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TABLE I. - Tangents and Externals to a 1° Curve, <br />Chord =100 ft. <br />Int. <br />Angle <br />Tangent <br />External. <br />Int. <br />Angle <br />Tangent External <br />Ink <br />Angie <br />Tangent <br />External <br />48° <br />2257.0 <br />428.5 <br />50° ' <br />2071.`8 <br />592.3 <br />57° <br />3110.9 <br />790.1 <br />10' <br />2266.6 <br />432.0 <br />10' <br />268 1. 9 <br />596.6 <br />10' <br />3121:7 <br />795.2 <br />20 <br />2276.2 <br />435.6 <br />20 <br />2692.1 <br />6U0.9 <br />26 <br />3132.6 <br />800.4 <br />30 <br />-2285.9 <br />439.2 <br />30 <br />2702.3 <br />6U5.3 <br />- 30 <br />3143.4 <br />S05.6 <br />40 <br />2295.6 <br />442:8 <br />40 <br />2712.5 <br />609.6 <br />40 <br />3154.2 <br />810.9 <br />50 <br />2305.2 <br />446.4 <br />50 <br />2722.7 <br />614,0 <br />50 <br />3165:1 <br />S16.1 <br />44 <br />2314.9 <br />450.0 <br />61 <br />2732.9 <br />618.4 <br />58 " <br />3176.0 <br />821.4 <br />10 <br />2324.6 <br />453.6 <br />10 <br />2743.1 <br />622.8 <br />117 <br />3186.9 <br />826.7 <br />20 <br />2334.8 <br />457,3 <br />- 20 <br />2753.4 <br />627.2 <br />20 <br />3197.8 <br />832,0 <br />30 <br />2344.1 <br />461.0 <br />30. <br />2763.7 <br />631.7 <br />3n <br />3208.8 <br />837.3 <br />40 <br />2353:8 <br />464.6 <br />40 <br />2773.9 <br />G36.2 <br />40. <br />3219.7 <br />842,7 <br />50 <br />2363.5 <br />468.4 <br />50 <br />2784.2 <br />640.7 <br />50 <br />3230.7 <br />848.1 <br />45 <br />2373.3 <br />472.1 <br />52 <br />2704,5 <br />645.2 <br />59 <br />3241.7 <br />853.5 <br />10 <br />2353.L <br />475.8 <br />-10 <br />2804.9 <br />(140.7 <br />10 <br />3252.7 <br />858.9 <br />20' <br />2392.8 <br />479.6 <br />- 20 <br />2515.2 <br />654.3 <br />20 <br />3263.7 <br />804.3 <br />30 <br />2402.6 <br />483.4 <br />30 <br />2S25.6 <br />658.8 <br />30 <br />3274.8 <br />869.8 <br />40 <br />2412.4 <br />437.2 <br />40 <br />2535.9 <br />663.4 <br />40 <br />3285.8 <br />875.3 <br />50 <br />2422.3 <br />491.0 <br />50 <br />2S45.3 <br />668.0 <br />50 <br />3296.9 <br />880.8 <br />46 <br />2432.1 <br />494.8 <br />53 <br />2850.7 <br />072.7 <br />60 <br />3308.0 <br />886.4 <br />10 <br />2441-.9 <br />498.7 <br />10 <br />2867.1 <br />677.3 <br />10 <br />3319.1 <br />892.0 <br />20 <br />2451.8 <br />502.5, <br />20 <br />2877.5 <br />682.0 <br />20 <br />3330.3, <br />897.5 <br />30 <br />2461.7 <br />506.4 <br />30 <br />2888.0 <br />686.7 <br />30 <br />3341.4 <br />903.2 <br />40 <br />2471:5 <br />510.3 <br />/ 40 <br />2898.4 <br />691.4 <br />40 <br />3352:6 <br />903.8 <br />60 <br />2481:4 <br />5I 4.3, <br />00 <br />2903.9 <br />696.1 <br />50• <br />3363c8 <br />914.5 <br />1852.6 <br />68 <br />3864.7 <br />X54 <br />75 <br />4396.5 <br />1492.4 <br />Y <br />4980.7 <br />47 - <br />2-191.3 <br />518.2 <br />1188.4 <br />2919.4 <br />700.9 <br />61 <br />3375.0 <br />920.2 <br />10 <br />2301.2 <br />522.2 <br />10 <br />2929.9 <br />705.7 <br />l0' <br />3386.3 <br />925.9 <br />20 <br />2311.2 <br />526.1 <br />20 <br />2940.4 <br />710.5 <br />20 <br />3397.5 <br />031.6 <br />30 <br />2521:1' <br />.530.1 <br />30 <br />2951.0• <br />715.3 <br />30 <br />3408.8 <br />937.3 <br />"40 <br />2531.1 <br />534.2 <br />40 <br />2961.5 <br />720.1 <br />40 <br />3420.1 <br />943.1 <br />50 <br />2541.0 <br />538.2 <br />50 <br />2972.1 <br />725.0 <br />50 <br />3431.4 <br />.948.9 <br />4B <br />2551:0 <br />542.2 <br />55 <br />2982.7 <br />729.9 <br />62 . <br />3442.7- <br />.954.3 <br />10 <br />2561.0_ <br />546.3. <br />10 <br />2903.3 <br />734.8 <br />10 <br />3454:1 <br />960.6. <br />20 <br />2571.0 <br />550.4 <br />20 <br />3003.0 <br />739.7 <br />20 <br />3465.4 <br />960.5 <br />30 <br />2581.0 <br />554.5 <br />30 <br />3014.5 <br />744.6 <br />30 <br />347G.8 <br />972.4 <br />40 <br />2591:0 <br />558.6 <br />40 <br />3025.2 <br />749.6 <br />40 <br />3488.3 <br />978.3 <br />50 <br />2601.1 <br />562.8 <br />50 <br />3035.8 <br />754.0 <br />50' <br />3499.7 <br />954.3 <br />49 - <br />2611.2 <br />566.9 <br />56 <br />3046.5 <br />759.6 <br />63 <br />3511.1 <br />990.2 <br />10 <br />2021.2 <br />571.1 <br />10 <br />3057.2 <br />764.6 <br />10 <br />3522.6 <br />906.2 <br />20 <br />2631.3 <br />575.3 <br />20 <br />3007.9 <br />769.7 <br />20 <br />3534.1 <br />1002.3 <br />30 <br />2641.4 <br />579.5 <br />30 _ <br />3073.7 <br />774.7 <br />30 <br />3545.6 <br />1008.3 <br />40 <br />265 L.5 <br />583.8 <br />40 <br />3089.4 <br />779.8 <br />40 <br />3557.2 <br />1014.4 <br />50 <br />MEG <br />588.0 <br />50' <br />3100.2 <br />754.9 <br />50 <br />3568.7 <br />1020.5. <br />Corrections to be Added (T=Tangent. E=External,) <br />Angle <br />curve 5' 10° <br />15° 20° 1 254 <br />30° <br />35° 40° 1 45° 50° 1 55° 1 60° 65° <br />70° <br />40° <br />T-.13 .28 <br />.40 .53 .67 <br />.80.93 <br />.106 1.20 1.34 1.49 1.64 1.79 <br />1.94 <br />71°' <br />E -.023 .046 <br />.070 .093 .117 <br />.141 <br />.172 .203 .234 ..267 .277 .290 .315 <br />.341 <br />15° <br />T-15 .30 <br />.44 .60 .76 <br />.91 <br />1.06 1.21 .1.37 1.52 1.70 1.37 2.04 <br />2.21 <br />10' <br />E=-630 .060 <br />,093 .119 .153 <br />.184 <br />316 .254: .269 ,325 ,351 .378 Ail <br />.445 <br />50° <br />T-.17 .34 <br />.51 .68 .85 <br />1.02 <br />119 1.36 1.54 1.72 1.91 2.10 2.29 <br />2.48 <br />---E-.037 <br />_.075 <br />.116 .151 .189 <br />,.227 <br />.260 .305 .345 .384 ,425 .407 .508 <br />.550 <br />55° <br />T-.19 :38 <br />.57 ,76 .95 <br />1.14 <br />1.32 ,1.52 1.72 1.92 2.14 2.35 2.56 <br />2.77 <br />40 <br />E-.040 .093 <br />.142 ,188 .236 <br />-.283 <br />.332 3.81 .420 AM .530 .582 .641 <br />.700' <br />60° <br />T�.21 ,42 <br />.63 05 <br />1.27 <br />1.49 l.il 1.94 Zai 2.38 2.60 2.83-. <br />3.07 <br />50 <br />_ E -_G50 ..112 <br />.108 !'211':283 <br />.340 <br />.398 .457, .516 .575 .636 .697 .754 <br />.851 <br />° <br />71 22 Afl <br />1.343 <br />1.412 <br />1.483 ,64 Ln.13 2.597 2.711 .63 2 .13 1339 <br />3:922 <br />1625.8 <br />10 <br />E 067 1 .135 <br />,.204 273 <br />40 <br />?.525 845 <br />1.01 <br />TABLE I: - Tangents and Externals to a 1° Curve, V <br />Chord =100 ft_ <br />Int. <br />Angle <br />Tan ent <br />g <br />External' <br />fit' <br />Angle <br />Tangent <br />External <br />Int. <br />Angle <br />Tan ent <br />g . <br />F.xtemal <br />61° <br />3580.3• <br />1026.6 <br />71°' <br />4086.9 <br />1308.2 <br />73° <br />4630.8 <br />1643.0 <br />10' <br />330 1. 9 <br />1032.8 <br />10' <br />4099.5 <br />1315.6 <br />10' <br />4G53.6 <br />1651.7 <br />20 <br />3("03.5 <br />1039.0 <br />20 <br />4112.1 <br />1322.9 <br />20 <br />4GG7.4 <br />1660.5 <br />30 <br />3615.1 <br />1045.2° <br />30 <br />4124.8 <br />1330.3 <br />30 <br />4681.3 <br />1G69.2 <br />40 <br />3626.8 <br />1051.4 <br />40 <br />4137.4 <br />1337.7 <br />40 <br />4695.2 <br />1678.1 <br />50 <br />3638.5 <br />1057.7 <br />50 <br />4150.1 <br />1345.1 <br />50 <br />4709.2, <br />1636.0 <br />55 <br />3650,2 <br />1063.9 <br />72 <br />4162.8 <br />1352.6 <br />79 <br />4723.2 <br />1625.8 <br />10 <br />3661.0 <br />1070.2-, <br />40 <br />4175.6 <br />1360.1 <br />10 <br />4737.2 <br />1704.7 <br />20 <br />3673.7 <br />1076.6 <br />20 <br />4188.5 <br />1367.6 <br />20 <br />4751.2 <br />1713.7 <br />30 <br />3685.4 <br />1082.9 <br />30 <br />4-201.2 <br />137.;.2 <br />30 <br />4765.3 <br />1722:7 <br />40 <br />3697.2 <br />1089.3 <br />_ '40 <br />4214.0 <br />1382-8 <br />40 <br />4779.4 <br />1731.7 <br />50 <br />3709.0 <br />1095.7 <br />50 <br />4226.8 <br />1390.4 <br />50 <br />4793.6 <br />1740.8 <br />66 <br />3720.9 <br />1102.2 <br />73 • <br />4230.7 <br />1398.0 <br />80 <br />4807.7 <br />1749.9 <br />10 <br />3732.7 <br />1108.6 <br />10 <br />4252.6 <br />1405.7 <br />10 <br />4822.0 <br />17,59.0 <br />20 <br />3744.0 <br />1115.1 <br />20 <br />4265.6 <br />1413.5 <br />20 <br />4836.2 <br />1768.2 <br />30 <br />3756.5 <br />1121.7 <br />30 <br />4278.5 <br />1421.2 <br />30 <br />4850.5 <br />1777.4 <br />40 <br />3768.5 <br />1128.2 <br />40 <br />4291.5 <br />1429.0 <br />40 <br />4864.8 <br />1786.7 <br />50 <br />3780.4 <br />1134.8 <br />" 50 <br />4304.6 <br />1436.8 <br />50 <br />4879.2 <br />1796.0 <br />67 <br />3792.4 <br />1141.4 <br />74 <br />4317.6 <br />1444.6 <br />91 <br />4893.6 <br />1805.3 <br />10 <br />3904.4 <br />1148.0 <br />. - 10 <br />4330.7 <br />1452.5 <br />10 <br />4908.0 <br />1814.7 <br />20 <br />381G.4 <br />1154.7 <br />20 <br />4343.8 <br />1460.4 <br />20 <br />4922.5 <br />1824.1 <br />30 <br />3828.4 <br />1161.3 <br />30 <br />4356.9 <br />1168.4 <br />30 <br />4937.0 <br />1833.6 <br />40 <br />3840.5 <br />1168.1 <br />40 <br />4370.1 <br />1476.4 <br />40 <br />4951.5 <br />1843.1 <br />50 <br />3852.0 <br />1174.8 <br />50 <br />4383.3 <br />1484.4 <br />50 <br />4966.1 <br />1852.6 <br />68 <br />3864.7 <br />1181.61 <br />75 <br />4396.5 <br />1492.4 <br />82 <br />4980.7 <br />1862.2 <br />10 <br />3870:8 <br />1188.4 <br />10 <br />4409.8 <br />1.500.5 <br />•10 <br />4995.4 <br />1871.8 <br />20 <br />3869.0 <br />1195.2 <br />20 <br />4423.1 <br />1508.6 <br />20 <br />5010.0 <br />1881.5 <br />30 <br />3901.2 <br />1202.9 <br />30 <br />4:16.4 <br />1510.7 <br />30 <br />5024.8 <br />1891.2 <br />40 <br />3913.4 <br />1208.9 <br />40 <br />4449.7 <br />1524.9 <br />'40 <br />5039.5 <br />1900.9 <br />50 <br />3925.6 <br />1215.8 <br />50' <br />4463.1 <br />1533.1 <br />50 <br />5054.3 <br />1910.7 <br />g9 . <br />3937.9 <br />12227 <br />76 <br />4476.5 <br />1541_4 <br />83 <br />5069.2 <br />1920.5 <br />10 <br />3950.2 <br />1229.7 <br />to' <br />4489.9 <br />1549.7 <br />10 <br />5084.0 <br />1930.4 <br />20 <br />3962.5 <br />1236.7 <br />20 <br />4503.4 <br />1558.0 <br />20 <br />5099.0 <br />1940.3 <br />30 . <br />3074.8 <br />1243.7 <br />30 <br />4516.9 <br />1566.3 <br />30 <br />5113.9 <br />1950.3 <br />40 <br />3997.2 <br />1250.8 <br />40 <br />4530.4 <br />1574.7 <br />40 <br />5128.9 <br />1960.2 <br />50 , <br />3099.5 <br />1257.9 <br />50 <br />4514.0 <br />1583.1 <br />50 <br />5143.9 <br />1970,3 <br />70 <br />4011.9 <br />1265.0 <br />77 <br />4557.6 <br />1591.6 <br />84 <br />5159.0 <br />1980.4 <br />10 <br />4024.4 <br />1272.1 <br />10 <br />4571.2 <br />1600.1 <br />10 <br />5174.1 <br />1990.5 <br />20 <br />4036.8 <br />1270,3 <br />-20 <br />4584:8 <br />1608.6 <br />.20 <br />5189.3 <br />2000.G <br />30 <br />4049.3 <br />1286.5 <br />30 <br />4598.5 <br />1617.1 <br />30 <br />5204.4 <br />2010.8 <br />40 <br />4061.8 <br />1293,6 <br />40 <br />4612.2 <br />1625.7 <br />40 <br />5219.7 <br />2021.1 <br />50 <br />4074.4 <br />1300,0 <br />50 <br />4626.0 <br />1634.4 <br />50 <br />5234.9 <br />2031,4 <br />Corrections to be Added (T=Tangent. E=External.) <br />Curve 5° 100 <br />W20° <br />25° <br />30° <br />35° <br />1 40° <br />45° 50° <br />55° 60° 65° 70° <br />_Angle <br />000 <br />T-.21 .42 <br />.63 .84 <br />1.05 <br />1.27 <br />1,49 <br />1.71 <br />1.94 2.17 <br />2.38 2.60 2.83 3.07 <br />E=.055 .112 <br />.168 .225 <br />.283 <br />.340 <br />398 <br />,457 <br />.516 .575 <br />.636 ,897 ,774 ,851 <br />65° <br />T=.23 .46 <br />.69 .93 <br />1.16 <br />1.40 <br />3.64 <br />1.88 <br />2.13 2.38 <br />2.63 2.88 3.13 3.39 <br />E=.067 .135 <br />.204 .273 <br />.343 <br />.412 <br />.463 <br />.554 <br />:625 .697 <br />.711 ..845 .922 1,01 <br />T-25 .51 <br />76 1.02 <br />1.28 <br />1.54 <br />1.80 <br />2.06 <br />2.33 2.60 <br />2,88 3.16 3.44 3.72 <br />P=.080 .159 <br />.240 .321 <br />,403 <br />.465 <br />.568 <br />.652 <br />.735 .819 <br />:906 .094 1.08 1.17 <br />75° <br />T- .27 .56 <br />.33 1.12 <br />1.40 <br />1.69 <br />2.27 <br />2.57 2.87 <br />3.16 3.47 3.78 4.09- <br />=.095 .182 <br />.266 .383 <br />,480 <br />.578 <br />.678 <br />:6781 <br />.7771 <br />•877 .977 <br />1.07 1.18 1.29 1.30 <br />80° <br />_E <br />'t=.30 .61 <br />91 1.22 <br />1.53 <br />1.84 <br />2.15 <br />2.48 <br />2.78 3.10 <br />3.44 3.78 4.12 4.46 <br />E-.110- .220 <br />.332 .445 <br />.558 <br />.671 <br />.787 <br />12.28 12.70 <br />.903 <br />1:02 1.13 <br />1.25 I.38 1.50 1.62_ <br />85° <br />T=.33 66 <br />1.00 1.33 <br />1.68102 <br />3.05 3:40 <br />3.77 4.14 4.55 4.80 <br />E=.128 .259 <br />.391 824 <br />.G57 <br />.7901 <br />42G111.06 <br />1.20 1.34 <br />1.47 1.62 1.76 1.91 <br />