|
II TABLE I. - Tangents and Externals to a V Curve.
<br />Chord =100 It.
<br />Int..tangent
<br />Angle
<br />10° 15° 20°
<br />External
<br />Int'
<br />Angle
<br />Tangent
<br />External
<br />Int.
<br />Angle-
<br />Tangent
<br />External
<br />1°
<br />50.00
<br />.22
<br />8°
<br />400.66
<br />13.99
<br />15°
<br />754.32
<br />49.44
<br />10'
<br />58.34
<br />.30
<br />10'
<br />409.03
<br />.14.58
<br />-.10'
<br />762,80
<br />50.55
<br />20
<br />66.67
<br />.39
<br />20
<br />417.41
<br />15.18
<br />20
<br />771,29
<br />51.68
<br />30
<br />75:01
<br />.49
<br />30
<br />425.79
<br />15.80
<br />30
<br />779,77
<br />52,82
<br />40
<br />83.34
<br />.61-
<br />40
<br />434.17
<br />16.43
<br />40
<br />788,26
<br />53.97
<br />50
<br />91.68
<br />.73
<br />5Q
<br />442.55
<br />17.07
<br />50
<br />796.75
<br />55,13
<br />2-
<br />100.01
<br />.87
<br />.9
<br />450.93
<br />17.72
<br />16 .
<br />.805.25
<br />.56 31
<br />10
<br />108.35.
<br />1.02
<br />10
<br />459.32
<br />'18. 38
<br />10
<br />813,75,
<br />57,50
<br />20
<br />116.68
<br />1.19
<br />20
<br />467..71
<br />19.06
<br />20
<br />822,25
<br />58.70
<br />30
<br />125.02
<br />1.36
<br />30
<br />AM 10
<br />19.75
<br />- 30
<br />830,76
<br />59.91
<br />40
<br />133.36
<br />1.55
<br />40
<br />484.49
<br />20.45
<br />40
<br />839.27
<br />61.14
<br />50
<br />141.70
<br />1.75
<br />50
<br />492,88
<br />21.16
<br />50
<br />847.78
<br />62.38
<br />3
<br />150.04
<br />1.96
<br />10
<br />501.28
<br />21.89
<br />17
<br />856,30
<br />63.63
<br />10
<br />158.38
<br />2.19
<br />10
<br />509.68
<br />22.62
<br />10,
<br />864,82
<br />64.90
<br />20
<br />166.72
<br />2.43
<br />20
<br />"518.08
<br />23.38
<br />20
<br />873.35
<br />66.18
<br />30
<br />175.06
<br />2.67
<br />30
<br />526.48
<br />24.14
<br />30
<br />881.88
<br />67.47
<br />40
<br />.183.40
<br />2.93
<br />40
<br />534.89
<br />24.91
<br />40
<br />890.41
<br />68.77
<br />50--
<br />191.74
<br />3.21
<br />50
<br />543.29
<br />25.70
<br />50
<br />898.95
<br />70.09
<br />4
<br />200.08'
<br />3.49
<br />11
<br />551.70
<br />26.50
<br />18
<br />907.49
<br />71.42
<br />10
<br />208.43
<br />3.79
<br />10
<br />560.11
<br />27.31
<br />10
<br />916,03-
<br />72.76
<br />20
<br />216.77
<br />4.10
<br />20
<br />568.53
<br />28.14
<br />20
<br />924.58
<br />74.12
<br />30
<br />225.12
<br />4.42
<br />30
<br />576.95
<br />28.97
<br />30
<br />933.13
<br />75.49
<br />40
<br />233.47
<br />4.76
<br />40
<br />5S5.36
<br />29.82
<br />40
<br />941.69
<br />76.86
<br />50
<br />241.81
<br />5.10
<br />50
<br />593.79
<br />30.68
<br />50
<br />950.25
<br />78.26
<br />5
<br />250.16
<br />5.46
<br />12
<br />602.21"
<br />31.56
<br />' 19
<br />958.81
<br />79.67
<br />10
<br />258.51
<br />5.83
<br />10
<br />610.64
<br />.32.45
<br />10
<br />967.38
<br />81.09
<br />20
<br />266.86
<br />6.21
<br />20
<br />619.07
<br />33.35
<br />.20
<br />975.96
<br />82.53
<br />30
<br />275.21
<br />6.61
<br />30
<br />627.50
<br />_
<br />34.26
<br />30
<br />984.53
<br />83.97
<br />40
<br />283.57
<br />7.01
<br />40
<br />635.93
<br />35.18
<br />40
<br />993.12
<br />85.43
<br />50
<br />291.92
<br />7.43
<br />50
<br />644.37
<br />36.12
<br />50
<br />1001.7
<br />86,90
<br />6
<br />300.28
<br />7.86
<br />13
<br />652.81
<br />37.07
<br />20
<br />1010.3
<br />88.39
<br />10
<br />308.64
<br />8.31
<br />10
<br />661.25
<br />38.03
<br />10
<br />1018.9
<br />89.89
<br />20
<br />316.99
<br />8.76
<br />20 •
<br />669.70
<br />39.01
<br />20
<br />1027.5
<br />91.40
<br />30
<br />325.35
<br />9.23
<br />30
<br />678.15
<br />39.99
<br />30
<br />1036.1
<br />92,92
<br />40
<br />333.71
<br />9.71
<br />40
<br />686.60
<br />40.99
<br />40
<br />1044.7
<br />94.46
<br />b0
<br />342,08
<br />10.20
<br />50
<br />695.06
<br />42.00
<br />50
<br />1053.3
<br />96,01
<br />7
<br />350.44.
<br />10.71
<br />14
<br />703.51
<br />43.03
<br />21
<br />1061.9
<br />97.57
<br />10
<br />358,81
<br />11,22
<br />10
<br />711.97
<br />" 44.07
<br />10
<br />1070.6
<br />99.16
<br />20
<br />367.17
<br />11.75
<br />20
<br />720.44
<br />-45.12
<br />20
<br />1079.2
<br />100.75
<br />30
<br />'375.54
<br />12.29
<br />30'
<br />728.90
<br />46.18
<br />30
<br />1087.8
<br />102.35
<br />40
<br />383.91
<br />12.85'
<br />40
<br />737,37.
<br />47.25
<br />40-
<br />1096.4
<br />103.97
<br />50
<br />392.28
<br />13.41
<br />50
<br />745.85
<br />48.34
<br />50
<br />1105.1
<br />105.60
<br />Corrections'to be Added (T =Tangent. E =External:)
<br />Angle &,rve 5°
<br />10° 15° 20°
<br />25° 30°
<br />1 30
<br />1 40°
<br />45°
<br />50°
<br />55°
<br />1 60°
<br />1 65°
<br />70°
<br />5o' T=.02
<br />.03 .05 .06
<br />.08.10
<br />.11
<br />-13
<br />.15
<br />.16
<br />.18
<br />.20
<br />.21
<br />.23
<br />E=.000
<br />.000 .001 .001
<br />.002 •002
<br />.002
<br />.003
<br />.003
<br />.004
<br />.004
<br />'.004
<br />:005
<br />•005
<br />Io* T =.03
<br />.06 .09 .13
<br />.16 .19
<br />.22
<br />.25'
<br />.28
<br />;.31
<br />.34
<br />.38
<br />.42
<br />•48
<br />E =.001
<br />.003 .004 ,.006
<br />.007 .008
<br />.009
<br />.011
<br />.012
<br />.014
<br />.015
<br />.017
<br />.018
<br />.020
<br />15o T=.04
<br />.10 .14 .19
<br />.24 .29
<br />.34
<br />.39
<br />.45
<br />.51
<br />.53
<br />.58
<br />.63
<br />•68
<br />E=.003
<br />.007 .010 .014
<br />'.018 .023
<br />.027
<br />.029
<br />.032
<br />.035
<br />'.039
<br />.043
<br />.047
<br />.051
<br />20° T=•O6
<br />.13 .19 .26L.028
<br />.39
<br />.45
<br />.51
<br />.58
<br />.65
<br />..72'
<br />.,.79
<br />.84
<br />•�
<br />E =.006
<br />.011 .017 .02
<br />.034
<br />.038
<br />.045
<br />.051
<br />.057
<br />'.003
<br />.070
<br />.076
<br />'•025o
<br />T=.08
<br />.16 .24 .33
<br />.49
<br />.58
<br />.67
<br />.75
<br />.83'
<br />.90E=.009
<br />321.1
<br />40
<br />1200.5
<br />124.41
<br />.018 .027 .03
<br />.056
<br />.065
<br />.074
<br />.083
<br />.093
<br />.108
<br />.120
<br />.127
<br />135
<br />i
<br />TABLE L - Tangents and Externals to a 1° Curve.
<br />Chord=100 ft.
<br />Int'"
<br />':.Angle
<br />Tangent
<br />External
<br />Int.
<br />Angle
<br />T ent
<br />an8
<br />External
<br />Int.
<br />Angle
<br />Tangent
<br />g
<br />External
<br />22_°"- '.1113.7
<br />107.24
<br />29°
<br />1481.8
<br />188.51
<br />361
<br />1861.7
<br />294.9
<br />10!
<br />1122.4
<br />108.90
<br />10'
<br />1490.7
<br />190.74
<br />10'
<br />1870.9
<br />297.7
<br />20
<br />1131.0
<br />110.57
<br />20
<br />1499.6
<br />192.99
<br />20
<br />1880.1
<br />300.6
<br />30
<br />1139.7
<br />112.25
<br />30
<br />1508.5`
<br />195.25
<br />30
<br />1889.4
<br />303.5
<br />40
<br />1148.4
<br />113.95
<br />40
<br />1517:4
<br />197.53
<br />40
<br />1898.6
<br />306.4
<br />50
<br />1157.0
<br />115.66
<br />, 50
<br />1526.3
<br />199.82
<br />50
<br />1907.9
<br />309.3
<br />.036
<br />'.046
<br />.056
<br />.065
<br />.074
<br />.083
<br />-.093
<br />.106
<br />:120 .127 .135
<br />23
<br />- 1165.7
<br />117.38
<br />30
<br />1535.3:
<br />202.12
<br />37
<br />1917.1
<br />312.2
<br />10
<br />1174.4
<br />119.12
<br />10
<br />1544.2
<br />204.44
<br />10
<br />1926.4
<br />315.2
<br />20
<br />1183.1
<br />120.87
<br />20
<br />1553.1
<br />206.77
<br />20
<br />1935.7
<br />318.1*
<br />.30'
<br />1191.8
<br />122.63
<br />30
<br />1562.1
<br />209.12
<br />30
<br />1945,0
<br />321.1
<br />40
<br />1200.5
<br />124.41
<br />40
<br />1571.0
<br />211.48
<br />40
<br />1954,3
<br />324.1
<br />50
<br />1209.2
<br />126.20
<br />50
<br />1580.0
<br />213.86
<br />50
<br />1963,6
<br />327.1
<br />24
<br />1217.9
<br />128.00
<br />31
<br />1589.0
<br />216.3
<br />38
<br />1972,9
<br />330.2
<br />10
<br />1226.6
<br />129.82
<br />10
<br />1598.0
<br />218.7
<br />10
<br />1982,2
<br />333:2
<br />20
<br />1235.3
<br />131 65
<br />20
<br />1606.9
<br />221.1
<br />20
<br />1991,5
<br />336,3
<br />f' 30
<br />1244.0
<br />133.50
<br />30
<br />1615.9
<br />223.5
<br />30
<br />2000.9
<br />339.3
<br />40
<br />1252.8
<br />135.35
<br />40
<br />1624.9
<br />226.0
<br />40
<br />2010,2
<br />342.4
<br />50
<br />1261.5
<br />137.23
<br />50
<br />1633.9
<br />228.4
<br />50
<br />2019,6
<br />345.5
<br />251270.2
<br />139.11
<br />32
<br />1643.0
<br />230.9
<br />39
<br />2029,0
<br />348.6
<br />10
<br />1279.0
<br />141.01
<br />10
<br />1652.0
<br />233.4
<br />10
<br />2038,4
<br />351,8
<br />20
<br />1287.7
<br />142.93
<br />20
<br />1661.0
<br />235.9
<br />20
<br />2047.8
<br />354.9
<br />30
<br />1296.5
<br />144.85
<br />30
<br />1670.0
<br />238.4
<br />30
<br />2057,2
<br />358.1
<br />40
<br />1305.3
<br />146.79
<br />40
<br />1679.1
<br />241.0
<br />40
<br />2066.6
<br />361.3
<br />50
<br />1314,0
<br />148.75
<br />50
<br />1688.1
<br />243.5
<br />50
<br />2076.0
<br />364.5
<br />26
<br />1322.8
<br />150.71
<br />33
<br />1697.2
<br />246.1
<br />40
<br />2085.4
<br />367.7
<br />10
<br />1331.6
<br />152.69
<br />10
<br />1706.3
<br />248.7
<br />10
<br />2094,9
<br />371.0
<br />20
<br />1340.4
<br />154.69
<br />20
<br />1715.3
<br />251.3
<br />20
<br />2104,3
<br />374.2
<br />30
<br />1349.2
<br />156.70
<br />30
<br />1724.4
<br />253.9
<br />30
<br />2113.8
<br />377.5
<br />40
<br />1358.0
<br />158.72
<br />40
<br />1733.5
<br />256.5
<br />40
<br />2123,3
<br />380.8
<br />50
<br />1366.8
<br />160.76
<br />50
<br />1742.6
<br />259.1
<br />50
<br />2132.7
<br />384.1
<br />27
<br />.1375.6
<br />162.81
<br />34
<br />1751.7
<br />261.8
<br />41
<br />2142.2'
<br />387.4
<br />10
<br />1384.4
<br />164:86
<br />10
<br />1760.8
<br />264.5
<br />- 10
<br />2151.7
<br />390.7
<br />20
<br />1393.2
<br />166.95
<br />20
<br />1770.0
<br />267.2
<br />'20
<br />2161,2
<br />394.1
<br />30
<br />1402.0
<br />169.04
<br />30
<br />1779.1
<br />269.9
<br />30
<br />2170.8
<br />397.4
<br />40
<br />1410.9
<br />171.15
<br />40
<br />1788.2
<br />272.6
<br />40
<br />2180.3
<br />400.8
<br />50
<br />'1419.7
<br />173.27
<br />.50.
<br />1797.4.
<br />275.3
<br />50 '
<br />2189.9
<br />404.2
<br />28
<br />1428.6
<br />175.41
<br />35
<br />1806.6
<br />278.1
<br />42
<br />.2199.4
<br />407.6
<br />10
<br />1437.4
<br />177.55
<br />.10
<br />1815.7
<br />280.8
<br />10
<br />2209,0
<br />411.1
<br />20
<br />1446.3
<br />179.72
<br />20
<br />1824.9
<br />283.6
<br />20
<br />2218.6
<br />414.5
<br />30
<br />,1455.1
<br />181.89
<br />30
<br />1834.1
<br />286.4
<br />30
<br />2228.1
<br />418.0
<br />40
<br />1464.0
<br />184.08
<br />40
<br />1843.3
<br />289.2
<br />40
<br />2237,7
<br />421.4
<br />50.
<br />1472.9
<br />186.29
<br />50
<br />1852.5
<br />292.0
<br />50
<br />2247.3
<br />425.0
<br />Corrections to be Added (T =Tangent. E = External.)
<br />dnt:
<br />o,
<br />Angle Curve5o,
<br />10°
<br />15 o
<br />0
<br />20
<br />25 0
<br />30 0
<br />35°
<br />40 0
<br />45°
<br />50 o
<br />0
<br />55
<br />0 0
<br />60 65 700
<br />'too T=.06
<br />.13
<br />.19
<br />.28
<br />- .32
<br />.39-.
<br />.45
<br />.51
<br />58
<br />.65 "
<br />.72
<br />.79 $4 .90
<br />E=.000
<br />.011
<br />.017
<br />.022
<br />.028
<br />.034
<br />...038
<br />.045
<br />.051
<br />.057
<br />.063
<br />•.070 .076 .083
<br />25° T=.08
<br />.16
<br />.24
<br />.33
<br />.40
<br />.49
<br />.58
<br />.67
<br />.75
<br />.83
<br />:90
<br />.99 1.06" 1.14
<br />E =.009
<br />018
<br />.027
<br />.036
<br />'.046
<br />.056
<br />.065
<br />.074
<br />.083
<br />-.093
<br />.106
<br />:120 .127 .135
<br />30° T=10
<br />.10
<br />.29
<br />.39
<br />.49
<br />.59
<br />.69
<br />.79
<br />.89
<br />.99
<br />1.09
<br />1.20 1.29 1.39
<br />E=.013
<br />.025
<br />.038
<br />.051
<br />.065
<br />.078
<br />.090
<br />.103
<br />.116
<br />.129
<br />.149
<br />.170 .179 .188
<br />35° T=.11
<br />.22
<br />.34
<br />.47
<br />.58
<br />.69.80
<br />.93
<br />1.05
<br />1.17
<br />1.29
<br />1.42 1.54 1.68
<br />. E =.018
<br />.035
<br />.054
<br />.072
<br />.086
<br />.109
<br />.131
<br />.153
<br />.175
<br />.197
<br />.213
<br />.230 ".247 .264
<br />406, T=.13
<br />.26
<br />.40
<br />.53
<br />.67
<br />.80
<br />.93
<br />1.06
<br />1.20
<br />1.34
<br />1.49
<br />1.64 1.79 1.94
<br />E =.023
<br />.046
<br />.070
<br />.093
<br />.117
<br />.141
<br />.172
<br />.203
<br />.234
<br />.265
<br />.277
<br />.290 .315 .341
<br />45°, T=,15
<br />.30
<br />.44
<br />.60
<br />.76
<br />.91
<br />1.06
<br />1.21
<br />1.37
<br />1.52
<br />1.70
<br />1.87 2.04 2.21
<br />- E=.030
<br />.060
<br />.093
<br />.119
<br />.153
<br />.184'
<br />.216
<br />.254
<br />.289
<br />.325
<br />.351
<br />.378 .411 •445
<br />0
<br />0
<br />
|