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TABLE L - Tangents, and Externals to a V Curve. <br />( _ Chord=100 ft. <br />e <br />�I <br />(f <br />1� <br />Int. <br />. Angle <br />Tangent <br />External <br />Int. <br />Angle- <br />Tangent <br />External <br />Int. <br />Angle <br />Tangent <br />External <br />1° <br />50.00 <br />.22 <br />8° <br />400.66 <br />' 13.99 <br />Iry <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 />425.70 <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 />91.65 <br />.73 <br />50 <br />442.55 <br />17.07 <br />50 <br />79T.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 />18.33 <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 />58";70' <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 />50 <br />141.70 <br />1.75 <br />50 <br />402.88 <br />21.16 <br />50 <br />547.78- <br />62.38 <br />3 <br />150.04 <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 />175.00 <br />2.67 <br />30. <br />526.48 <br />24.14 <br />30 <br />SS1.88 <br />67.47 <br />40 <br />153.40 <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 />89S.95 <br />70.09.! <br />4 <br />200.08 <br />3.49 <br />11 <br />551.70 <br />26.50 <br />1S <br />907.49 <br />71.42 <br />10 <br />208.43 <br />3.79 <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 />565.53 <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 />20 <br />933.13 <br />75.49 <br />40 <br />233.47 <br />4.7640 <br />30 <br />585.36 <br />29.82 <br />130 <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 />266.86 <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 />83.07 <br />40 <br />283.57. <br />7.01 <br />40 <br />635.03 <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 />7.86 <br />13 <br />652.81 <br />37.07 <br />20 <br />1010.3 <br />88.39. <br />10 <br />308.64 <br />8.31 <br />10 <br />661.25 <br />39.03 <br />.10 <br />1018.9 <br />59.89 <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 />39:09 <br />30 <br />1036.1 <br />.92.92 <br />40 <br />333.71 <br />9.71 <br />40 <br />6186.60 <br />40.09 <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 />1053.3 <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 />1070.6 <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 />12.20 <br />30 <br />723.90 <br />46.18 <br />30 <br />1087.8 <br />.102.35 <br />40 <br />383.91 <br />12.85 <br />40 <br />737.37 <br />47.25 <br />40 <br />1096.4- <br />103.97 <br />50 <br />392.28 <br />13.41 <br />50 <br />745,. 85 <br />- 48.34 <br />50 <br />-1105.1: <br />105.60 <br />Corrections to be Added (T Tangent. E=External.) <br />TABLE I. - Tangents and Externals to a 1° Curve. III <br />Chord=100 ft. _ <br />-Int. <br />Tangent <br />External <br />Angle <br />Tangent <br />External <br />Angle <br />Angle <br />Tangent <br />External <br />.22°1113.7 <br />.09 .10 <br />107.24. <br />29° <br />1481.8 <br />188.51 <br />36° <br />1861.7 <br />294.9 <br />10, <br />1122.4 <br />108.90 <br />.10' <br />1490.7 <br />190.74 <br />10' <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 />113.9.., <br />40 <br />1517.4 <br />107.53 <br />40 <br />1898.6 <br />306.4 <br />„ <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 />.90 <br />E =.006 .011 <br />.017 .022 <br />.028 .034 <br />.038 <br />.045 .051 .057 .063 <br />.070 <br />.070 <br />.083 <br />C`•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 />1.544.2 <br />204.44 <br />10 <br />1926.4 <br />-315.2 <br />-:" 20 <br />1183..1 <br />120.8720 <br />.34.47 <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 />1217.0 <br />128.00 <br />31 <br />1589.0 <br />216.3 <br />38 <br />1972.9 <br />330.2 <br />10 <br />1220.6 <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 />1901.5 <br />336.3 <br />30 <br />1244.0 <br />133.50 <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 />32 <br />1643.0 <br />230.9 <br />39 <br />2029.0 <br />345.6 <br />10 <br />1279.0 <br />141.01 <br />10 <br />1652.0 <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 />355.1 <br />40.1 <br />1305.3 <br />140.79 <br />40 <br />1679.1 <br />241.0 <br />-40 <br />2006.6 <br />361.3 <br />50 <br />1314.0 <br />148.75 <br />50 <br />1688.1 <br />243.5 <br />50 <br />2076.0 <br />364.5 <br />••26`' <br />1322.8 <br />150.71 <br />33 <br />1697.2 <br />246.1 <br />40 <br />2055.4 <br />367.7 <br />10 <br />1331.0 <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 />2104.3 <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 />153.72 <br />40 <br />1733.5 <br />256.5 <br />40 <br />2123.3 <br />380.8 <br />50 <br />1306.8. <br />160.76 <br />50 <br />1742.6 <br />259.1 <br />50 <br />2132.7 <br />384.1 <br />27 <br />1375.6 <br />•162.81. <br />34 - <br />1751.7 <br />261.8 <br />41 <br />2142.2 <br />397.4 <br />10 <br />1354_ <br />164.86 <br />10 <br />1760.8 <br />264.5 <br />10 <br />2151.7 <br />390.7 <br />20 <br />1393..42 <br />166.95 <br />20 <br />1770.0 <br />267.2 <br />20 <br />2161.2 <br />394.1 <br />1'30 <br />1402.0 <br />169.01 <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 />2150.3 <br />400.8 <br />50 <br />1419.7 <br />173.27 <br />50 <br />1797.4 <br />275.3 <br />50 <br />2189.9 <br />4U4.2 <br />28 <br />1428.6 <br />175.41 <br />35d <br />ISOG.6 <br />27S.1 <br />42 <br />2199.4 <br />407.6 <br />10 <br />1437.4 <br />177.55 <br />10 <br />1515.7• <br />250.8 <br />10 <br />2209.0 <br />411.1 <br />^0. <br />MAG.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 />1S1.89 <br />30 <br />1834.1 <br />256.4 <br />30 <br />2228.1 <br />418.0 <br />40 <br />146,1.0 <br />1S4.08 <br />40 <br />1543.3 <br />2S9.2 <br />40 <br />2237.7 <br />421.4 <br />_ <br />50 <br />'1472.9 <br />1. 186.29 <br />50 <br />1352.5 <br />292.0 <br />50 <br />22.17.3 <br />425.0 <br />Int.e Curve 5° 10° <br />Angie <br />151 20° <br />1 25° 30° <br />35° <br />40° 45° 50° 55° <br />1 60° <br />65° <br />40° <br />5° T =.02 .03.05 <br />.06 <br />.09 .10 <br />.11 <br />.13 .15 .16 .18 <br />.20 <br />91 <br />w3 <br />E=.000 A00 <br />.001 .001 <br />.002 .002 <br />.002 <br />.003 .003 .004 .004 <br />.004 <br />•.005 <br />.005 <br />lo° T=.03 .06 <br />.09 .13 <br />.16 .19 <br />.22 <br />.25 :38• .31 .34 <br />.38 <br />.42 <br />.46 <br />B=,001 .003 <br />.004 .006 <br />.007 .008 <br />.009 <br />.011 .012 .014 .015 <br />.017 <br />.018 <br />.020 <br />IS° T=.04 .10 <br />.14 .19 <br />.24 .29 <br />.34 <br />.39 .45 .51 .53 <br />.58 <br />.63 <br />.68 <br />E'=.003 .007 <br />.010 .014 <br />.013 .023 <br />.027 <br />.020 .032 .035 .039 <br />.043 <br />.047 <br />_.051 <br />20° T=.06 .13 <br />.19 .26 <br />.32 .39 <br />.45 <br />.51 .58 .65 .72 <br />.79 <br />.84 <br />.90 <br />E =.006 .011 <br />.017 .022 <br />.028 .034 <br />.038 <br />.045 .051 .057 .063 <br />.070 <br />.070 <br />.083 <br />25° T=.08 .IG <br />.24 .33 <br />.40 .49 <br />.58 <br />.67 .75 .83 .90 <br />.99 <br />1.06 <br />1.14 <br />1Z=.000 .018 <br />.027 .036 <br />.046 .056 <br />.065 <br />.074 .083 .093 .106 <br />.120 <br />.127 <br />.135 <br />Corrections to be Added (T=Tangent. E=External.) <br />lnt.. Cunt 5°. <br />Angle <br />10° <br />15° <br />2D° <br />25° <br />30° <br />35° <br />40° <br />45° <br />50° <br />55° 60° <br />65° <br />70° <br />Zp° T=.00 <br />.13 <br />.19 <br />26 <br />.32 <br />.39 <br />.45 <br />..51 <br />.58 <br />.65 <br />.72 .79 <br />.84 <br />.90 <br />E=.00 <br />.011 <br />.017 <br />.022 <br />.028 <br />.034 <br />.038 <br />.045 <br />.051 <br />.057 <br />.063 .070 <br />.076 <br />.083 <br />25° T=.08 <br />IG <br />24.33 <br />.40 <br />.49 <br />.58 <br />.67 <br />.75 <br />.83 <br />.90 .99 <br />1.06 <br />1.14 <br />E=.009 <br />.018 <br />.027 <br />.030 <br />.046 <br />.056 <br />.055 <br />.074 <br />.083 <br />.093 <br />.106 .120 <br />.127 <br />.135 <br />300 T=10 <br />.19 <br />.29 <br />.39 <br />.49 <br />.59 <br />.69 <br />.79 <br />.89 <br />.99 <br />1.09 1.20 <br />1.29 <br />1.39 <br />E=.013 <br />.025 <br />.035 <br />.051 <br />.065 <br />.078 <br />.090 <br />.103 <br />.110 <br />.129 <br />.149 .170 <br />.179 <br />.188 <br />350 ' T,I1 <br />22 <br />.34.47 <br />.58 <br />.69 <br />.80 <br />.93 <br />1.05 <br />1.17 <br />1.29 1.42 <br />1.54 <br />1.66 <br />E =.018 <br />.035 <br />.054 <br />.072 <br />.086 <br />.109 <br />.131 <br />.153 <br />.175 <br />.197 <br />.213 .230 <br />.247 <br />264 <br />400 T=13 <br />.26 <br />40 <br />.53 <br />.67 <br />.80 <br />.93 <br />1.06 <br />1.20 <br />1.34 <br />1.49 1.54 <br />1.79 <br />1;94 <br />E =.023 <br />.046 <br />.070 <br />.093 <br />.117 <br />.141 <br />.172 <br />.203 <br />.234 <br />.265 <br />.277 .290 <br />.315 <br />.341 <br />A5° T=.15 <br />9.0 <br />.44 <br />.60 <br />.76 <br />.911.08 <br />1.21 <br />1.37 <br />1.52 <br />1.70 1.87 <br />2.04 <br />2.21 <br />E=.030 <br />.060 <br />.093 <br />.119 <br />.153 <br />.184 <br />.216 <br />.254 <br />.289 <br />.325 <br />.351 .378 <br />.411 <br />.445 <br />19 <br />