|
N TABLE I. -Tangents and Externals to a V Curve.
<br />Chord=100 ft.
<br />Int.
<br />Angle
<br />Tangent
<br />External
<br />Int.
<br />Angle
<br />Tangent External
<br />g
<br />Int.
<br />Angle
<br />Tangent
<br />External
<br />45'
<br />2257.0
<br />428.5
<br />501
<br />2671.8
<br />592.3
<br />51°
<br />3110.9
<br />790.1
<br />10'
<br />2266,6
<br />432.0
<br />10'
<br />2651.9
<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 />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 />44
<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 />1.0
<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 />G31.7
<br />30
<br />3208,8
<br />837.%
<br />40
<br />1353.8
<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 />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 />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 />2t02.0
<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 />880.8
<br />46
<br />2432.1
<br />494.8
<br />I
<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 />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 />908.8
<br />60
<br />2481.4
<br />514.3
<br />50
<br />2908.9
<br />696.1
<br />' 56
<br />3363.8
<br />- 914.5
<br />47
<br />2191.3
<br />518.2
<br />54
<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 />46
<br />2651.0
<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 />9G0,6
<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 />49
<br />'2GtI,2
<br />566.9
<br />56
<br />3046.5
<br />759.0
<br />63,
<br />3511.1
<br />990.2
<br />_110
<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 />2U
<br />20G7.9
<br />769,7
<br />20
<br />3534.1
<br />1002.3
<br />30
<br />2041A
<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 />1014A
<br />50
<br />266].G
<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 />V0 5' 10°
<br />15°
<br />20°
<br />25°+
<br />30° 35° 40°
<br />45°
<br />50°
<br />55°
<br />60° 65°
<br />70°
<br />40°
<br />T=,13 120,
<br />.40
<br />.53
<br />.67
<br />.80 AS .106
<br />1.20
<br />1.34
<br />1.49
<br />1.64 1.79
<br />1.94
<br />--F=.023
<br />•046
<br />•070
<br />.093
<br />.111
<br />.172 .203
<br />.234
<br />.2G5
<br />.277
<br />.290 .315
<br />.311
<br />45°
<br />T=.15 30
<br />.44
<br />.60
<br />.76
<br />_.141
<br />.91 1.06 1.21
<br />1.37
<br />1.52
<br />1.70
<br />1.87 2,01
<br />2.21
<br />_
<br />E=.030 •060
<br />'_T=
<br />:093
<br />.119
<br />.153
<br />.184 .216 .254
<br />.289
<br />.325
<br />.351
<br />.378 .411
<br />.W
<br />3638.5.
<br />1
<br />T=•17 .34
<br />51
<br />.68
<br />.85
<br />1.02 1.19 136
<br />1.54
<br />1.72
<br />1.01
<br />2.10 2.29
<br />2.48
<br />72
<br />E=.037 .075
<br />.116
<br />.151
<br />.189
<br />.227 .266 .305
<br />.345
<br />,384
<br />.425
<br />A67 .508
<br />.550
<br />55°
<br />I T=.I9 38
<br />.57
<br />1704.7
<br />20
<br />1,14 1.32 1,52
<br />1.72
<br />1.92
<br />2.14
<br />2.35 2,56
<br />2.7
<br />J_
<br />E =.046 ,093
<br />.142
<br />T,225.233
<br />1082.9
<br />.283 .332 3.8I
<br />420
<br />.479
<br />.530
<br />.562 .641
<br />.700
<br />40
<br />T=.21 AS
<br />63
<br />40
<br />4214.0
<br />127 1,49 1.71
<br />1'04,12:,
<br />17
<br />2,38
<br />2,60 2.83
<br />307
<br />1095.7
<br />E=.056 E .112
<br />,108
<br />1390.4
<br />50
<br />.340 .398 .457
<br />,51
<br />575
<br />.636
<br />,697 .774
<br />.851
<br />65°
<br />T='.237 46
<br />.69
<br />.93
<br />1.16a
<br />140 1.64 1.88
<br />2.13
<br />2.38
<br />2.63
<br />2.88 3.13
<br />3.38
<br />10
<br />E-.067 ,135
<br />.204
<br />.273
<br />.343
<br />.413 .483 .554
<br />.625
<br />.697
<br />.711
<br />.91 .922
<br />1.01
<br />TABLE 1. - Tangents and Externals to a 1° Curve, V_
<br />Chord =100 ft.
<br />Ent .
<br />Angle
<br />Tangent
<br />External
<br />fit'
<br />Angle
<br />Tan ent
<br />g
<br />External
<br />Int. (Tangent
<br />Angle
<br />40°
<br />External
<br />64°
<br />3550.3
<br />1026.6
<br />71°
<br />40S6.9
<br />1308,2
<br />78°
<br />4639.8
<br />1043.0
<br />101
<br />3591.0
<br />1032.8
<br />10'
<br />4099.5
<br />1315.6
<br />10'
<br />4653.6
<br />1651.7
<br />20,
<br />3003.5
<br />1039.0
<br />20
<br />4112,1
<br />1322.9
<br />20
<br />4667.4
<br />1060.5
<br />30
<br />3515.1
<br />1045.2
<br />30
<br />4124.8
<br />1330.3
<br />30
<br />',
<br />4681.3
<br />1069.2
<br />40
<br />3626.8
<br />1051.4
<br />40
<br />4137A
<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 />3600.2
<br />1063.0
<br />72
<br />4162.S
<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 />4MB 5
<br />1367.G
<br />20
<br />4751.2
<br />1713,7
<br />30
<br />3685.4
<br />1082.9
<br />30
<br />4301. 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 />86
<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 />37.14.6
<br />1115.1
<br />20
<br />4265,0
<br />1113.5
<br />20
<br />4836.2
<br />1768.2
<br />30
<br />37,56.5
<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 />11.28.2
<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 />4301.6
<br />1436.8
<br />50
<br />4870:2
<br />1796.0
<br />67
<br />3792.4
<br />1141.4
<br />74
<br />4317.6
<br />I444.6
<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 />3$16,4
<br />1154.7
<br />20
<br />4313.8
<br />1460.4
<br />20
<br />4922,5
<br />1.424,1
<br />30
<br />3828,4
<br />1161.3
<br />30
<br />435G.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 />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 />3364.7
<br />1181.6
<br />75
<br />4396.5
<br />1492.4
<br />82
<br />4980.7
<br />1862.2
<br />.10
<br />3376.S
<br />1188.4
<br />10
<br />4109.8
<br />1500-5
<br />10
<br />4995.4
<br />1871.8
<br />20
<br />3389.0
<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 />151E-7
<br />30
<br />5029,8
<br />139 1. 2
<br />40
<br />3913.4
<br />1208.9
<br />40
<br />4449,7
<br />1524.9
<br />40
<br />5030.5
<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 />1220.7
<br />10
<br />44S9.9
<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 />1533.1
<br />50
<br />5143.9
<br />1970.3
<br />76
<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 />4636.8
<br />1279.3
<br />20
<br />4584.8
<br />1-08.6
<br />20
<br />5189.3
<br />2000.6
<br />30
<br />4040.3
<br />1286.5
<br />30
<br />4598,5
<br />1.517.1
<br />30
<br />5204.4
<br />2010.8
<br />40 -
<br />4061.8
<br />1293.6
<br />40
<br />4012.2
<br />1612.5.7
<br />40
<br />5219.7
<br />2021.1
<br />50'
<br />4074A
<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 />5°
<br />10°
<br />15° 20°
<br />25°
<br />30°
<br />35°
<br />40°
<br />45°
<br />50°
<br />55°
<br />60° 65°
<br />70°
<br />t:
<br />-Angle
<br />1.105
<br />1.27
<br />1.49
<br />1
<br />1.94
<br />2.17
<br />2.38
<br />2
<br />3
<br />BO.
<br />E=.056
<br />.112
<br />1G8 .225
<br />.283
<br />.340
<br />.398
<br />457
<br />516
<br />.575
<br />.630
<br />? 697 .774
<br />.851
<br />T=.23
<br />.46
<br />.69 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 3.13
<br />3.89
<br />65°
<br />F=.067
<br />.135
<br />.204_ 373
<br />.343
<br />.412
<br />.483
<br />.554
<br />.525
<br />.697
<br />.711
<br />.845 .922
<br />1.01
<br />T=.25
<br />.76 1.02
<br />1,28
<br />L54
<br />1.80
<br />2.06
<br />2.33
<br />2.60
<br />2,88
<br />3.16 3.44
<br />3.72
<br />70°
<br />E=.080
<br />.51
<br />.159
<br />.240 .321
<br />.403
<br />.485
<br />.568
<br />.652
<br />.735
<br />.819
<br />.900
<br />.994 1.08
<br />1.17
<br />T=.27
<br />.83 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 3.78
<br />4.09
<br />75°
<br />E-095
<br />.56
<br />.182
<br />.286 .383
<br />,480
<br />.578
<br />.678
<br />.777
<br />.877
<br />.977
<br />1.07
<br />1.18 1.29
<br />L30
<br />=.30
<br />01
<br />.91 I'22 '1.53
<br />134
<br />2.15
<br />2.46
<br />2.78
<br />3.10
<br />3.44
<br />3.78 4.12
<br />4.96
<br />80'
<br />E =.110
<br />.220
<br />.332 .445
<br />.558
<br />.671
<br />.787
<br />.903
<br />t_02
<br />1,13
<br />1.25
<br />3.77
<br />1.38 1.50
<br />4,14 4.65
<br />1.62_
<br />4.80
<br />_
<br />85° T=.33
<br />66
<br />1.00 1.33
<br />1,68
<br />2.02
<br />2.36 2.70
<br />3.05
<br />3.40
<br />E=.128.
<br />.259
<br />.301 .5241
<br />.657
<br />.790
<br />.92G 1.06
<br />1.20
<br />1.34
<br />1.47
<br />1.62 1.70
<br />1.41
<br />
|