|
13
<br />II TABLE I. - Tangents and Externals to a V Curve.
<br />Chord =100 ft.
<br />Int.In
<br />Angle
<br />Tangent
<br />External
<br />^
<br />: Anglt. e ,
<br />Tangent
<br />Exteinal
<br />Int.
<br />Angle
<br />Tangent
<br />External
<br />10
<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 />101
<br />409.03
<br />14,58
<br />10'
<br />762.80
<br />50,55
<br />2066.67
<br />.000
<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 />50
<br />442.55
<br />17,07
<br />_50.
<br />796.75
<br />55..13
<br />E..
<br />.100.01
<br />.87
<br />9
<br />450:93.
<br />17:72•.16
<br />.19 .24
<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_•;116'.68
<br />.014 .018
<br />- :1.19-
<br />20
<br />467.71
<br />19.06
<br />.20
<br />:822:25'
<br />9'58.70
<br />30 -
<br />125.02
<br />. ` 1.36
<br />`_ --.30 '.
<br />476:10"
<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 />.045
<br />•,
<br />1.75'
<br />-
<br />'50
<br />492:88
<br />21.16
<br />50"
<br />78
<br />" 62.38
<br />T=.08
<br />,141:70
<br />.24
<br />' .33 .40
<br />.49 .58
<br />.67
<br />.75
<br />.847
<br />.90
<br />8
<br />150,04
<br />1.96
<br />10,
<br />501:28
<br />•;21.89
<br />-17
<br />856.30'
<br />'63.63 .
<br />10`"'458.38
<br />.083
<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 />38
<br />20 r-873.35'
<br />2000:9
<br />66.18 ,
<br />'-67.47
<br />30
<br />175.06
<br />2.67
<br />30
<br />526.48.
<br />.,23
<br />24,14
<br />30
<br />881.88
<br />342.4
<br />40
<br />183.40
<br />2.93
<br />40
<br />,
<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 />10
<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 />585.* 3629
<br />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 />201.
<br />:975.96
<br />82.53
<br />30
<br />275.21
<br />6.61
<br />30
<br />627.50.
<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 />.137.07
<br />"20,'
<br />1010.3
<br />88.39
<br />10
<br />308.64
<br />8.31
<br />10•661'.25
<br />1770.0
<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 />1 40.99
<br />40
<br />1044.7
<br />94.46
<br />50
<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 />'36717
<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 />105160
<br />Corrections to be Added (T = Tangent. ! E = External.) ,
<br />Int.
<br />Angle
<br />Curve 5°
<br />10°
<br />15°
<br />20° 256
<br />30°- 350
<br />40°
<br />45°
<br />50°
<br />55°
<br />1 60°
<br />65°
<br />70°
<br />5o
<br />T=.02
<br />.03
<br />.05
<br />.06 :08'"
<br />.10 ..11
<br />.13 ,
<br />.15
<br />.16
<br />.18
<br />.20
<br />.21
<br />.23
<br />297.7
<br />E=.000
<br />.000
<br />.001
<br />.001'. -'.002
<br />.002 - .002
<br />.003
<br />.00
<br />.004
<br />.004
<br />.004
<br />.005
<br />.005
<br />loo
<br />T=.03
<br />.06
<br />.09
<br />.13 .16
<br />.19 .22.
<br />.25
<br />--.28,
<br />,.31
<br />:34
<br />.38
<br />.42
<br />.46
<br />1898.6
<br />E=.001
<br />.003
<br />.004
<br />'.006 .007
<br />.008 .009
<br />.011
<br />.012
<br />.014
<br />.015
<br />.017
<br />.018
<br />.020
<br />117.38.
<br />T=.04
<br />.10
<br />':P4
<br />.19 .24
<br />.29 .34
<br />',39
<br />.45
<br />.51
<br />.53
<br />.58
<br />.63
<br />.68
<br />15°
<br />E =.003
<br />.007
<br />.010
<br />.014 .018
<br />.023 .027
<br />.029
<br />.032
<br />.035
<br />.039
<br />.043
<br />.047
<br />.051
<br />200T=.O6
<br />,13
<br />30
<br />.32
<br />.39 .45
<br />.51
<br />.58
<br />.65
<br />.72
<br />.79
<br />.84
<br />.90
<br />.1571.0
<br />E =.006
<br />,011
<br />.017
<br />.022 ..028
<br />.034 .038
<br />.045
<br />.051
<br />.057
<br />.063
<br />.070
<br />.076
<br />.083
<br />25o
<br />T=.08
<br />.16'
<br />.24
<br />' .33 .40
<br />.49 .58
<br />.67
<br />.75
<br />A3
<br />.90
<br />.99
<br />1.06
<br />1.14
<br />"`'10
<br />E =.009
<br />-018
<br />.027
<br />'.036 .046
<br />.056 .065
<br />.074
<br />.083
<br />.093
<br />.106
<br />.120
<br />.127
<br />.135
<br />T"LE L _ Tangents and -Externals of a 1° Curve.
<br />-Chord =100 f t.
<br />Int.
<br />Angle
<br />Tangent
<br />External
<br />Int.
<br />Angle
<br />Tangent
<br />External
<br />Int'
<br />Angle
<br />Tangent
<br />External
<br />220
<br />1113.7
<br />.107:24 ;
<br />290
<br />1481.8'
<br />188.51
<br />36°'
<br />1861.7
<br />294.9
<br />10f
<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 />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 i
<br />"`'10
<br />1598.0
<br />218.7
<br />10
<br />1982.2
<br />333.2
<br />20
<br />1235.3
<br />13165
<br />. 20
<br />1606.9
<br />221.1
<br />20
<br />1991:5
<br />336.3
<br />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 />..25 -
<br />1270.2•
<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 />101
<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 />60
<br />1688,1
<br />243.5
<br />50
<br />'2076.0
<br />" 364.5
<br />;.-261322.8
<br />150.71
<br />33 .
<br />1697.2
<br />246.1
<br />40
<br />2085.4
<br />367.7
<br />7 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 />.,3 90,7
<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 />'
<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 />1453.1
<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 />Int,
<br />Angle _
<br />Curve P
<br />10°
<br />15°
<br />20°
<br />250
<br />30°
<br />35°
<br />40°
<br />1 45°
<br />50°
<br />55°
<br />60° .65°
<br />'70°
<br />200
<br />T=:06
<br />.13
<br />.19
<br />.26
<br />.32
<br />.39.45
<br />.51
<br />.58
<br />.65
<br />.72
<br />.79 .84
<br />.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
<br />.083
<br />25°
<br />T=.08
<br />.16
<br />.24,
<br />.33
<br />.40.49
<br />.58
<br />.87
<br />.75
<br />.83
<br />.90
<br />.99 1.06
<br />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
<br />.135
<br />30°
<br />T�.10
<br />.19
<br />.29
<br />.39
<br />.49
<br />'.59
<br />.69.79
<br />.89
<br />.99
<br />1.09
<br />1.20 1.29
<br />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
<br />.188
<br />35°
<br />T=.11
<br />.22
<br />.34
<br />.47
<br />.. 8
<br />.69
<br />.80
<br />.93
<br />1.05
<br />1.17
<br />1.29
<br />1.42 1.54
<br />1.66
<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
<br />'.264
<br />40o
<br />T=13
<br />626
<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
<br />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
<br />.341
<br />45°
<br />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
<br />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
<br />.445
<br />
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