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IV <br />j <br />AOgl <br />External <br />Angie <br />Tangent <br />External <br />43' 1 <br />Tangent <br />g <br />3 <br />� I <br />428.5 <br />50° <br />2671.8 <br />592.3 <br />57° <br />it <br />790.1 <br />0' <br />2266.6 <br />432.0 <br />10' <br />2681.9 <br />596.6 <br />10' <br />3121.7 <br />795.2_ <br />0 <br />2276.2 <br />435.6 <br />'439.2 <br />20 <br />2692.1 <br />600.9 <br />20 <br />3132.6 <br />800.4 <br />0 <br />4 <br />TABLE I. - Tangents and Externals to a 1° Curve. <br />Chord= 100 ft. <br />e <br />g0 <br />40 <br />50 <br />10 <br />ry0 <br />40 <br />50 <br />10 <br />30 <br />40 <br />y0 <br />Tangent <br />External <br />Angie <br />Tangent <br />External <br />Angie <br />Tangent <br />External <br />26 .40 .67 .80 .93 1.20 1.34 1.49 1.64 1.79 1.94 <br />2257.0 <br />428.5 <br />50° <br />2671.8 <br />592.3 <br />57° <br />it <br />790.1 <br />0' <br />2266.6 <br />432.0 <br />10' <br />2681.9 <br />596.6 <br />TABLE I. - Tangents and Externals to a 1° Curve. <br />Chord= 100 ft. <br />e <br />g0 <br />40 <br />50 <br />10 <br />ry0 <br />40 <br />50 <br />10 <br />30 <br />40 <br />y0 <br />Tangent <br />External <br />Angie <br />Tangent <br />External <br />Angie <br />Tangent <br />External <br />26 .40 .67 .80 .93 1.20 1.34 1.49 1.64 1.79 1.94 <br />2257.0 <br />428.5 <br />50° <br />2671.8 <br />592.3 <br />57° <br />3110.9 <br />790.1 <br />0' <br />2266.6 <br />432.0 <br />10' <br />2681.9 <br />596.6 <br />10' <br />3121.7 <br />795.2_ <br />0 <br />2276.2 <br />435.6 <br />'439.2 <br />20 <br />2692.1 <br />600.9 <br />20 <br />3132.6 <br />800.4 <br />0 <br />2285.9 <br />.46 69 93 1.16 6 1.88 2.13 2.38 2.63 2.88 3.13 3.39 <br />30- <br />2702.3 <br />605.3 <br />30 <br />3143.4 <br />805.6 <br />0 <br />2295.6' <br />442.8 <br />'40 <br />2712.5 <br />609.6 <br />40 <br />3154.2. <br />810.9 <br />0 <br />2305.2 <br />446.4 <br />50 <br />2722.7 <br />614.0 <br />50 <br />3165.1, <br />816.1 <br />65 <br />2314.9 <br />450.0 <br />51 <br />2732.9 <br />618.4 <br />58 <br />3176.0 <br />821.4 <br />0 <br />2324.6 <br />453.6 <br />10 <br />2743.1 <br />622.8 <br />10 <br />3186.9 <br />826.7 <br />0 <br />2334.3 <br />457.3 <br />20 <br />2753.4 <br />627.2 <br />20 <br />3197.8 <br />832.0 <br />0 <br />2344.1 <br />461.0 <br />30 <br />2763.7 <br />631.7 <br />30 <br />-3208.8 <br />837.3 <br />0 <br />2353.8 <br />464.6 <br />40 <br />2773.9 <br />636.2 <br />40 <br />3219.7 <br />842.7 <br />0 <br />2363.5 <br />468.4 <br />50 <br />2784.2 <br />640.7 <br />50 <br />3230.7 <br />848.1 <br />66 <br />2373:3' <br />472.1 <br />52 • <br />2794.5 <br />645.2 <br />59 <br />3241.7 <br />853.5 <br />0' <br />2383.1 <br />475.8 <br />10 <br />2804.9 <br />649.7 <br />10 <br />3252.7 <br />858.9 <br />0 <br />.2392.8 <br />479.6 <br />20 <br />2815.2 <br />654.3 <br />20 <br />3263.7 <br />864.3 <br />0 <br />2402.6 <br />.483.4 <br />30 <br />2825.6 <br />658.8 <br />:' 30 <br />3274.8 <br />869.8 <br />0 <br />2412.4 <br />487.2 <br />40 <br />2835.9 <br />663.4 <br />40 <br />3285.8 <br />875.3 <br />0 <br />2422.3 <br />491.0 <br />50 <br />2846.3 <br />668.0 <br />50 <br />3296.9 <br />880.8 <br />67 <br />2432.1 <br />494:8 <br />53 <br />2856.7 <br />672.7 <br />60 <br />3308.0 <br />886.4 <br />0 <br />2441.9 <br />498.7 <br />10 <br />2867.1 <br />677.3 <br />10 <br />3319.1 <br />892.0 <br />0 <br />2451.8 <br />502.5 <br />20 <br />2877.5 <br />682.0 <br />20 <br />3330:3 <br />897.5 <br />0 <br />2461.7 <br />506.4 <br />30 <br />2888.0 <br />686.7 <br />30 <br />3341.4 <br />-903.2 <br />0 <br />2471.5 <br />510.3 <br />40 <br />2898.4 <br />691.4 <br />40 <br />3352.6 <br />908.8 <br />0 <br />2481.4 <br />514.3 <br />50 <br />2908.9 <br />696.1 <br />50' <br />3363.8 <br />914.5 <br />68 <br />2491.3 <br />518.2 <br />54- <br />2919.4 <br />700.9 <br />61 <br />3375.0 <br />920.2 <br />0 <br />2501.2 <br />522.2 <br />110 <br />2929.9 <br />705.7 <br />10 <br />3386.3 <br />925.9 <br />0 <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 />..2531.1 <br />.3913.4 <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 />69 <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 />0 <br />2581.0 <br />554.5 <br />30 <br />3014.5- <br />•744.6 <br />30 <br />3476.8 <br />972.4 <br />1 <br />2591.0 <br />555.6 <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 />96 <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 />2611.2 <br />566.9 <br />56 <br />3046.5 <br />759:6 <br />63 <br />3511.1 <br />990.2 <br />20 <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 />3067.9 <br />769.7 <br />_ 20 <br />3534.1 <br />1002.3 <br />40 <br />2641:4 <br />579.5 <br />y 30 <br />3078.7 <br />774.7 <br />30 <br />3545.6 <br />1008.3 <br />50 <br />2651.5 <br />583.8 <br />40 <br />3089.4 <br />779.8 <br />40 <br />3557.2 <br />1014.4 <br />2661.6 <br />588.0 <br />50, <br />3100.2 <br />784.9 <br />50 <br />3568.7 <br />1020.5 <br />Corrections tobe-Added (T Tangent.- 'E =External.)-' <br />Tangent <br />Curve 5° ' <br />10° 15° 25' 30° 35° 40° 456 50° 55° 60° 656 70° <br />�t <br />External <br />' Angie <br />A-0' <br />T=.13 <br />26 .40 .67 .80 .93 1.20 1.34 1.49 1.64 1.79 1.94 <br />3580.3 <br />: <br />E=•023 <br />_'106 <br />.046 .070 .:.117 ..141 .172 .203 -.234 .265 '.277 .290 .315 .341 <br />f.60 <br />40° <br />T=.15 .30 .44 .76 .91 1.06 1.21 1.37 1.52 1.70 1.87 2.04 2.21 <br />78° <br />E=030.....098.153 <br />.184 ..216 .254 .289 .325 .351 .378 .411T=.17 <br />4$° <br />•. <br />.34 .51 .85 1.02 1.19 1.36 1.541.72 1.91 2.10 2.29 2.48 <br />10' <br />4099.5 <br />•075 ,.116- .189. .227 .266 .305 .345 .384 .425 .467 .508 .550 <br />50°E=•037_ <br />T=.19 <br />.57- .76.95 1.14 1.32 1.52 1.72 1.92 2.14 2.35 2.56 2.77 <br />20 <br />E=•046 <br />.38 <br />..093 .142 .188 .236 .283 :.332 3.81 .420 .479 .530 -.582 ..641 .700 <br />,o <br />T=.21 - <br />:.42 .63 .84 1.05 49 1.71 1.94 2.17 2.38 2.60 - 2.83 3.07 <br />600 <br />E=•056 <br />.112 .168 .225 .283398 .457 .516 .575 .636 .697 .774 .851 <br />�LJ401:4843 <br />30 <br />T=.23 <br />.46 69 93 1.16 6 1.88 2.13 2.38 2.63 2.88 3.13 3.39 <br />6so <br />E=.067 <br />.185 -.204 '.273 .343 .554 A25 .697 .711 .845 .922 1.01 <br />':,30 <br />4681.3 <br />1669.2 <br />, <br />40 <br />3626.8 <br />l <br />Tnsnn L - Tangents and Externals to a V Curve. <br />Chord =100 ft.= <br />Angle <br />Tangent <br />External <br />Angle <br />Tangent <br />External <br />' Angie <br />Tangent <br />External <br />64° <br />3580.3 <br />1026.6 <br />71' <br />4086.9 <br />1308.2 <br />78° <br />4639.8 <br />1643.0 <br />10' <br />3591.9 <br />1032.8 <br />10' <br />4099.5 <br />1315.6 <br />10' <br />4653.6 <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 />3615.1 <br />1045.2 <br />30• <br />4124.8 <br />1330.3 <br />':,30 <br />4681.3 <br />1669.2 <br />, <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 />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 />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 />4252.6 <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 />3816.4 <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 />1468.4 <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 />4951.5 <br />1843.1 <br />50 <br />3852.6 <br />1174.8 <br />50 <br />4383.3 <br />1484.4 <br />,40 <br />50 <br />4966.1 <br />1852.6 <br />68 <br />3864.7 <br />1181.6 <br />75 <br />4396.5 <br />1492.4 <br />82 <br />4980.7 <br />1862.2 <br />10 <br />3876.8 <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 />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 />69 <br />3937.9 <br />1222.7 <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 />4544.0 <br />1583.1 <br />50 <br />5143.9 <br />1970.3 <br />96 <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 />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 />-i.-t-Curve <br />5° <br />10° <br />15° <br />20° <br />25° <br />30° <br />35° <br />40° <br />45° <br />50° <br />55° <br />60° <br />65° <br />70° <br />Angle <br />60o <br />T=.21 <br />.42 <br />.63 <br />.84 <br />1.05 <br />1.27 <br />1.49 <br />1.71 <br />1.94 <br />2.17 <br />2.38 <br />2.60. <br />2.83 <br />3.07 <br />E=.056 <br />.112 <br />.168 <br />.225 <br />.283 <br />.340 <br />.398 <br />.457 <br />AM <br />.575 <br />.636 <br />.697 <br />.774 <br />,851 <br />65° <br />T=•23 <br />.46 <br />.69 <br />.93 . <br />1.16 <br />1.40 <br />1.64 <br />1.88 <br />2.13 <br />2.38 <br />2.63 <br />2.88 <br />3.13 <br />3.39 <br />E=.067 <br />.1?5 <br />.204 <br />.273 <br />.343 <br />.412 <br />.483 <br />.554 <br />.625 <br />.697 <br />.711 <br />.845 <br />.922 <br />1.01 <br />70' <br />T=.25 <br />.51 <br />.76 <br />1.02 <br />1.28 <br />1.54 <br />1.80 <br />2.06 <br />2.33 <br />2.60 <br />2.88 <br />3.16 <br />3.44 <br />3.72 <br />E=.080 <br />.159 <br />.240 <br />.321 <br />.403 <br />.485 <br />.568 <br />.652 <br />.735 <br />.819 <br />.906 <br />.994 <br />1.08 <br />1.17 <br />75° <br />T=.27 <br />.56 <br />.83 <br />1.12 <br />1.40 <br />1.69 <br />1.98 <br />2.27 <br />2.57 <br />2.87 <br />3.16 <br />3.47 <br />3.78 <br />4.09 <br />E=.095 <br />.182 <br />.286 <br />.383 <br />.480 <br />.578 <br />.678 <br />.777 <br />.877 <br />.977 <br />1.07 <br />1.18 <br />1.29 <br />1.39 <br />801, <br />T=.30 <br />61 <br />.91 <br />1.22 <br />1.53 <br />1.84 <br />2.15 <br />2.46 <br />2.78 <br />3.10 <br />3.44 3.78 <br />4.12. <br />4.46 <br />E=.110 <br />.220 <br />.332 <br />.445 <br />.558 <br />.671 <br />.787 <br />.903 <br />1.02 <br />1.13 <br />1.25 <br />1.38 <br />1.50 <br />1.62 <br />SSo <br />T=.33 <br />.66 <br />11.00 <br />1.33 <br />1.68 <br />2.02 <br />12.36 <br />2.70 <br />3.05 13.40 <br />3.77 <br />4.14 <br />14.55 <br />JL89 <br />E=.128 <br />.259 <br />.391 <br />.524 <br />.657,,2"01 <br />X6 <br />1.06 1.20 <br />11.34 <br />1.47 <br />1.62 <br />11.76 <br />11.91 <br />