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TV TAs1.1z I. - Tangents and Externals to a 11 Curve. <br />Chord =100 ft. <br />Angle <br />Tangent <br />External <br />Angle <br />Tangent *External <br />'Angie <br />Tangent <br />External <br />!8° <br />2257.0 <br />428.5 <br />500 <br />2671.8 <br />592.3 <br />57° <br />3110.9 <br />790.1 <br />10' <br />2266.6 <br />432.0 <br />10' <br />'20 <br />2681.9 <br />596.6 <br />10' <br />3121.7 <br />795.2 <br />20 <br />2276.2 <br />435.6 <br />1.72 1.91 2.10 2.29 2.48 <br />2692:1 <br />600.9 <br />20 <br />3132.6 <br />800.4 <br />30 <br />2285:9 <br />439.2 <br />30 <br />2702.3 <br />605.3 <br />30 <br />'3143.4 <br />805.6 <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 />816.1 <br />4l! <br />2314.9 <br />450.0 <br />51 <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 />10 <br />3186.9 <br />826.7 <br />20 <br />2334.3 <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 />'30 <br />3208.8 <br />837.3 <br />40 <br />2353:8 <br />.464.6 <br />40 <br />2773.9 <br />636.2 <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 />l5.. <br />2373.3 <br />472.1 <br />52. - <br />2794.6 <br />645.2 <br />59 <br />3241.7 <br />853.5 <br />10 <br />.2383:1- <br />475.8 <br />10 <br />2804.9 <br />G49.7 <br />10 <br />3252.7 <br />858.9 <br />20 <br />2392:8 <br />479.6 <br />20 <br />2815.2 <br />654.3 <br />20 <br />3263.7 <br />864.3 <br />30 <br />2402.6 <br />AS3.4- <br />30 <br />2825.6 <br />058.8 <br />30 <br />3274.8 <br />869.8 <br />.40 <br />2412.4 <br />487.2 <br />.40 <br />2835.9 <br />663.4 <br />40 - <br />'3285.8 <br />875.3 <br />50 <br />.2422:3. <br />491.0 <br />"50 <br />2846.3 <br />668.0 <br />.50 <br />3290.0 <br />880.8 <br />46'." <br />2432.1' <br />494:8 <br />53 - <br />2856.7 <br />G72:7 <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 />1 40 <br />3352.6 <br />908.8 <br />50 <br />2481.4 <br />•514.3 <br />50 <br />2908.9 <br />696.1 <br />50 <br />3363.8 <br />914.5 <br />1852.6 <br />68 <br />3864.7 <br />1181.6 <br />76 <br />4396.5 <br />1492.4 <br />83 • <br />4980.7 <br />47': <br />2491.3 <br />518.2 <br />54 - <br />2910:4 <br />700.9 <br />61 <br />3375.0 <br />920.2 <br />10 <br />.2501.2 <br />522.2 <br />10 <br />2929.9' <br />705.7 <br />10. <br />3386.3 <br />925.9 <br />20 <br />;2511.2 <br />526.1. <br />20 <br />2940.4 <br />710.5 <br />' .20 <br />3397.5 <br />931.6 <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 />1920.5 <br />2551.0 <br />542.2, <br />55 <br />2982:7 <br />729.9 <br />62. <br />3442.7 <br />954.8 <br />10 . <br />2561.0 <br />546.3 <br />10 <br />2993.3 <br />734.8 <br />10 <br />3454.1 <br />960.6 <br />,.•20 <br />2571.0 <br />550.4 <br />20 <br />3003.9 <br />739.7 <br />20 <br />3465.4 <br />966.5 <br />30 <br />2581:0 <br />554.5 <br />30 <br />3014.5 <br />744.6 <br />30 <br />3476.8 <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 />754.6 <br />50 <br />3499.7 <br />984.3 <br />!0 <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 />2621.2 <br />571.1 <br />10 <br />3057.2 <br />764.6 <br />10 <br />3522.6 <br />996.2 <br />20 <br />2631.3 <br />575.3 <br />20 <br />30G7.9 <br />769.7 <br />.20 <br />3534.1 <br />1002.3 <br />•30 <br />2641.4 <br />579.5 <br />30 <br />3078.7. <br />774.7 <br />30 <br />3545.6 <br />1008.3 <br />.40 <br />2651:5 <br />-583.8 <br />40 <br />3089.4 <br />779.8 <br />40 <br />3557.2 <br />1014.4 <br />50 <br />2661.6 <br />588.0 <br />50 <br />3100.2 <br />784.9 <br />50 . <br />3568.7 <br />1020.5 <br />Corrections to be Added (T=Tangent. E=External.) - <br />Int. <br />Angle <br />Curve 5° 10° <br />15° 20° 25° <br />30° 1 35° 40° 45° <br />1 50° 55° 60° 65° 70° <br />40° <br />T,13 .26 <br />.40 .53 .67 <br />.80 .93 .106 1.20 <br />1.34 1.49 1.64 1.79 194 <br />3580.3 <br />E=•023 .016 <br />.070 .093 .117 <br />.141 .172 .203 .234 <br />.265 .277 -.290 .315 .341 <br />45° <br />T=.16 .30 <br />.44 .60 .76 <br />.91 1.06 1.21 1.37 <br />1.32 1.70 1.87 2.04 2.21 <br />_ <br />E=.030 .060 <br />.093 .119 am <br />.134 .216 .254 .289 <br />,325 .351 .378 .411 .445 <br />500 <br />•T=.17 .34 <br />.51 G8 .85 <br />1.02 1.19 1.36 1.54 <br />1.72 1.91 2.10 2.29 2.48 <br />20 <br />E=.037 .075 <br />:116 .151 .189 <br />.227 .266 .305 .345 <br />.384 .425 AG7 .508 .550 <br />,;5o <br />T=.19 .38 <br />.57 .78 .95 <br />1.14 1.32 1.52 1.72 <br />1.92 2.14 2.35 2.58 2.77 <br />4124.8 <br />E=.040 093 <br />.142 .188 .236 <br />.283 .332 3.81 .420 <br />.479 .530 .582 .641 .700 <br />60o <br />T=.21 .42 <br />.63 .84 1.05 <br />1.27 1.49 1.71 1.94 <br />2.17 2.38 `2.80 2.83 3.07 <br />1337.7 <br />_ E=.05g .112 <br />.168 .225 .233 <br />.340 .398 .457 .516 <br />.575 .638 .697 .774 .851 <br />mo <br />T=.23 .!8 <br />.69 .93 1.18 <br />1.40 1.64 1.88 2.13 <br />2.38 2.83 2.88 3.13 3.39 <br />50 <br />E=.087 .135 <br />.204 .273 .343 <br />.412 ;.483 .554 .625 <br />.697 .711 .81M .922 1.01 <br />0 <br />i <br />TABLE I. - Tangents and Externals to a 1° Curve. V <br />Chord =100 ft. <br />Int. <br />Angle <br />Tangent <br />External <br />Int. <br />-Angle <br />Tangent <br />g <br />External <br />Int. <br />Angle <br />Tangent <br />External <br />64° <br />3580.3 <br />1026.6 <br />71° <br />4086.9 <br />1308.2 <br />78° <br />4630.8 <br />1643.0 <br />10' <br />3591.9 <br />1032.8 <br />10' <br />4099.5 <br />1315.6 <br />10' <br />4053.6 <br />1651.7 <br />20 <br />3603.5 <br />1039.0 <br />20 <br />4112.1 <br />1322.9 <br />20 <br />4667.4 <br />1660.5 <br />30 <br />361.5.1 <br />1045.2 <br />30 <br />4124.8 <br />1330.3 <br />30 <br />4681.3 <br />1669.2 <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 />1686.9' <br />65 <br />3650.2 <br />1063.9 <br />72 <br />4162.8 <br />1352.6 <br />79 <br />4723.2 <br />1695.8 <br />10 <br />3661.9 <br />1070.2 <br />'10 <br />4175:6 <br />1360.1 <br />10 <br />4737.2 <br />1701.7 <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 />4201.2 <br />1375.2 <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 />4239.7 <br />1398.0 <br />80 <br />4807.7 <br />1749.9 <br />10 <br />3732.7 <br />1108.6 <br />10 <br />4252.0 <br />1405.7 <br />10 <br />4822.0 <br />1759:0 <br />20 <br />3744.6 <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 />81 <br />4893.6 <br />1805.3 <br />- 10 <br />3804.4 <br />1148.0 <br />10 <br />4330.7 <br />1452.5 <br />10 <br />4908.0 <br />1814:7 <br />20 <br />3316.4 <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 />1.168.4 <br />30 <br />4937:0 <br />1333.G <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 />3352.6 <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 />1181.6 <br />76 <br />4396.5 <br />1492.4 <br />83 • <br />4980.7 <br />1862.2 <br />10 <br />3576.8 <br />1188.4 <br />10 <br />4409.8 <br />1500.5 <br />10 <br />4995.4 <br />1871.8 <br />20 <br />3889.0 <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 />1202.0 <br />30 <br />4436.4 <br />1516.7 <br />30 <br />3024.8 <br />1891.2 <br />40 <br />3913.4 <br />1208.0 <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 />69 <br />3937.0 <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 />10 <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 />3974.8 <br />1243.7 <br />30 <br />4516.9 <br />1566.3 <br />30 <br />5113.9 <br />_1950.3 <br />40 <br />3987.2 <br />1250.8 <br />40 <br />4530.4 <br />1574.7 <br />40 <br />5128.9 <br />1960.2 <br />50 <br />3999.5 <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 />5150.0 <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 />1279.3 <br />20 <br />4584.8 <br />1608.6 <br />20 <br />5189.3 <br />2000.6 <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 />1300.9 <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 />Int. <br />Curve S° 10° 15° 20° <br />25° 30° <br />35° <br />1 40° 1 <br />45° 50° <br />I SS- <br />1 60° 65° 70° <br />- <br />_Angle <br />°. <br />1283 70 <br />.40 <br />1.398[2.27 <br />.71 <br />.17 <br />1.518 2 <br />?838 38 <br />.07 <br />60 x,774 3,851 <br />? <br />E 058 .112 .166 .225 <br />3405 <br />575 <br />697 <br />T=.23 .46 .69 .93 <br />1.16 1.40 <br />1:64 <br />2.13- 2.38 <br />2.63 <br />2.88 3.13 3.39 <br />65° <br />E =.067 .135 .204 .273 <br />.343 .412 <br />.483 <br />-.625 .697 <br />.711 <br />.845 .922 1.01 <br />70° <br />T=.25 .51 76 1.02 <br />].28 1.54 <br />1.80 <br />2.33 2.60 <br />2.88 <br />3.16 3.44 3.72 <br />E =.080 .159 .240 .321 <br />A03 .485 <br />.568 <br />.735 .819 <br />.906 <br />.994 1.08 1.17 <br />75° <br />T =.27 .58 83 1.1'2 <br />1.40 1.69 <br />1.98 <br />2.57 2.87 <br />3.16 <br />3.47 3.78 4.09 <br />E5 .182 .286 383 <br />.480 .578 <br />'.678 <br />.877 .977 <br />1.07 <br />1.18 1.29 1.89 <br />800=•30 <br />.81 91 1.22 <br />1.53 1.84 <br />2.15 <br />2.46 <br />2.78 3.10 <br />3.44 <br />3.78 4.12 4.46 <br />_ <br />E =.110 .220 .332 .445 <br />.558 .671. <br />.787 <br />.903 <br />1.02 1.13 <br />1.25 <br />1.38 1.50 1.62 <br />�o <br />T=.33 86 1.00 1133 <br />1.68 2.02 <br />2.30 <br />2.70 <br />3.05 3.40' <br />3.77 <br />4.14 4.55 4.89 <br />E-128 .259 .391 .524 <br />.657 .790 <br />MG <br />1.06 <br />1.20 1.14 <br />1.47 <br />1.62 1.78 1.91 <br />