Transformação de Coordenadas UTM em Coordenadas Geográficas_Cleomar_MC-171

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Transformação de Coordenadas UTM em Coordenadas Geográficas Determinação dos Coeficientes para o Elipsóide SAD-69 Raio Equatorial a = 6,378,160.000 Raio Polar b = 6,356,774.71920 Achatamento f = 1 / 298,25000004356 f = 0.003352891868748 Cálculo das Excentricidades 1ª excentricidade e = 0.081820179987 0.006694541853 2ª excentricidade e' = 0.082095437110624 0.006739660794384 Cálculo dos Coeficientes A, B, C, D, E, F A = A = 1.00505262472424 B = B = 0.005063232048721350 C = C = 0.0000106281071208084 D = D = 0.0000000208218961688800 E = E = 0.0000000000393275334900 F = F = 0.0000000000000655534000 111,133.348784972 16,038.9549461031 16.8334899163916 0.02198605234308 0.00003114475752 0.00000004153110329763 ((a 2 - b 2 ) 1/2 ) / a e 2 também pode ser calculado pela f e 2 = f * (2 - f) e 2 = ((a 2 - b 2 ) 1/2 ) / b e' 2 = 1 + 3 / 4e 2 + 45 / 64e 4 + 175 / 256e 6 + 11025 / 16384e 8 + 43659 / 3 / 4e 2 + 15 / 16e 4 + 525 / 512e 6 + 2205 / 2048e 8 + 72765 / 65536 15 / 64e 4 + 105 / 256e 6 + 2205 / 4096e 8 + 10395 / 16384e 10 35 / 512e 6 + 315 / 2048e 8 + 31185 / 131072e 10 315 / 16384e 8 + 3465 / 65536e 10 639 / 131072e 10 Cálculo dos Coeficientes a, b, g, d, e, x (determinação de f' ) a = (Aa(1-e 2 )p) / 180 => b = (Ba(1-e 2 ) / 2 = g = (Ca(1-e 2 ) / 4 = d = (Da(1-e 2 )) / 6 => e = (Ea(1-e 2 )) / 8 => x = (Fa(1-e 2 )) / 10 =>

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Transcript of Transformação de Coordenadas UTM em Coordenadas Geográficas_Cleomar_MC-171

SAD69 Transformao de Coordenadas UTM em Coordenadas GeogrficasDeterminao dos Coeficientes para o Elipside SAD-69Raio Equatorial a =6,378,160.000Raio Polar b =6,356,774.71920Achatamento f =1 / 298,25000004356f =0.003352891868748Clculo das Excentricidades1 excentricidade e =((a2 - b2)1/2) / ae2 tambm pode ser calculado pela frmulae =0.081820179987e2 = f * (2 - f)e2 =0.0066945418532 excentricidade e' =((a2 - b2)1/2) / be' =0.082095437110624e'2 =0.006739660794384Clculo dos Coeficientes A, B, C, D, E, FA =1 + 3 / 4e2 + 45 / 64e4 + 175 / 256e6 + 11025 / 16384e8 + 43659 / 65536e10A =1.00505262472424B =3 / 4e2 + 15 / 16e4 + 525 / 512e6 + 2205 / 2048e8 + 72765 / 65536e10B =0.005063232048721350C =15 / 64e4 + 105 / 256e6 + 2205 / 4096e8 + 10395 / 16384e10C =0.0000106281071208084D =35 / 512e6 + 315 / 2048e8 + 31185 / 131072e10D =0.0000000208218961688755E =315 / 16384e8 + 3465 / 65536e10E =0.0000000000393275334871F =639 / 131072e10F =0.0000000000000655534023Clculo dos Coeficientes a, b, g, d, e, x (determinao de f' )a =(Aa(1-e2)p) / 180 => a =111,133.348784972b =(Ba(1-e2) / 2 => b =16,038.9549461031g =(Ca(1-e2) / 4 => g =16.8334899163916d =(Da(1-e2)) / 6 => d =0.02198605234308e =(Ea(1-e2)) / 8 => e =0.00003114475752x =(Fa(1-e2)) / 10 => x =0.00000004153110329763MEMRIA DE CLCULOCoordenadas do Ponto Sistema UTMN =9,700,835.355MC = Meridiano CentralE =574,013.57945SoluoDeterminao de q, q2, q3, q4, q5, q6E' =| 500.000 - E | => E' =74,013.579q =0,000001 * E' => q =0.074013579q2 =0.005478009876389q3 =0.000405447116749q4 =0.000030008592206q5 =0.000002221043310q6 =0.000000164387364Clculo da Latitude - Determinao de f'N' =10.000.000 - N => N' =299,164.6451 Aproximao f'1 =(N' / 0,9996) * (1 / a)f'1 =2.69302025013732 Aproximao f'2 =(1/a)(B'+bsen2f1 - gsen4f1 + dsen6f1 - esen8f1 + xsen10f1)B' = N' / 0,9996f'2 =2.70653886067f2 f13 Aproximao f'3 =(1/a)(B'+bsen2f2 - gsen4f2 + dsen6f2 - esen8f2 + xsen10f2)f'3 =2.7066065221f3 f24 Aproximao f'4 =(1/a)(B'+bsen2f3 - gsen4f3 + dsen6f3 - esen8f3 + xsen10f3)f'4 =2.7066068607f4 f35 Aproximao f'5 =(1/a)(B'+bsen2f4 - gsen4f4 + dsen6f4 - esen8f4 + xsen10f4)f'5 =2.7066068624f5 f46 Aproximao f'6 =(1/a)(B'+bsen2f5 - gsen4f5 + dsen6f5 - esen8f5 + xsen10f5)f'6 =2.7066068624f6 = f5f'6 ' " =2.422378470Determinao dos Coeficientes VIIq2, VIIIq4, D'6q6Clculo da Grande Normal N = a / (1 - e2 x sen2f')1/2 =N =6,378,207.60725674VII =(tgf' / 2N2sen1") x (1+e'2cos2f') x (1 / KO2) x 1012VII =120.748515017VIIq2 =0.66146156em segundosVIII =(tgf' / 24N4sen1")*(5+3tg2f'+6e'2cos2f'-6e'2sen2f'-3e'4cos4f'-9e'4cos2f'sen2f')*((1/KO4)*1024VIII =1.240995234885VIIIq4 =0.0000372405199em segundosD'6 =(tgf' / 720N6sen1")*(61+90tg2f'+45tg4f+107e'2cos2f'-162e'2sen2f'-45e'2'tg2f'sen2f')*((1/KO6)*1036D'6 =0.012485018D'6q60.000000002052em segundosClculo da Latitudef =f' - VIIq2 + VIIIq4 - D'6q6f =2.7064231334Digite o valor da clula B81f ' " =2.422312328002 42' 23,123280" SClculo da LongitudeDeterminao dos Coeficientes IXq, Xq3, E'5q5IX =(secf' / Nsen1") x (1 / KO) x 106IX =32,388.06395IXq =2,397.15653X =(secf' / 6N3sen1") x (1+ 2tg2f' + e'cos2f') x (1/KO3) x 1018X =134.2822412Xq3 =0.0544443E'5 =(secf' / 120N5sen1") x (5 + 28tg2f' + 24tg4f' + 6e'2cos2f' + 8e'sen2f) x (1/KO5) x 1030E'5 =0.8335731E'5q5 =0.0000018514Clculo da LongitudeDl" =IXq - Xq3 + E'5q5Dl" =2,397.1021Dl =0.66586Dl ' " =0.395710209Como o ponto est a leste do MC temos:l =MC - Dll =44.33413831Digite o valor da clula B101l ' " =44.200289791344 20' 02,897913" W

&C&"Arial,Itlico"&8&F&R&"Arial,Itlico"&8Pg. 0&P / 0&N

WGS-84Transformao de Coordenadas UTM em Coordenadas GeogrficasDeterminao dos Coeficientes para o Elipside WGS-84Raio Equatorial a =6,378,137.000Raio Polar b =6,356,752.31425Achatamento f =1 / 298,257223563f =0.003352810664747Clculo das Excentricidades1 excentricidade e =((a2 - b2)1/2) / ae2 tambm pode ser calculado pela frmulae =0.081819190833e2 = f * (2 - f)e2 =0.0066943799892 excentricidade e' =((a2 - b2)1/2) / be' =0.082094437940397e'2 =0.006739496740750Clculo dos Coeficientes A, B, C, D, E, FA =1 + 3 / 4e2 + 45 / 64e4 + 175 / 256e6 + 11025 / 16384e8 + 43659 / 65536e10A =1.00505250178706B =3 / 4e2 + 15 / 16e4 + 525 / 512e6 + 2205 / 2048e8 + 72765 / 65536e10B =0.005063108596089830C =15 / 64e4 + 105 / 256e6 + 2205 / 4096e8 + 10395 / 16384e10C =0.0000106275901539007D =35 / 512e6 + 315 / 2048e8 + 31185 / 131072e10D =0.0000000208203782503226E =315 / 16384e8 + 3465 / 65536e10E =0.0000000000393237129025F =639 / 131072e10F =0.0000000000000655454778Clculo dos Coeficientes a, b, g, d, e, x (determinao de f' )a =(Aa(1-e2)p) / 180 => a =111,132.952547955b =(Ba(1-e2) / 2 => b =16,038.5086590352g =(Ca(1-e2) / 4 => g =16.8326131538687d =(Da(1-e2)) / 6 => d =0.02198437386273e =(Ea(1-e2)) / 8 => e =0.00003114162465x =(Fa(1-e2)) / 10 => x =0.00000004152593974734MEMRIA DE CLCULOCoordenadas do Ponto Sistema UTMN =9,700,835.355MC = Meridiano CentralE =574,013.57945SoluoDeterminao de q, q2, q3, q4, q5, q6E' =| 500.000 - E | > E' =74,013.579q =0,000001 * E' => q =0.074013579q2 =0.005478009876389q3 =0.000405447116749q4 =0.000030008592206q5 =0.000002221043310q6 =0.000000164387364Clculo da Latitude - Determinao de f'N' =10.000.000 - N => N' =299,164.6451 Aproximao f'1 =(N' / 0,9996) * (1 / a)f'1 =2.69302985191862 Aproximao f'2 =(1/a)(B'+bsen2f1 - gsen4f1 + dsen6f1 - esen8f1 + xsen10f1)B' = N' / 0,9996f'2 =2.70654818324f2 f13 Aproximao f'3 =(1/a)(B'+bsen2f2 - gsen4f2 + dsen6f2 - esen8f2 + xsen10f2)f'3 =2.7066158416f3 f24 Aproximao f'4 =(1/a)(B'+bsen2f3 - gsen4f3 + dsen6f3 - esen8f3 + xsen10f3)f'4 =2.7066161802f4 f35 Aproximao f'5 =(1/a)(B'+bsen2f4 - gsen4f4 + dsen6f4 - esen8f4 + xsen10f4)f'5 =2.7066161819f5 f46 Aproximao f'6 =(1/a)(B'+bsen2f5 - gsen4f5 + dsen6f5 - esen8f5 + xsen10f5)f'6 =2.7066161819f6 = f5f'6 =2.422381825Determinao dos Coeficientes VIIq2, VIIIq4, D'6q6Clculo da Grande Normal N = a / (1 - e2 x sen2f')1/2 =N =6,378,184.60626157VII =(tgf' / 2N2sen1")*(1+e'2cos2f')*((1/KO2)*1012VII =120.749782647VIIq2 =0.66146850em segundosVIII =(tgf' / 24N4sen1")*(5+3tg2f'+6e'2cos2f'-6e'2sen2f'-3e'4cos4f'-9e'4cos2f'sen2f')*((1/KO4)*1024VIII =1.241017185657VIIIq4 =0.0000372411786em segundosD'6 =(tgf' / 720N6sen1")*(61+90tg2f'+45tg4f+107e'2cos2f'-162e'2sen2f'-45e'2'tg2f'sen2f')*((1/KO6)*1036D'6 =0.012485328D'6q60.000000002052em segundosClculo da Latitudef =f' - VIIq2 + VIIIq4 - D'6q6f =2.7064324510Digite o valor da clula B81f ' " =2.42231568202 42' 23,15682" SClculo da LongitudeDeterminao dos Coeficientes IXq, Xq3, E'5q5IX =(secf'/Nsen1")*(1/KO)*106IX =32,388.18099IXq =2,397.16519X =(secf' / 6N3sen1") x (1+ 2tg2f' + e'cos2f') x (1/KO3) x 1018X =134.2836773Xq3 =0.0544449E'5 =(secf' / 120N5sen1") x (5 + 28tg2f' + 24tg4f' + 6e'2cos2f' + 8e'sen2f) x (1/KO5) x 1030E'5 =0.8335880E'5q5 =0.0000018514Clculo da LongitudeDl" =IXq - Xq3 + E'5q5Dl" =2,397.1107Dl =0.66586Dl ' " =0.395711075Como o ponto est a leste do MC temos:l =MC - Dll =44.3341359029Digite o valor da clula B101l ' " =44.20028892544 20' 02,88925" W

&C&"Arial,Itlico"&8&F&R&"Arial,Itlico"&8Pg. 0&P / 0&N

Crrego AlegreTransformao de Coordenadas UTM em Coordenadas GeogrficasDeterminao dos Coeficientes para o Elipside CRREGO ALEGRERaio Equatorial a =6,378,388.000Raio Polar b =6,356,912.000Achatamento f =1 / 297,000745015f =0.003366994921004Clculo das Excentricidades1 excentricidade e =((a2 - b2)1/2) / ae2 tambm pode ser calculado pela frmulae =0.081991787315e2 = f * (2 - f)e2 =0.0067226531872 excentricidade e' =((a2 - b2)1/2) / be' =0.082268785899531e'2 =0.006768153133383Clculo dos Coeficientes A, B, C, D, E, FA =1 + 3 / 4e2 + 45 / 64e4 + 175 / 256e6 + 11025 / 16384e8 + 43659 / 65536e10A =1.00507397604371B =3 / 4e2 + 15 / 16e4 + 525 / 512e6 + 2205 / 2048e8 + 72765 / 65536e10B =0.005084673079760690C =15 / 64e4 + 105 / 256e6 + 2205 / 4096e8 + 10395 / 16384e10C =0.0000107180827675144D =35 / 512e6 + 315 / 2048e8 + 31185 / 131072e10D =0.0000000210866424000527E =315 / 16384e8 + 3465 / 65536e10E =0.0000000000399953092757F =639 / 131072e10F =0.0000000000000669413502Clculo dos Coeficientes a, b, g, d, e, x (determinao de f' )a =(Aa(1-e2)p) / 180 => a =111,136.537125157b =(Ba(1-e2) / 2 => b =16,106.9942741682g =(Ca(1-e2) / 4 => g =16.9761256090962d =(Da(1-e2)) / 6 => d =0.02226576635779e =(Ea(1-e2)) / 8 => e =0.00003167382678x =(Fa(1-e2)) / 10 => x =0.00000004241074802900MEMRIA DE CLCULOCoordenadas do Ponto Sistema UTMN =9,700,342.639MC = Meridiano CentralE =573,697.94045SoluoDeterminao de q, q2, q3, q4, q5, q6E' =| 500.000 - E | => E' =73,697.940q =0,000001 * E' => q =0.073697940q2 =0.005431386360244q3 =0.000400281986094q4 =0.000029499957794q5 =0.000002174086120q6 =0.000000160225668Clculo da Latitude - Determinao de f'N' =10.000.000 - N => N' =299,657.3611 Aproximao f'1 =(N' / 0,9996) * (1 / a)f'1 =2.69737819499602 Aproximao f'2 =(1/a)(B'+bsen2f1 - gsen4f1 + dsen6f1 - esen8f1 + xsen10f1)B' = N' / 0,9996f'2 =2.71097554824f2 f13 Aproximao f'3 =(1/a)(B'+bsen2f2 - gsen4f2 + dsen6f2 - esen8f2 + xsen10f2)f'3 =2.7110438889f3 f24 Aproximao f'4 =(1/a)(B'+bsen2f3 - gsen4f3 + dsen6f3 - esen8f3 + xsen10f3)f'4 =2.7110442324f4 f35 Aproximao f'5 =(1/a)(B'+bsen2f4 - gsen4f4 + dsen6f4 - esen8f4 + xsen10f4)f'5 =2.7110442341f5 f46 Aproximao f'6 =(1/a)(B'+bsen2f5 - gsen4f5 + dsen6f5 - esen8f5 + xsen10f5)f'6 =2.7110442341f6 = f5f'6 =2.423975924Determinao dos Coeficientes VIIq2, VIIIq4, D'6q6Clculo da Grande Normal N = a / (1 - e2 x sen2f')1/2 =N =6,378,435.96565217VII =(tgf' / 2N2sen1")*(1+e'2cos2f')*((1/KO2)*1012VII =120.941522016VIIq2 =0.65688013em segundosVIII =(tgf' / 24N4sen1")*(5+3tg2f'+6e'2cos2f'-6e'2sen2f'-3e'4cos4f'-9e'4cos2f'sen2f')*((1/KO4)*1024VIII =1.242902023636VIIIq4 =0.0000366655572em segundosD'6 =(tgf' / 720N6sen1")*(61+90tg2f'+45tg4f+107e'2cos2f'-162e'2sen2f'-45e'2'tg2f'sen2f')*((1/KO6)*1036D'6 =0.012503574D'6q60.000000002003em segundosClculo da Latitudef =f' - VIIq2 + VIIIq4 - D'6q6f =2.7108617776Digite o valor da clula B81f ' " =2.423910239902 42' 39,102399"Clculo da LongitudeDeterminao dos Coeficientes IXq, Xq3, E'5q5IX =(secf'/Nsen1")*(1/KO)*106IX =32,387.02308IXq =2,386.85688X =(secf' / 6N3sen1") x (1+ 2tg2f' + e'cos2f') x (1/KO3) x 1018X =134.2740299Xq3 =0.0537475E'5 =(secf' / 120N5sen1") x (5 + 28tg2f' + 24tg4f' + 6e'2cos2f' + 8e'sen2f) x (1/KO5) x 1030E'5 =0.8334886E'5q5 =0.0000018121Clculo da LongitudeDl" =IXq - Xq3 + E'5q5Dl" =2,386.8031Dl =0.66300Dl ' " =0.3946803138Como o ponto est a leste do MC temos:l =MC - Dll =44.33699913Digite o valor da clula B101l ' " =44.201319686244 20' 13,196862" W

&C&"Arial,Itlico"&8&F&R&"Arial,Itlico"&8Pg. 0&P / 0&N

Astro ChuTransformao de Coordenadas UTM em Coordenadas GeogrficasDeterminao dos Coeficientes para o Elipside ASTRO CHURaio Equatorial a =6,378,388.00000Raio Polar b =6,356,911.94613Achatamento f =1 / 297f =0.003367003367003Clculo das Excentricidades1 excentricidade e =((a2 - b2)1/2) / ae2 tambm pode ser calculado pela frmulae =0.081991889975e2 = f * (2 - f)e2 =0.0067226700222 excentricidade e' =((a2 - b2)1/2) / be' =0.082268889603383e'2 =0.006768170196574Clculo dos Coeficientes A, B, C, D, E, FA =1 + 3 / 4e2 + 45 / 64e4 + 175 / 256e6 + 11025 / 16384e8 + 43659 / 65536e10A =1.00507398883034B =3 / 4e2 + 15 / 16e4 + 525 / 512e6 + 2205 / 2048e8 + 72765 / 65536e10B =0.005084685920228930C =15 / 64e4 + 105 / 256e6 + 2205 / 4096e8 + 10395 / 16384e10C =0.0000107181367646164D =35 / 512e6 + 315 / 2048e8 + 31185 / 131072e10D =0.0000000210868016159470E =315 / 16384e8 + 3465 / 65536e10E =0.0000000000399957117125F =639 / 131072e10F =0.0000000000000669421883Clculo dos Coeficientes a, b, g, d, e, x (determinao de f' )a =(Aa(1-e2)p) / 180 => a =111,136.536655449b =(Ba(1-e2) / 2 => b =16,107.0346766251g =(Ca(1-e2) / 4 => g =16.9762108461473d =(Da(1-e2)) / 6 => d =0.02226593409935e =(Ea(1-e2)) / 8 => e =0.00003167414495x =(Fa(1-e2)) / 10 => x =0.00000004241127832753MEMRIA DE CLCULOCoordenadas do Ponto Sistema UTMN =9,700,835.355MC = Meridiano CentralE =574,013.57945SoluoDeterminao de q, q2, q3, q4, q5, q6E' =| 500.000 - E | > E' =74,013.579q =0,000001 * E' => q =0.074013579q2 =0.005478009876389q3 =0.000405447116749q4 =0.000030008592206q5 =0.000002221043310q6 =0.000000164387364Clculo da Latitude - Determinao de f'N' =10.000.000 - N => N' =299,164.6451 Aproximao f'1 =(N' / 0,9996) * (1 / a)f'1 =2.69294300281602 Aproximao f'2 =(1/a)(B'+bsen2f1 - gsen4f1 + dsen6f1 - esen8f1 + xsen10f1)B' = N' / 0,9996f'2 =2.70651809804f2 f13 Aproximao f'3 =(1/a)(B'+bsen2f2 - gsen4f2 + dsen6f2 - esen8f2 + xsen10f2)f'3 =2.7065863280f3 f24 Aproximao f'4 =(1/a)(B'+bsen2f3 - gsen4f3 + dsen6f3 - esen8f3 + xsen10f3)f'4 =2.7065866709f4 f35 Aproximao f'5 =(1/a)(B'+bsen2f4 - gsen4f4 + dsen6f4 - esen8f4 + xsen10f4)f'5 =2.7065866727f5 f46 Aproximao f'6 =(1/a)(B'+bsen2f5 - gsen4f5 + dsen6f5 - esen8f5 + xsen10f5)f'6 =2.7065866727f6 = f5f'6 =2.42237120Determinao dos Coeficientes VIIq2, VIIIq4, D'6q6Clculo da Grande Normal N = a / (1 - e2 x sen2f')1/2 =N =6,378,435.80828458VII =(tgf' / 2N2sen1")*(1+e'2cos2f')*((1/KO2)*1012VII =120.742384755VIIq2 =0.66142798em segundosVIII =(tgf' / 24N4sen1")*(5+3tg2f'+6e'2cos2f'-6e'2sen2f'-3e'4cos4f'-9e'4cos2f'sen2f')*((1/KO4)*1024VIII =1.240850221829VIIIq4 =0.0000372361683em segundosD'6 =(tgf' / 720N6sen1")*(61+90tg2f'+45tg4f+107e'2cos2f'-162e'2sen2f'-45e'2'tg2f'sen2f')*((1/KO6)*1036D'6 =0.012482856D'6q60.000000002052em segundosClculo da Latitudef =f' - VIIq2 + VIIIq4 - D'6q6f =2.7064029530Digite o valor da clula B81f ' " =2.42230506302 42' 23,05063" SClculo da LongitudeDeterminao dos Coeficientes IXq, Xq3, E'5q5IX =(secf'/Nsen1") x (1/KO) x 106IX =32,386.90466IXq =2,397.07073X =(secf' / 6N3sen1") x (1+ 2tg2f' + e'cos2f') x (1/KO3) x 1018X =134.2715951Xq3 =0.0544400E'5 =(secf' / 120N5sen1") x (5 + 28tg2f' + 24tg4f' + 6e'2cos2f' + 8e'sen2f) x (1/KO5) x 1030E'5 =0.8334518E'5q5 =0.0000018511Clculo da LongitudeDl" =IXq - Xq3 + E'5q5Dl" =2,397.0163Dl =0.66584Dl ' " =0.39570163Como o ponto est a leste do MC temos:l =MC - Dll =44.33416214Digite o valor da clula B101l ' " =44.20029837144 20' 02,98371" W

&C&"Arial,Itlico"&8&F&R&"Arial,Itlico"&8Pg. 0&P / 0&N

SIRGAS2000Transformao de Coordenadas UTM em Coordenadas GeogrficasDeterminao dos Coeficientes para o Elipside SIRGAS2000Raio Equatorial a =6,378,137.000Raio Polar b =6,356,752.31414Achatamento f =1 / 298,2500000f =0.003352891868748Clculo das Excentricidades1 excentricidade e =((a2 - b2)1/2) / ae2 tambm pode ser calculado pela frmulae =0.081819191043e2 = f * (2 - f)e2 =0.0066943802 excentricidade e' =((a2 - b2)1/2) / be' =0.082094438152603e'2 =0.006739496775592Clculo dos Coeficientes A, B, C, D, E, FA =1 + 3 / 4e2 + 45 / 64e4 + 175 / 256e6 + 11025 / 16384e8 + 43659 / 65536e10A =1.00505250181317B =3 / 4e2 + 15 / 16e4 + 525 / 512e6 + 2205 / 2048e8 + 72765 / 65536e10B =0.005063108622308840C =15 / 64e4 + 105 / 256e6 + 2205 / 4096e8 + 10395 / 16384e10C =0.0000106275902636934D =35 / 512e6 + 315 / 2048e8 + 31185 / 131072e10D =0.0000000208203785726920E =315 / 16384e8 + 3465 / 65536e10E =0.0000000000393237137139F =639 / 131072e10F =0.0000000000000655454794Clculo dos Coeficientes a, b, g, d, e, x (determinao de f' )a =(Aa(1-e2)p) / 180 => a =111,132.952547b =(Ba(1-e2) / 2 => b =16,038.5087g =(Ca(1-e2) / 4 => g =16.832613327d =(Da(1-e2)) / 6 => d =2.1984374E-02e =(Ea(1-e2)) / 8 => e =3.11416253E-05x =(Fa(1-e2)) / 10 => x =4.15259408E-08MEMRIA DE CLCULOCoordenadas do Ponto Sistema UTMN =8,702,112.000MC = Meridiano CentralE =750,002.000-171SoluoDeterminao de q, q2, q3, q4, q5, q6E' =| 500.000 - E | => E' =250,002.000q =0,000001 * E' => q =0.2500q2 =0.062501000004000q3 =0.015625375003000q4 =0.003906375001500q5 =0.000976601563125q6 =0.000244152343984Clculo da Latitude - Determinao de f'N' =10.000.000 - N => N' =1,297,888.0001 Aproximao f'1 =(N' / 0,9996) * (1 / a)f'1 =11.683369632 Aproximao f'2 =(1/a)(B'+bsen2f1 - gsen4f1 + dsen6f1 - esen8f1 + xsen10f1)B' = N' / 0,9996f'2 =11.74049830f2 f13 Aproximao f'3 =(1/a)(B'+bsen2f2 - gsen4f2 + dsen6f2 - esen8f2 + xsen10f2)f'3 =11.74076197f3 f24 Aproximao f'4 =(1/a)(B'+bsen2f3 - gsen4f3 + dsen6f3 - esen8f3 + xsen10f3)f'4 =11.74076318f4 f35 Aproximao f'5 =(1/a)(B'+bsen2f4 - gsen4f4 + dsen6f4 - esen8f4 + xsen10f4)f'5 =11.74076319f5 f46 Aproximao f'6 =(1/a)(B'+bsen2f5 - gsen4f5 + dsen6f5 - esen8f5 + xsen10f5)f'6 =11.74076319f6 = f5f ' Em GG MM SSf'6 ' " =11.44267474811.4426747476SDeterminao dos Coeficientes VIIq2, VIIIq4, D'6q6Clculo da Grande Normal N = a / (1 - e2 x sen2f')1/2 =N =6,379,021.1474VII =(tgf' / 2N2sen1") x (1+e'2cos2f') x (1 / KO2) x 1012VII =530.571516VIIq2 =33.16125em segundosVIII =(tgf' / 24N4sen1")*(5+3tg2f'+6e'2cos2f'-6e'2sen2f'-3e'4cos4f'-9e'4cos2f'sen2f')*((1/KO4)*1024VIII =5.58218604VIIIq4 =0.021806em segundosD'6 =(tgf' / 720N6sen1")*(61+90tg2f'+45tg4f+107e'2cos2f'-162e'2sen2f'-45e'2'tg2f'sen2f')*((1/KO6)*1036D'6 =0.058121876D'6q60.000014191em segundosClculo da Latitudef =f' - VIIq2 + VIIIq4 - D'6q6f =11.7315577827f ' Em GG MM SSf ' " =11.435360801811.4353608018SClculo da LongitudeDeterminao dos Coeficientes IXq, Xq3, E'5q5IX =(secf' / Nsen1") x (1 / KO) x 106IX =33,039.0403IXq =8,259.8261X =(secf' / 6N3sen1") x (1+ 2tg2f' + e'cos2f') x (1/KO3) x 1018X =148.0047598Xq3 =2.3126299E'5 =(secf' / 120N5sen1") x (5 + 28tg2f' + 24tg4f' + 6e'2cos2f' + 8e'sen2f) x (1/KO5) x 1030E'5 =1.048419882E'5q5 =0.0010238885Clculo da LongitudeDl" =IXq - Xq3 + E'5q5Dl" =8,257.5145Dl =2.29375l ' " Em GG MM SSDl ' " =2.1737514542.1737514542Como o ponto est a Oeste do MC temos:l =MC + Dll =-168.70624596l ' " Em GG MM SSl ' " =-168.4222485458-168.4222485458O

&C&"Arial,Itlico"&8&F&R&"Arial,Itlico"&8Pg. 0&P / 0&N

Plan3