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TAn1,E I. - Tangents and Externals to a V Curve. <br />Chord =100 ft. <br />Apgle <br />Tangent <br />External <br />Angie <br />'Tangent <br />External <br />gnslc <br />Tangent <br />Ezternal <br />1° <br />50.00 <br />:22 <br />8° <br />400:66 <br />13.99 <br />15° <br />754.32 <br />49.44 <br />10' <br />58.34 <br />.30 <br />10' <br />409.03 <br />14.58 <br />10' <br />762.80 <br />50.55 <br />20 <br />66.67 <br />.39. <br />20 <br />417.41 <br />15.18 <br />20 <br />771.29 <br />-51.68 <br />30 <br />75.01 <br />49 <br />30 <br />425.79 <br />15.80 <br />30 <br />- 779.77 <br />-52.82 <br />40 <br />'83.34 <br />61 <br />40 <br />434.17 <br />16.43 <br />40 <br />788.26 <br />53.97 <br />50 <br />91.68 <br />.73 <br />50 <br />. 442.55 <br />17.07 <br />50 <br />796.75 <br />55.13 <br />=2 <br />100.01 <br />.87 <br />9 <br />450.93 <br />17.72 <br />16 <br />805.25 <br />56.31 <br />10 <br />108.35.- <br />1.02 <br />10 <br />459.32 <br />18.38 <br />10 <br />813.75 <br />57.50' <br />20 <br />116.68 <br />1.19 <br />20 <br />467.71 <br />19.06 <br />20 <br />822.25 <br />5870 <br />30 <br />125.02 <br />1.36 <br />30 <br />476.10 <br />19:75 <br />30 <br />830.76 <br />59..91 <br />40 <br />133.36' <br />1.55 <br />40' <br />484.49 <br />20.45 <br />40 <br />839.27 <br />61.14 <br />56' <br />141:70 <br />.1.75 <br />50 <br />492.88 <br />21.16 <br />50 <br />847.78 <br />62.38 <br />3 <br />150.64 <br />1.96 <br />10 <br />501.28 <br />21.89 <br />17 <br />856.30 <br />63.63 <br />10 <br />158.38_. <br />2.19 <br />10 <br />509.68 <br />22.62 <br />10 <br />864:82 <br />64.90 <br />20 <br />166.72 <br />2.43 <br />20 <br />518.08 <br />23.38 <br />20 <br />873:35 <br />66.18 <br />30 <br />175:06 <br />2.67 <br />30 <br />526.48 <br />24.14 <br />30 <br />881.88 <br />67.47 <br />'40 <br />183.40 <br />2.93 <br />40 <br />534.89 <br />24.91 <br />40 <br />590:41 <br />68.77 <br />50 <br />191.74 <br />3.21 <br />50 <br />543.29 <br />25.70 <br />50 <br />898.95 <br />70.09 <br />4 <br />200.08 <br />3.49 <br />11 <br />551.70 <br />26.50 <br />18 <br />907-.49 <br />71.42 <br />10 <br />208.43 <br />3.70 <br />10 <br />560.11 <br />27.31 <br />10 <br />916.03 <br />72.76 <br />20 <br />216.77 <br />4.10 <br />20 <br />568.53 <br />28.14 <br />20 <br />924.58 <br />74.12 <br />30 <br />225.12 <br />4.42 <br />30 <br />576.95 <br />28.97 <br />30 <br />933.13 <br />75.49 <br />40 <br />233.47 <br />•4.76 <br />40 <br />585.36 <br />29.82 <br />40 <br />941.69 <br />76.86 <br />50 <br />241.81 <br />_ 5.10 <br />. 50 <br />593.79' <br />30.68 <br />50 <br />950.25' <br />78.26 <br />5 <br />250.10 <br />5.46 <br />12 <br />602.21 <br />31.56 <br />19 <br />958.81 <br />79.67• <br />10 <br />258.51 <br />5.83. <br />10 <br />610.64 <br />32.45 <br />10 <br />967.38 <br />81.09 <br />20 <br />266.80 <br />6.21 <br />20 <br />619.07 <br />33.35 <br />20 <br />975.96 <br />82.53 <br />30 <br />275.21 <br />6.61 <br />30 <br />627.50 <br />34.26 <br />30 <br />984.53 <br />83.97 <br />40 <br />283.57 <br />7.01 <br />40 <br />635.93 <br />35.18 <br />40 <br />993.12 <br />85.43 <br />50 <br />291.92 <br />7.43 <br />50 <br />644.37 <br />36.12 <br />50 <br />1001.7 <br />86.90 <br />6 <br />300.28 <br />'308.64 <br />7.86 <br />13 <br />652.81 <br />37.07 <br />20 <br />1010.3 <br />88.39 <br />10 <br />8.31 <br />10 <br />661.25 <br />38.03 <br />10 <br />1018:9- <br />69.69 <br />20 • <br />316.99 <br />8.76 <br />20' <br />669.70 <br />39.01 <br />20 <br />1027.5 <br />91.40 <br />30 <br />325.35 <br />9.23 <br />30 <br />678.15 <br />39.99 <br />30 <br />1036.1 <br />92.92 <br />40 <br />333.71 <br />9.71 <br />40 <br />686.60 <br />40.99 <br />40 <br />1044.7' <br />94.46 <br />50 <br />342.08 <br />10.20 <br />50' <br />695.06 <br />42.00 <br />50 <br />1053:8• <br />96.01 <br />7 <br />350.44 <br />10.71 <br />14 <br />703.51 <br />43.03 <br />21 - <br />1061.9 <br />97.57 <br />10 <br />358.81' <br />11.22 <br />10 <br />711.97. <br />44.07 <br />10 <br />1070.0 <br />99.16 <br />20 <br />367.17 <br />11.75 <br />20 <br />720.44 <br />45.12 <br />20 <br />1079".2 <br />100.75 <br />30 <br />375.54 <br />12.29 <br />30 <br />728.90 <br />46.18 <br />30 <br />1087.8' <br />1.02.35 <br />40 <br />383.91 <br />12.85 <br />" 40 <br />737.37 <br />47.25 <br />40 <br />1096.4 <br />103.07 <br />50 <br />392.28 <br />13.41 <br />50 <br />745.85 <br />48.34 <br />50 <br />1108.1 <br />105.60 <br />Corrections to be Added (T =Tangent. E=External.)- - <br />Int. <br />Angle <br />Curve 5° <br />101 IS- 20° 25° <br />30° <br />350 40° 45° <br />500 <br />550 <br />60° <br />65° <br />700 <br />bo <br />T=.02 <br />.03 .05 .06 .08 <br />.10 <br />.11 •.13 .15 <br />.16 <br />.18 <br />.20 <br />.21 <br />.23 <br />108.90 <br />E-.000 <br />.000 .001 .001 .002 <br />.002 <br />.002 '.003 .003 <br />.004 <br />.004 <br />.004 <br />.005 <br />.005 <br />loo <br />T =.03 <br />.06 .09 ".13 .16 <br />.19 <br />.22 .25 .28 <br />31' <br />.34 <br />.98 <br />.42 <br />.46 <br />1508.5 <br />E =.001 <br />.003 .004 .006 .007 <br />.003 <br />.009 .011 .012 <br />.014 <br />.015 <br />.017 <br />.018 <br />.020 <br />lSo <br />T=:04 <br />.10 .14 .19 .24 <br />.29 <br />.34 .39 .45 <br />.51 <br />.53 <br />.58 <br />.63 <br />.68 <br />50 <br />E =.003 <br />.007 .010 .014 .018 <br />.023 <br />.027 .029 .032 <br />.035 <br />.039 <br />.043 <br />.047 <br />.051 <br />20° <br />T =.O6 . <br />.13 .19 .28 .32 <br />.39 <br />.45 .51 .58 <br />.65 <br />.72 <br />•.79 <br />.84 <br />.90 <br />315.2 <br />E =.006 <br />.011 .017 .022 .028 <br />.034 <br />.038 .015 .11 <br />.057 <br />.R0631g:2010 <br />20 <br />.076 <br />.083 <br />25° <br />T=.08 <br />.18 .24 .33 .40 <br />.49 <br />.58 .87 .75 <br />.83 <br />.1.06 <br />1945.0' <br />321.1 <br />1.14 <br />1200.5 <br />E=.009 <br />.018 .027 .030 .010 <br />.050 <br />.085 ".074 .083 <br />.093 <br />. <br />324.1 <br />.127 <br />.135 <br />TABLE I' Tangents and Externals to.a 1° Curve. III <br />Chnrd =100 ft. <br />InkTangent <br />Angle <br />Curve S° <br />External <br />Int. <br />Angle <br />Tangent <br />External <br />Int' <br />" Angle <br />Tangent <br />External <br />`55'' <br />•1113.7 <br />107.24 <br />290 <br />1481.8 <br />188.51 <br />36° <br />3861.7 <br />.294.9 <br />101 <br />1122.4 <br />108.90 <br />101 <br />1490 .7, <br />190.74 <br />101 <br />1870.9 <br />297.7 <br />20' <br />'1131.0- <br />110.57 <br />`20 <br />1499.6 <br />192.99 <br />20 <br />1880.1 <br />'300.6, <br />30 <br />1139.7 <br />112.25 <br />30 <br />1508.5 <br />195.25 <br />30 <br />1889.4 <br />'303.5 <br />40 <br />'1148.4 <br />113.95 <br />. 40 <br />1517.4 <br />197.53 <br />401898.6 <br />.036 <br />306.4 <br />'50 <br />1157.0 <br />115.66 <br />50 <br />1526.3 <br />199.82 <br />50 <br />1907.9 <br />309.3 <br />23 <br />1165.7 <br />117.38 <br />30 <br />1535.3 <br />202.12 <br />37 <br />1917.1 <br />312.2 <br />10 <br />1174.4 <br />119.12 <br />10 <br />'1544.2 <br />204:44 <br />10 <br />1926.4 <br />315.2 <br />20 <br />1183.1 <br />120.87 <br />20 <br />1553:1 <br />206.77 <br />20 <br />1935.7 <br />318.1 <br />30 <br />1191.8 <br />122.63 <br />30 <br />.1562.1 <br />209.12 <br />30 <br />1945.0' <br />321.1 <br />40 <br />1200.5 <br />124.41 <br />•40 <br />1571.0 <br />211.48 <br />40 <br />1954.3 <br />324.1 <br />50 <br />1209.2 <br />126.20 <br />- 50 <br />1580.0 <br />213.86 <br />50 <br />1963.6 <br />327.1 <br />24 <br />1217.9 <br />128.00 <br />31 <br />15S9.0 <br />216.3 <br />38 <br />1972.9 <br />330:2 <br />10, <br />1226.6 <br />129.82 <br />10 <br />1598.0 <br />218.7 <br />10 <br />'1982.2 <br />333.2 <br />20 <br />1235.3 <br />131 65 <br />20 <br />1606.9 <br />221.1 <br />20 <br />1991.5 <br />336.3 <br />30 <br />1244.0 <br />133.50 <br />.'• <br />30 <br />1615.9 <br />223.5 <br />30 <br />, 2000.9 <br />339.3 <br />.-40 <br />1252.8 <br />135.35 <br />- 40 <br />1624.9 <br />226.0 <br />40 <br />2010.2 <br />342.4 <br />50 <br />1261.5 <br />137.23 <br />50' <br />1633.9 <br />228.4 <br />50 <br />2019.6 <br />345.5 <br />25 ' <br />1270.2 <br />139.11 <br />82 <br />'1643.0 <br />230.9 <br />39 <br />.2029.0 <br />34816 <br />10 <br />1279.0 <br />141.01 <br />10 <br />1052.0 <br />' 233.4 <br />10 <br />2038.4 <br />351.8 <br />20 <br />1287.7 <br />142.93 <br />20 <br />1661.0 <br />235.9 <br />20 <br />2047.8 ; <br />354.9 <br />30 <br />1296.5' <br />144.85 <br />30 <br />1670.0 <br />238.4 <br />30 <br />2057.2 <br />358.1 <br />40 <br />.1305.3 <br />146.79 <br />40 <br />•1679.1 <br />241.0 <br />40 <br />206"a.6 <br />361.3 <br />50 <br />'1314.0 <br />148.75 <br />-• 50 <br />1688.1 <br />243.5 <br />50 <br />2016.0 <br />364.5 <br />26 <br />1322:5 <br />150.71 <br />33'-. <br />1697.2 <br />246.1 <br />40 <br />2085.4 <br />367-7 <br />10 <br />1331.6 <br />152.69 <br />10 <br />1706.3 <br />248.7 <br />10 <br />2094.9 <br />371.0 <br />20 <br />1340.4 <br />154.69 <br />20 <br />'1715.3 <br />251'.3 <br />20 <br />`1104.3 <br />374.2 <br />30 <br />1349.2 <br />156.70 <br />30 <br />1724.4 <br />253.9 <br />30 <br />2113.8 <br />377.5 <br />40" <br />"1358.0 <br />158.72 <br />40 <br />1733:5 <br />256.5 <br />40 <br />2123.3 <br />380.8 <br />50 <br />1366.8 <br />160.76 <br />50 <br />1742.6 <br />259.1 <br />50 <br />2132.7 <br />384.1 <br />27 <br />1375.61G2.81 <br />34 <br />1751.7 <br />261.8 <br />41 <br />2142.2 <br />387.4 <br />10 ."1384.4 <br />`164.86 <br />10 <br />1760.8 <br />26'4.5 <br />10 <br />2151.7 <br />390.7 <br />20 <br />1393.2 <br />166.95 <br />20 <br />1770.0 <br />267.2 <br />20 <br />2181.2 <br />394.1 <br />30 <br />1402.0 <br />'1G9.04 <br />30 <br />1779.1 <br />269.9 <br />30 <br />2170.8 <br />397.4 <br />40 <br />1410.9 <br />171.15 <br />40 <br />1788.2, <br />272.6 <br />40 <br />2180.3 <br />400.8 <br />50 <br />1419.7 <br />173.27 <br />50 <br />1797.4 <br />275.3 <br />50 <br />2159.9 <br />404.2 <br />28 <br />142S.6' <br />175.41 <br />35 <br />1806.6 <br />278.1- <br />42 <br />2199.4 <br />407.6 <br />10 <br />1437:4 <br />177.55 <br />10 <br />1815.7 <br />280.8 <br />- 10 <br />2209.0 <br />411.1 <br />20 <br />1446.3 <br />179.72 <br />20- <br />1824.9 <br />283.6 <br />20 <br />2218.6 <br />414.5 <br />30 <br />1455.1 <br />181.89 <br />30 <br />1834.1 <br />286.4 <br />30 <br />'2228.1 <br />418.0 <br />40 <br />1464.0 <br />134.08 <br />40 <br />1843.3 <br />280.2 <br />40 <br />2237.7 <br />421.4 <br />50. <br />1472.9 <br />186.29 <br />50 <br />1852.5 <br />202.0 <br />50 <br />224.3 <br />425.0 <br />Corrections to be Added (T=.Tangent. E=External.). <br />"Int' <br />Angle <br />Curve S° <br />10° <br />15° <br />200' <br />25° 30' <br />35'. <br />40° <br />45°' -50' <br />`55'' <br />60° 65° <br />.70° <br />20° <br />T=.06 <br />13 <br />' .19 <br />.26 <br />.32 .39 <br />.45 <br />.51 <br />.58 •.65 <br />.72 <br />.79 .84 <br />.90 <br />E=.006' <br />.011 <br />.017 <br />.022 <br />.028 .034 <br />.038 <br />.045 <br />.051 .057 <br />.063 <br />'.070 ..076 <br />.083 <br />250 <br />T=.08 <br />.16 <br />.24 <br />.33 <br />.40 .49 <br />.58 <br />.67 <br />.75 .83.90 <br />.99 1.06 <br />1.14 <br />E =.009 <br />'.018 <br />.027 <br />.036 <br />.046 .056 <br />.065 <br />.074 <br />.083 .093 <br />.106 <br />.12 .127 <br />.135 <br />39° <br />T=.10 <br />.19 <br />.29 <br />•.39 <br />.49 .59 <br />.69 <br />.79 <br />.89 .99 <br />1.09 <br />120 1.29 <br />1.39 <br />E=.013 <br />.025 <br />.038 <br />.051 <br />.065 .078 <br />.090 <br />.103 <br />.116 .129 <br />.149 <br />'.170 .179 <br />.188 <br />35 o <br />T=.11 <br />.22 <br />..34 <br />.47 <br />.58 .69 <br />.80 <br />.93 <br />1.05 1.17 <br />1.29 <br />1.42 1.54 <br />1.66. <br />E=.018 <br />..035 <br />.054 <br />.072 <br />.086 .100 <br />.131 <br />.153 <br />.175 .197 <br />.213 <br />.230 .247 <br />.264 <br />40° <br />T=.13 <br />.20 <br />.40 <br />.53 <br />67 ..80 <br />.93 <br />1.08 <br />1.20 1.34 <br />1.49 <br />1.64 1.79 <br />1.94 <br />E=.023 <br />.040 <br />.070 <br />.093 <br />.117' .141 <br />.172 <br />.203 <br />.234 .255 <br />.277 <br />.290 .315 <br />.341 <br />450 <br />T=.15 <br />.30 <br />.44 <br />.60 <br />.76 .91 <br />1.06 <br />1.21 <br />1.37 1.52 <br />1.70 <br />1.87 2.04 <br />2.21 <br />E=.030 <br />.060 <br />.093 <br />.119 <br />.153 .184 <br />.216 <br />.254 <br />.289 320 <br />.351 <br />378 .411 <br />.445 <br />