|
Y
<br />IST TABLE I: Tangents and Externals to a 1° Curve.
<br />Chord =100 ft_
<br />Int,
<br />Angle
<br />Tangent
<br />External
<br />Ing'
<br />Am
<br />Tan ent'Eaternal
<br />g
<br />70°
<br />Int'
<br />Angle
<br />Tangent
<br />External
<br />43°
<br />2257.0
<br />428.5
<br />50'
<br />2671.8
<br />592.3
<br />57°
<br />3110.9
<br />790.1
<br />10'
<br />2266.6
<br />432.0
<br />lOr
<br />2681.9
<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 />600.9
<br />20
<br />.3 132.6
<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 />505.6
<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 />44
<br />2314,0
<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 />A53.6
<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 />822.0
<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 />4D
<br />2353.8
<br />4G4.6
<br />40
<br />2773.9
<br />636,2
<br />40
<br />3219.7
<br />842.7
<br />50
<br />2363.5
<br />4,68,4
<br />50.:
<br />2784;2
<br />640,7
<br />50
<br />323D.7
<br />849.1
<br />45
<br />2373:3
<br />472.1
<br />52
<br />2794.5
<br />645.2
<br />56
<br />3241:7
<br />853.5
<br />.10
<br />2383.1
<br />475.8
<br />10
<br />2804.0
<br />649.7
<br />10
<br />3252.7
<br />858.9
<br />20
<br />2392,8
<br />479.6
<br />.20
<br />281.5.2
<br />654,3
<br />20
<br />3263.7
<br />861.3
<br />30
<br />2402.6
<br />483.4
<br />30
<br />2825.6
<br />653.8
<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 />2546.3
<br />668.0
<br />50
<br />3296:0
<br />880.8
<br />46
<br />2432.1
<br />494.8
<br />53
<br />2850.7
<br />672.7
<br />60
<br />3303.0
<br />836.4
<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 />"877.5
<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 />2598.4
<br />691.4
<br />40
<br />3352.6
<br />908.3
<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 />47:... .'2491.3
<br />3864.7
<br />518.2
<br />64
<br />2919.4
<br />700.9
<br />61
<br />3375.0
<br />020.2
<br />10
<br />2501.2
<br />022.2
<br />-10
<br />2929:9
<br />705.7
<br />10
<br />3386.3
<br />925.9
<br />.20
<br />25I1.2
<br />520.1
<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 />843 1. 4
<br />948.9
<br />48
<br />2551,0
<br />542.2
<br />55
<br />.2982.7
<br />729.9
<br />G2
<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 />940.6
<br />20'
<br />257110
<br />550.4
<br />20
<br />3003.9
<br />739.7
<br />20
<br />3465,4
<br />96G.5
<br />.30
<br />2581.0
<br />554.5
<br />30
<br />3014.5
<br />744.(
<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 />.'5U
<br />3035,8
<br />754.6
<br />50'
<br />3499.7
<br />984.3
<br />'49
<br />2611.2
<br />566.0
<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 />3067.9
<br />769.7
<br />20
<br />3.5341
<br />1002.3
<br />30 .2641:4
<br />4049-,3
<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 />355557.2
<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=ExternaI.)
<br />Ent, "
<br />Angle Curgo 5° '10°, 15° 20°
<br />25°. .30°
<br />1 35° 1 40°
<br />45°
<br />50° 55°. 60° 65°
<br />70°
<br />40° T=A , .20 •:40. :.53
<br />.67 • .80
<br />.93 .105
<br />1.20
<br />1.34' 1,49. 1,64 1.79
<br />1.94
<br />.E=.023. .046 .070 .093
<br />.117 .141
<br />.172 .203
<br />.234
<br />.265 .277 290 .315
<br />.341
<br />45°' T=,15 .30 .44; .GD
<br />':76 91
<br />1.06 1.21
<br />1.37
<br />7.52 170 1,87 2.04
<br />2.21
<br />__ E=,030 .060 .003 .119
<br />..153 .184
<br />.216 .,254
<br />,289
<br />.325 ,351 ,378 .411
<br />.445
<br />50° T=.17 34 .51 .68
<br />.85 1.02
<br />1.19 L3G
<br />1.54
<br />1.72 1,91 2.10 2.29
<br />2,48
<br />E=.037 .075...116 .151
<br />,189..227
<br />.266 .305
<br />.345..384'
<br />,425 .467 .508
<br />.550
<br />T=.19 38 .57 .76
<br />.95 1.14.
<br />1.32 1.52
<br />1.7'2
<br />1.93 2.14 2.35 2.56
<br />2.77
<br />H=.040, .093 .142 .188
<br />:236 .283
<br />-.332 3.81
<br />.420
<br />c.479 .530 .532 .641
<br />.700
<br />600 ' T=.21 .42 .63 ,84
<br />1.05 1.27
<br />1.49 1.71
<br />L94'
<br />2.17 2.38 2,60 2.83
<br />3.07
<br />E =.050 .112 .168 ,225
<br />.283 .344
<br />.398 .457
<br />.516
<br />.575 . ,030 .697 .774
<br />.851
<br />65a T=.23 _46 .60 93
<br />1.16 140
<br />1.64 1.88
<br />2.13
<br />2.38 2.63 2.88 3.13
<br />3.39
<br />E=067 .135 .204 .273
<br />.343 .412
<br />'.483 .554
<br />.625
<br />.697 .711 .845 .9221.01
<br />1360.1
<br />TABLE I. - Tangents and Zxternals to a 1° Curve.
<br />Chord =100 it.
<br />V
<br />Int. -
<br />Angle
<br />Tangent
<br />External
<br />Int'
<br />'Angle
<br />Tangent
<br />External
<br />Int' .
<br />Angle
<br />Tangent
<br />Exteinal
<br />04°
<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 />•4.124.8
<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 />1G78.1
<br />50
<br />'3638.5
<br />1057,7
<br />50
<br />4150. 1
<br />1345.1
<br />50
<br />4709.2
<br />1656.9
<br />66.
<br />3650.2
<br />1063.9
<br />72
<br />4162.8
<br />1352.6
<br />73
<br />4723.2
<br />1605.8
<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 />4158.5
<br />1367.6
<br />2D
<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 />1093.7
<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,-3744.6
<br />.558
<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 />43700
<br />1476.4
<br />.40
<br />4951.5
<br />1843.1
<br />50
<br />3852.G
<br />1174.8-.
<br />.50
<br />4383.3
<br />1484.4
<br />30
<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 />3876.6
<br />1188.4
<br />10
<br />4409.8
<br />1500.5
<br />10
<br />4995.4
<br />1871.8
<br />_
<br />20
<br />3889.0
<br />1195.2
<br />20
<br />4423.1
<br />1508.6
<br />20
<br />5010,0
<br />188I.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 />3037.9
<br />1222.7
<br />76-
<br />4476.5
<br />1541.4
<br />83
<br />5069.2
<br />1020.5
<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 />3062.5
<br />1230.7
<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 />1060,2
<br />50
<br />3999.5,
<br />1257.9
<br />50
<br />4544.0
<br />1533.1
<br />50
<br />5143.9
<br />', 1070.3
<br />70
<br />4011.9
<br />1265.0.
<br />77
<br />4557.6
<br />.1591.6
<br />64 .
<br />5159.0
<br />1980.4
<br />10
<br />4024.4
<br />1272.1
<br />10
<br />4571.2
<br />.1000.1'
<br />10
<br />5174.1
<br />I990.5
<br />20
<br />4030.8
<br />1279.3
<br />20
<br />4584.8
<br />.1608.5
<br />20
<br />5189.3
<br />2000.6
<br />30
<br />4049-,3
<br />1256.5
<br />-30
<br />459 S.5
<br />'1617.1
<br />30
<br />5204.4
<br />2U10.8
<br />40
<br />4001.8
<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 />Curve 5° 10°
<br />15°
<br />20°
<br />25°
<br />30° 35°
<br />406
<br />45° 50°
<br />55°
<br />-60°
<br />65°
<br />70°
<br />Angle
<br />60°
<br />T=.21 - 42
<br />.63
<br />.84
<br />1.05
<br />1.27 1.49
<br />1.71
<br />1.94 2.17
<br />2.33
<br />2,60
<br />2.83
<br />3.07.'
<br />k1=.050_ .112
<br />.158
<br />,226
<br />�83
<br />.340 .398
<br />.457
<br />.516 .573
<br />.636
<br />.697
<br />,774
<br />.851
<br />'T=.23
<br />.69
<br />1.16
<br />1.40 1.64
<br />1.88
<br />2.13 2.38
<br />2.53
<br />2.886
<br />3.13
<br />3.39
<br />651
<br />.46
<br />-E=.OG7 .135
<br />.204
<br />.93�
<br />.272
<br />.343
<br />.412 .433
<br />.554
<br />.025 .697
<br />.711
<br />.8_,a
<br />9'.,
<br />1.01
<br />70°
<br />T=.25 .51
<br />.70
<br />1.02
<br />1.28
<br />1.54 1.80
<br />2.06
<br />2,33 2.60
<br />2.38
<br />3.16
<br />3.44
<br />3.72
<br />E=.080 ..159
<br />.240
<br />.321
<br />.403
<br />.485 .558
<br />.652
<br />.735 .819
<br />.905
<br />AM
<br />1.08
<br />1.17
<br />75°
<br />T=.27 .5fi
<br />83
<br />1.12.
<br />1.40
<br />1.69 1.98
<br />2.27
<br />2.57 2.57
<br />3.16
<br />3.47
<br />3.78
<br />4.09
<br />E=.095 .182
<br />.286
<br />'.383
<br />.480
<br />.57$ .678
<br />.777
<br />.S Z7 .977
<br />1.07
<br />1.18
<br />1.29
<br />1.30
<br />80°
<br />T=30 .61,.91
<br />L22
<br />1.53
<br />1.84 2.15
<br />2.40
<br />2.78 3.10
<br />3.44
<br />3.78
<br />4.12
<br />4.46
<br />E=.110 .220
<br />.332
<br />045
<br />.558
<br />.671 .787
<br />.903
<br />1.02 1.13
<br />1.25
<br />1.38
<br />1.50
<br />1.G2
<br />S5°
<br />T=.33 .66
<br />1. 00
<br />1.33
<br />1.68
<br />2.02 2.36
<br />2.70
<br />.05 3.
<br />340
<br />8.77
<br />4.14
<br />4.65
<br />4.89
<br />E=.128 .259
<br />.391
<br />.524
<br />.657
<br />.790 .926
<br />1.00
<br />1.20 1.34
<br />1.47
<br />1.62
<br />1.76
<br />1.91
<br />
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