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r <br />IV TAn1.E.I. - Tangents' and' Externals to a 1° Curve. <br />Chord =100 ft. <br />l <br />Angle <br />Tangent <br />External <br />nle <br />Tangent <br />Externa <br />Int. <br />Angle <br />Tangent <br />External <br />43°! <br />2257.0 <br />428.5 <br />50° <br />2671.8 <br />502.3' <br />5r <br />3110.9 <br />790.1 <br />10' <br />2266:6 <br />432.0 <br />10' <br />2681.9 <br />590.6 <br />10' <br />3121.7 <br />795.2 <br />20 <br />2276.2 <br />435.6 <br />20 <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 />510.9 <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 />44 <br />2314.9 <br />450.0 <br />51 <br />2732.9 <br />618.4 <br />58 <br />3176.0 <br />521.4 <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 />542.7 <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 />2794.5 <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 />649.7 <br />10 <br />32.52:7 <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 />564.3 <br />30 <br />2402.6 <br />483.4 <br />30 <br />2825.6 <br />658.8 <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 />3296.9 <br />SS0.8 <br />46 <br />2432.1, <br />494.8 <br />53 <br />2856.7 <br />672.7 <br />60 <br />3308.0 <br />886.4 <br />10 " <br />2441.9, <br />498.7 <br />'10 <br />2867.1 <br />G77.3 <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 />246 C.7 <br />500.4 <br />30 <br />2888.0 <br />686.7 <br />30 <br />3341.4 <br />003.2 <br />40 <br />2471.5 <br />.510.3 <br />40 <br />2395.4 <br />691.4 <br />40 <br />3352.6 <br />908.8 <br />50 <br />2481.4 <br />514.3 <br />50 <br />2908.9 <br />6961.1 <br />50' <br />3363.8 <br />914.5 <br />47 <br />2491.3 <br />518.2 <br />84 <br />2919.4 <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 />48 <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 />34S8.3 <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 />49 <br />2611.2 <br />,566.9 <br />50 <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 />7G4.6 <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 />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 />770.8 <br />40 <br />3557.2 <br />1014.4 <br />60 <br />2661.6 <br />'588.0 <br />50 <br />3100.2 <br />784.9 <br />50 <br />3563.7 <br />1020.5 <br />Corrections to be Added (T =Tangent. E=External.) <br />5° <br />Inngje <br />10° 1 15° 20° 25° <br />30° 35° 40° <br />45° <br />50° <br />55° 60° 651 70° <br />.Curve <br />Tangent <br />External <br />04° ' <br />3580.3 <br />1026.6 <br />71°.. <br />40S6.9 <br />1 <br />1.234 <br />1 <br />1 1.940 <br />1.290 1 <br />40° E=.023 <br />.016 .070 .093 .1117 <br />.141 .172.34 <br />.203 <br />10' <br />265 <br />277 395 <br />5° <br />.76 <br />184 1.216 1254 .21 <br />1.289 37 <br />1 .52 <br />21 <br />1:351 i 2.411 ? <br />.4 <br />E =.030 <br />060 .003 .199 .153 <br />. <br />20, <br />325 <br />378 445 <br />T=17 <br />.34 .51 .68 .85 <br />1.02 1.19 1.36 <br />1.54 <br />4124.8 <br />1.91, 2.10 2.29 2.48 <br />50° E =.037 <br />.075 .116 .151 .189 <br />.227 .266 .305 <br />.345 <br />3626.8 <br />.425 .467 .508 .550 <br />40 <br />4137.4 <br />1.283 11, 1 12 13.81 .52 <br />1.420.72 <br />.92 <br />2.530 .14 2 2.56.35 2.77 <br />? <br />E ---.046 <br />093 142 .188 .236 <br />332 <br />50 <br />4150.1 <br />582 700 <br />50 <br />14 1.0 <br />1.27 1 .49 1.71 <br />1.911 <br />F2.1 <br />238 2.60 83 3.07 <br />? <br />60° E 056 <br />118 .168 .225 283 <br />340 398 .457 <br />516 <br />4723.2 <br />036 097 774 851 <br />65 o T=.23 <br />.46 60 93 1.16 <br />1.40 I.G4 1.88 <br />2.13 <br />4175.6 <br />2.63 2.883.13 3.39 <br />E=,067 <br />.135 204 .273 .343 <br />.412.483.554 <br />.625.845 <br />3673.7 <br />.922 1.01 <br />TABLE I. - Tangents and Externals to a 1° Curve. <br />Chord =100 ft. <br />Angle <br />Tangent <br />External <br />Angie <br />Tangent <br />External <br />Angle <br />Tangent <br />External <br />04° ' <br />3580.3 <br />1026.6 <br />71°.. <br />40S6.9 <br />1308.2 <br />78° <br />4639.8 <br />1643.0 <br />„ .101 <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 />„ 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 />1GS6.9 <br />05 <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 />1367.0 <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 />13S2.8 <br />40 <br />4779.4 <br />1731.7 <br />50. <br />3709.0 <br />1095,7 <br />50. <br />4226.3 <br />1390.4 <br />50 <br />4793.6 <br />1740.8 <br />Be <br />3720.9 <br />1102,2 <br />73 <br />4239.7 <br />1393:0 <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 />4830.2 <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 />14 219. 0 <br />40, <br />4564.8 <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 />1706.0 <br />,67 <br />3792.4 <br />1141,4 <br />74 <br />4317.6 <br />1444.6 <br />81 <br />4593.6 <br />1805.3 <br />10 <br />3804.4 <br />114S,0 <br />10 <br />4330.7 <br />1452.5 <br />10 <br />490S.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 />1465.4 <br />30 <br />4937.0 <br />1833.6 <br />40 <br />3840.5 <br />1168.1 <br />40 <br />4370.1 <br />1476.410 <br />1951.6 <br />1543.1 <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 />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 />I871.8 <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 />1215.5 <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 />7G <br />4476.5 <br />1541.4 <br />83 <br />5069.2 <br />1920.5 <br />10 <br />3956.2 <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 />15,93.1 <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 />1G00.1 <br />10 <br />5174.1 <br />'1090.5 <br />20 <br />4036;.8 <br />1279.3 <br />20 <br />4584.8 <br />1608.6 <br />20 <br />°189.3 <br />2000.6 <br />30 <br />4049.3 <br />12S6.5 <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 />4012.2 <br />1625.1 <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. Curve 5° 10° 15° <br />20°25° <br />30° 35° <br />40° <br />45° 50° <br />55° <br />60° <br />65° <br />70° <br />Anglo <br />00° <br />1.283 .05 <br />1.340 .27 1.393 .40 <br />71 <br />1 <br />1.516 .94 2.575 <br />2 .38 <br />2.697 60 <br />83 <br />? <br />.07 <br />3,851 <br />E=,056 .112 .168 <br />.225 <br />457 <br />636 <br />774 <br />65° <br />1.343 <br />1.4102 1.483 -64 <br />1.354 <br />2.625 .13 2.697 <br />y.711 <br />2.845 .83 <br />3.922 <br />E=.007 .135 .204 <br />.2'73 <br />1.01 <br />70° T=.25 .51 .70 <br />1.02 <br />1.28- <br />1.54 1.80 <br />2.16 <br />2.33 2.00 <br />2.88 <br />3.16 <br />3.44 <br />3.72 <br />E=.080 .159 .240 <br />.321 <br />.403 <br />.435 .568 <br />.652 <br />.735 .810 <br />.906 <br />.991 <br />1.08 <br />1.17 . <br />75° T=.27 .56 .83 <br />1.12 <br />1:10 <br />1.69 1.93 <br />2.27 <br />2.51 2.87 <br />3.16 <br />3.47 <br />3.78 <br />4.09 <br />E=.095 .182 .286 <br />.383 <br />.480 <br />.578 .678 <br />.777 <br />.877 .977 <br />1.07 <br />1.18 <br />1.29 <br />1.39 <br />800 -T=.30 .61 .91 <br />1.22 <br />1.53 <br />1.8.1 2.15 <br />2.46 <br />2.78 13.10 <br />3.44 <br />-j.:31719.12 <br />4:46 <br />E=.110 .220 .332 <br />.445 <br />.558 <br />.671 .787 <br />.903 <br />1.02 1.13 <br />1.25 <br />8 <br />1.50 <br />1.62 <br />85. .66 1.00 <br />1.33 <br />1.18 <br />2.02 2.36 <br />2.70 <br />3.05 3.40 <br />3.77 <br />4.14 <br />4.55 <br />4.89 <br />1T=.33 <br />E=.128 .259 391 <br />..524 <br />.057 <br />.790 .9261:06 <br />120 1.34 <br />1.47 <br />1.62 <br />1.76 <br />1.81 <br />