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Hoja1CLCULO DE ERRORESANGULOS CALCULADOS POR REPETICION
CUADRILTERO ABCJANGULOS SIN COMPENSARANGULOS COMPENSADOSANGULOSgradosminsegANGULOSgradosminseg
ANG A605474ANG A605473.5
ANG J1074150ANG J1074149.5
ANG C826427ANG C826426.5
ANG B1077831ANG B1077830.5
SUMATORIA356237182SUMATORIA36002SUMATORIA36000Ecmax= +/- R *raiz(n)R=Mnima divisin limbo acimutalR=1"n=Nmero de vrticesn=2
Ecmax= +/-2.00segundosANGULOS PROMEDIOS DE LA LECTURA DE ANGULOS ANGULOSgradosminsegSumatoria terica de los ng. de la polig.=360grados1484962243627ERROR ANGULAR=2segundo =2segundosOKK33618474701532CONPENSACION DE ANGULOS53726186355926C=Er CIERRE/N=0.5747518592927
MXIMO ERROR DE CIERRE EN CADA TRINGULO
TRIANGULOSUMA DE ANGULOSERROR DE CIERREMAX.ERROR 4ORDENgradosminsegVALOR ABS.(seg)(seg)ABJ1795952830okACJ18003330okBCJ1800121230okABC18001130okPromedio615ok
CALCULO DE ERRORES
ANGULOSgradosminseg14849622436273361847470153253726186355926747518592927
e1 =11"C1 =2.75"e2 =8"C2 =2.00"e3 =-5"C3 =-0.63"e 4=-6C4=-0.32"ANGULOSgradosminsegDT1"logsen1484961.849.87657922436274.609.61951133618472.869.77246647015320.769.97369553726182.759.78383763559262.909.769120747511.969.86471885929271.249.935279suma18.9139.29760039.297605
COMPENSACIN POR APROXIMACIONES SUCECIVASANGULOSgradosminsegC1C2C3C4TOTAL1484962.75-0.630.322.4422436272.75-0.63-0.321.8033618472.00-0.63-0.960.4147015322.00-0.63-1.6-0.235372618-2.75-0.63-2.24-5.626355926-2.75-0.63-2.88-6.2674751-2.00-0.63-3.52-6.158592927-2.00-0.63-4.16-6.79
ANGULOS COMPENSADOSANGULOSgradosminseg148498.442243628.803361847.414701531.775372612.386355919.74747454.858592920.21
PENTAGONO CDEHJANGULOS CALCULADOS POR REPETICIONANGULOS PROMEDIOS DE LA LECTURA DE ANGULOS ANGULOS COMPENSADOS
ANGULOSgradosminsegANGULOS SIN COMPENSARANGULOS COMPENSADOS13324ANGULOSgradosminsegANGULOSgradosminseg23154253130155ANG C116845ANG A116845.44165605285024ANG J1615582ANG J1615582.46974157444955ANG H4410627ANG C4410627.4835410938337ANG E1415373ANG B1415373.4108363811115326ANG D737411ANG D737411.41233271354531SUMATORIA53529623814992857SUMATORIA54002SUMATORIA5352962401558204SUMATORIA54000Ecmax= +/- R *raiz(n)MXIMO ERROR DE CIERRE EN CADA TRINGULOR=Mnima divisin limbo acimutalR=1"n=Nmero de vrticesn=5TRIANGULOSUMA DE ANGULOSERROR DE CIERREMAX.ERROR 4ORDENgradosminsegVALOR ABS.(seg)(seg)Ecmax= +/-2.24segundosCIJ1795955530okCDI17959491130okSumatoria terica de los ng. de la polig.=540gradosDEI1795952830okEHI1800101030okERROR ANGULAR=2segundo =2.24segundosOKKIHJ18002230okPromedio7.215okCONPENSACION DE ANGULOS
C=Er CIERRE/N=0.4
CALCULO DE ERRORES
ANGULOSgradosminseg1332423154253130155416560528502469741574449558354109383371083638111153261233271354531149928571558204
e1 =5"C1 =1.67"e2 =-2"C2 =-0.67"e3 =-10"C3 =-3.33"e4 =8"C4 =2.67"e5 =11"C5 =3.67"e6 =-6"C6 =-1.20"e7 =-3"C4 =-0.13"ANGULOSgradosminsegDT1"logsen133243.249.73651123154253.389.7230793130155-1.779.8840514165606.929.46427952850243.829.683376697415-0.269.99668474449552.129.8482078354102.939.7658969383372.649.79464410836380.259.996853suma23.2848.94678948.946791
COMPENSACIN POR APROXIMACIONES SUCECIVASANGULOSgradosminsegC1C2C3C4C5C6C7133241.670.1323154251.67-0.133130155-0.670.13416560-0.67-0.135285024-3.330.13697415-3.33-0.1374449552.670.138354102.67-0.139383373.670.1310836383.67-0.13111153261.67-1.2123327-0.67-1.21354531-3.33-1.2149928572.67-1.215582043.67-1.2
ANGULOS COMPENSADOS
ANGULOSINICIALESCTOTAL(seg)COMPENSADOSgradosminseggradosminseg133241.83325.823154251.5315426.53130155-0.5130154.5416560-0.8165559.25285024-3.2285020.8697415-3.597411.574449552.8444957.88354102.535412.59383373.8383310.810836383.583641.5111153260.5115326.5123327-1.93325.11354531-4.554526.5149928571.5992858.515582042.558206.5
CUADRILTERO EFGHANGULOS CALCULADOS POR REPETICION
ANGULOS SIN COMPENSARANGULOS COMPENSADOSANGULOSgradosminsegANGULOSgradosminseg
ANG H978616ANG A978615.5
ANG G1166882ANG J1166881.5
ANG F827029ANG C827028.5
ANG E6072111ANG B6072110.5
SUMATORIA355296238SUMATORIA36002SUMATORIA36000
Ecmax= +/- R *raiz(n)R=Mnima divisin limbo acimutalR=1"n=Nmero de vrticesn=2
ANGULOS PROMEDIOS DE LA LECTURA DE ANGULOSEcmax= +/-2.00segundosANGULOSgradosminseg1192158Sumatoria terica de los ng. de la polig.=360grados2552810342584ERROR ANGULAR=2segundo =2segundosOKK46211415545739CONPENSACION DE ANGULOS6195225763182C=Er CIERRE/N=0.58415153
MXIMO ERROR DE CIERRE EN CADA TRINGULO
TRIANGULOSUMA DE ANGULOSERROR DE CIERREMAX.ERROR 4ORDENgradosminsegVALOR ABS.(seg)(seg)EGH1795953730okFGH17959491130okEFG1795959130okEFH18003330okPromedio5.515ok
CALCULO DE ERRORES
ANGULOSgradosminseg119215825528103425844621141554573961952257631828415153
e1 =-5"C1 =-1.25"e2 =9"C2 =2.25"e3 =7"C3 =0.88"e 4=-1"C4 =-0.05"ANGULOSgradosminsegDT1"logsen11921585.999.52061925528101.459.9158343425842.269.83352146211411.119.94671755457391.489.91315661952255.829.5314117631821.069.95103484151532.359.824369suma21.5239.21833139.218331"COMPENSACIN POR APROXIMACIONES SUCECIVASANGULOSgradosminsegC1C2C3C4TOTAL1192158-1.250.880.05-0.322552810-1.250.88-0.05-0.423425842.250.880.053.1846211412.250.88-0.053.0855457391.250.880.052.1861952251.250.88-0.052.08763182-2.250.880.05-1.328415153-2.250.88-0.05-1.42
ANGULOS COMPENSADOSANGULOSgradosminseg1192157.68255289.58342587.184621144.085545741.186195227.08763180.688415151.58
RESISTENCIA DE LA FIGURACUADRILTERO ABCJPRIMER CAMINO
D =10n =6n`=6S =4S` =4C =4(D - C)/D =0.6entonces:
ANGULOSgradosminsegAB/sen4=BJ/sen(2+3)148498.442243628.8Para el ngulo (2+3)A =1.1713361847.41Para el ngulo 4B =0.7564701531.775372612.38A^2 + A*B + B^2 =2.8276355919.74747454.85BJ/sen(6+7)=CJ/sen88592920.21Para el ngulo 8A =1.241Para el ngulo (6+7)B =0.256
A^2 + A*B + B^2 =1.923
RESISTENCIA R =2.85SEGUNDO CAMINO
D =10n =6n`=6S =4S` =4C =4(D - C)/D =0.6entonces:
ANGULOSgradosminsegAB/sen7=AC/sen(1+8)148498.442243628.8Para el ngulo (1+8)A =-0.6973361847.41Para el ngulo 7B =1.9584701531.775372612.38A^2 + A*B + B^2 =2.9546355919.74747454.85AC/sen(4+5)=CJ/sen38592920.21Para el ngulo 3A =2.865Para el ngulo (4+5)B =-0.672
A^2 + A*B + B^2 =6.735
RESISTENCIA R =5.81TERCER CAMINO
D =10n =6n`=6S =4S` =4C =4(D - C)/D =0.6entonces:
ANGULOSgradosminsegAB/sen4=AJ/sen1148498.442243628.8Para el ngulo 1A =1.8423361847.41Para el ngulo 4B =0.7564701531.775372612.38A^2 + A*B + B^2 =5.3566355919.74747454.85AJ/sen6=CJ/sen38592920.21Para el ngulo 3A =2.865Para el ngulo 6B =2.899
A^2 + A*B + B^2 =24.919
RESISTENCIA R =18.17CUARTO CAMINO
D =10n =6n`=6S =4S` =4C =4(D - C)/D =0.6entonces:
ANGULOSgradosminsegAB/sen7=BC/sen2148498.442243628.8Para el ngulo 2A =4.5973361847.41Para el ngulo 7B =1.9584701531.775372612.38A^2 + A*B + B^2 =33.9686355919.74747454.85BC/sen5=CJ/sen88592920.21Para el ngulo 8A =1.241Para el ngulo 5B =2.750
A^2 + A*B + B^2 =12.516
RESISTENCIA R =27.89CONCLUSIN: EN EL CUADRILTERO ABCJ EL CAMINO QUE OFRECE MENOR RESISTENCIA ES EL PRIMER CAMINO CON UN R = 2.85PENTAGONO CDEHJPRIMER CAMINO
D =18n =10n`=10S =6S` =6C =6(D - C)/D =0.67entonces:
ANGULOSgradosminsegCJ/sen11=JI/sen113325.82315426.54Para el ngulo 1A =3.2383130154.46Para el ngulo 11B =-0.9844165559.25285020.8A^2 + A*B + B^2 =8.266697411.547444957.8JI/sen4=HI/sen3835412.549383310.8Para el ngulo 3A =-1.7691083641.54Para el ngulo 4B =6.91611115326.47123325.13A^2 + A*B + B^2 =38.7241354526.4714992858.47HI/sen6=EH/sen131558206.47Para el ngulo 13A =1.525Para el ngulo 6B =-0.261
A^2 + A*B + B^2 =1.995
RESISTENCIA R =32.66
SEGUNDO CAMINO
D =18n =10n`=10S =6S` =6C =6(D - C)/D =0.67entonces:
ANGULOSgradosminsegCJ/sen11=JI/sen113325.82315426.54Para el ngulo 1A =3.2383130154.46Para el ngulo 11B =-0.9844165559.25285020.8A^2 + A*B + B^2 =8.266697411.547444957.8JI/sen4=HJ/sen12835412.549383310.8Para el ngulo 12A =3.2381083641.54Para el ngulo 4B =6.91611115326.47123325.13A^2 + A*B + B^2 =80.7051354526.4714992858.471558206.47HJ/sen12=HI/sen3
Para el ngulo 3A =-1.769Para el ngulo 12B =3.238
A^2 + A*B + B^2 =7.886
HI/sen6=EH/sen13
Para el ngulo 13A =1.525Para el ngulo 6B =-0.261
A^2 + A*B + B^2 =1.995
RESISTENCIA R =65.90
TERCER CAMINO
D =18n =10n`=10S =6S` =6C =6(D - C)/D =0.67entonces:
ANGULOSgradosminsegCJ/sen11=CI/sen213325.82315426.54Para el ngulo 2A =3.3823130154.46Para el ngulo 11B =-0.9844165559.25285020.8A^2 + A*B + B^2 =9.076697411.547444957.8CI/sen9=DI/sen10835412.549383310.8Para el ngulo 10A =0.2541083641.54Para el ngulo 9B =2.64211115326.47123325.13A^2 + A*B + B^2 =7.7171354526.4714992858.47DI/sen7=EI/sen81558206.47Para el ngulo 8A =2.932Para el ngulo 7B =2.118
A^2 + A*B + B^2 =19.291
EI/sen5=EH/sen13
Para el ngulo 13A =1.525Para el ngulo 5B =3.824
A^2 + A*B + B^2 =22.776
RESISTENCIA R =39.24CONCLUSIN: EN EL PENTGONO CDEHJ EL CAMINO QUE OFRECE MENOR RESISTENCIA ES EL PRIMER CAMINO CON UN R = 32.66CUADRILTERO EFGHPRIMER CAMINO
D =10n =6n`=6S =4S` =4C =4(D - C)/D =0.6entonces:
ANGULOSgradosminsegEH/sen4=EG/sen(2+3)1192157.68255289.58Para el ngulo (2+3)A =-0.312342587.18Para el ngulo 4B =1.1104621144.085545741.18A^2 + A*B + B^2 =0.9846195227.08763180.68EG/sen(6+7)=FG/sen88415151.58Para el ngulo 8A =2.350Para el ngulo (6+7)B =0.252
A^2 + A*B + B^2 =6.176
RESISTENCIA R =4.30SEGUNDO CAMINO
D =10n =6n`=6S =4S` =4C =4(D - C)/D =0.6entonces:
ANGULOSgradosminsegEH/sen7=FH/sen(1+8)1192157.68255289.58Para el ngulo (1+8)A =1.156342587.18Para el ngulo 7B =1.0594621144.085545741.18A^2 + A*B + B^2 =3.6826195227.08763180.68FH/sen(4+5)=FG/sen38415151.58Para el ngulo 3A =2.260Para el ngulo (4+5)B =-1.080
A^2 + A*B + B^2 =3.835
RESISTENCIA R =4.51TERCER CAMINO
D =10n =6n`=6S =4S` =4C =4(D - C)/D =0.6entonces:
ANGULOSgradosminsegEH/sen4=GH/sen11192157.68255289.58Para el ngulo 1A =5.990342587.18Para el ngulo 4B =1.1104621144.085545741.18A^2 + A*B + B^2 =43.7686195227.08763180.68GH/sen6=FG/sen38415151.58Para el ngulo 3A =2.260Para el ngulo 6B =5.825
A^2 + A*B + B^2 =52.202
RESISTENCIA R =57.58
CUARTO CAMINO
D =10n =6n`=6S =4S` =4C =4(D - C)/D =0.6entonces:
ANGULOSgradosminsegEH/sen7=EF/sen21192157.68255289.58Para el ngulo 2A =1.449342587.18Para el ngulo 7B =1.0594621144.085545741.18A^2 + A*B + B^2 =4.7546195227.08763180.68EF/sen5=FG/sen88415151.58Para el ngulo 8A =2.350Para el ngulo 5B =1.476
A^2 + A*B + B^2 =11.169
RESISTENCIA R =9.55CONCLUSIN: EN EL CUADRILTERO EFGH EL CAMINO QUE OFRECE MENOR RESISTENCIA ES EL PRIMER CAMINO CON UN R = 4.30
RUTA A SEGUIR:
CLCULO DEL ERROR DE CIERRE DE LA BASELONGITUDES CORREGIDAS TOMADAS EN CAMPO
BASE DE PARTIDA AB :57.051mBASE DE LLEGADA FG :44.630m
entonces:
AB/sen4=BJ/sen(2+3)
Despejando de la relacin de senos BJ =52.973m
BJ/sen(6+7)=CJ/sen8
Despejando de la relacin de senos CJ =45.974m
ANGULOSgradosminseg148498.442243628.83361847.414701531.775372612.386355919.74747454.858592920.21
entonces:
ANGULOSgradosminsegCJ/sen11=JI/sen113325.82315426.54Despejando de la relacin de senos JI =27.667m3130154.464165559.2JI/sen4=HI/sen35285020.8697411.54Despejando de la relacin de senos HI =72.733m7444957.8835412.54HI/sen6=EH/sen139383310.81083641.54Despejando de la relacin de senos EH =59.361m11115326.47123325.131354526.4714992858.471558206.47
entonces:
ANGULOSgradosminsegEH/sen4=EG/sen(2+3)1192157.68255289.58Despejando de la relacin de senos EG=66.383m342587.184621144.08EG/sen(6+7)=FG/sen85545741.186195227.08Despejando de la relacin de senos FG=44.618m763180.688415151.58ERROR REAL:BASE CALCULADA-BASE MEDIDA-0.012mmERROR RELATIVO:ER/BC1/3772