.3096014593-3078.9899585256-10807.18026785460.2775487467217.6693019952-0.0000309405-0.00196973140.2775178062217.66733226385.3926943077343.3095822638

X utmY utmxyNmn^2mpm3732573.0826196344403456.31685932232666.1490792654405218.404221016387154.190683970.00400654436361665.894906362729494.0926611084392649.13659147229585.9270319214394406.89935121

estVisadoLHDistanciaAcimutK1D UTM3458.21780.91448306399649.2756.3071773717801.52738226381.0002657639651.8394202431

XY4732804.6279583654413105.37852097Son coordenadas aproximadas del punto 3Nn^2p46387139.947666310.0040110226361623.336312610.6922297460.0472685185Con estas coordenadas calculamos unas segundas coordenadas aproximadas.

estVisadoLHDistanciaAcimutdT 1 a 2Acimut corregidoK1 2K1 3K1 mD UTM3458.21780.91448306399649.2756.3071773717801.52738226380.00002775646.3071496152801.52561523421.0002657631.00026445031.00026510669651.8330868709

xy232897.7870731954414871.32705179

XYDifAXAY4732804.3599829544413105.37861257-0.2679754120.0000916021Nn^2p46387139.947735540.0040110226361623.336519480.69222974930.0472684642Con estas coordenadas calculamos unas segundas coordenadas aproximadas.

estVisadoLHDistanciaAcimutdT 1 a 2Acimut corregidoK1 1K1 2K1 mD UTM3458.21780.91448306399649.2756.3071773717801.52738226380.00002775646.3071496153801.52561523491.0002657631.00026444881.00026510599651.8330794903

xy232897.518990554414871.32714343

XYDifAXAY4732804.364413105.37860519-0.0000000766-0.0000073807732804.3524413105.402Realizamos el cierre acimutal

estVisadoLHAXAYAcimutdTAcimut CorregidoDesorientacion43158.238852.4856100434-231.2773632434-9649.0617458690.0239643081201.5256152349-0.0000277656-0.00176761450.0239365424201.52384762040.679919152743.2849976204

X utmY utmxyNmn^2mpm4732804.364413105.38232897.5189904734414871.327136046387155.973021740.00400598396361671.220555393732573.0826196344403456.31685932232666.1490792654405218.40422101

estVisadoLHAcimutdTAcimut corregida46368.28455.78499939826.464918550811.56949762040.00001605420.00102204016.464902496711.5684755803

XYxyNmn^2mpm4732804.364413105.37860519232897.5189904734414871.327136046387181.201603450.00399805276348638.471147456733825.564418663.16197048233919.1247739144420431.33450428Ahora comparamos con las coordenadas dato

XYAXAYacimut4732804.354413105.4021021.215557.760.181717071211.5684680515Dif acimut-0.00000752896733825.564418663.16197048

Junio 2011Dadas las coordenadas geodsicas y las alturas elipsoidales de dos puntos en el elipsoide SGR80.HElipsoideP11.5-60.5980.765a6378137P2-1.5-59.5540.42e0.00669438e'0.0067394968ko0.99961. Coordenadas UTM de ambas estaciones en sus correspondiente husos.Coordenadas Geodsicas

ElipsoideHuso 30V11.5-60.5a6378137V2-1.5-59.5V10.02617993880.0436332313e0.00669438A1.0050525005m6367449.13715172V2-0.02617993880.0610865238e'0.0067394968B0.0050631064n16038.5018446176ko0.9996C0.0000106265p16.8308874102Sm V1165861.794183347D0.0000000205q0.0216548239Sm V2-165861.794183347

Nn^2pXYHusoV16378151.628969530.00673487876335560.37139776V1778181.474588262165954.39362015820V26378151.628969530.00673487876335676.43303716V2889573.4663200839833892.7797007220

Huso 31V11.5-60.5V2-1.5-59.5V10.0261799388-0.0610865238A1.0050525005m6367449.13715172V2-0.0261799388-0.0436332313B0.0050631064n16038.5018446176C0.0000106265p16.8308874102Sm V1165861.794183347D0.0000000205q0.0216548239Sm V2-165861.794183347

Nn^2pXYHusoV16378151.628969530.00673487876335676.43303716V1110426.533679917166107.22029927621V26378151.628969530.00673487876335560.37139776V2221818.5254117389834045.60637984212. Distancia UTM entre ambas estaciones

XYHNn^2pElipsoideV1778181.474588262165954.393620158980.7650.0261799388-0.06108652386378151.628969530.00673487876335676.43303716a6378388V2889573.466320083-166107.220299276540.42-0.0261799388-0.04363323136378151.628969530.00673487876335560.37139776e0.00672267e'0.0067681702ko0.9996AXAYD utmV1 a V2111391.991731821-332061.613919434350247.185942672K V1.0014763096K M1.0005573008Kd1.0010167349km1.00101680523. Distancia elipsoidal.D2349891.43911113D1349847.271403739R6356849.44234427