|
II TABLE 1. - Tangents and Externals to a V Curve.
<br />Chord =100 It.
<br />Angle
<br />Tangent
<br />External
<br />Angle
<br />Tangent
<br />External
<br />Angle
<br />Tangent
<br />Axternal
<br />A.
<br />50.00'
<br />.22
<br />S"
<br />400.66
<br />13.09
<br />15'
<br />754.32
<br />49.44
<br />10'
<br />53.34
<br />.30
<br />10'
<br />409,03
<br />14.58
<br />10'
<br />702,80
<br />50.5
<br />ZO
<br />06:67
<br />.39
<br />20
<br />417.41
<br />15.18
<br />20
<br />771.29
<br />.51.68
<br />30
<br />75.01
<br />.40-
<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 />60
<br />- 91.68
<br />.73
<br />50
<br />442.55
<br />17.07
<br />50.'
<br />796.75
<br />55.13
<br />2-
<br />100.01
<br />S7
<br />9
<br />450:93
<br />17.72
<br />16.
<br />805.25
<br />50.31
<br />10
<br />108.35
<br />1.02
<br />10
<br />459.32
<br />18.38
<br />14
<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 />^0.
<br />125.02
<br />1.36
<br />30
<br />476.10
<br />19,75
<br />30
<br />830.76
<br />50.91
<br />40.
<br />133.3G
<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 />1.42
<br />1.54
<br />1.96
<br />10
<br />501.28
<br />21.89
<br />17
<br />856.30
<br />03.63
<br />10
<br />158.38
<br />2.19
<br />10
<br />509.68
<br />22.62
<br />10
<br />834.82
<br />64.90
<br />10
<br />1G6.72
<br />2.43
<br />20
<br />518.08
<br />23.38
<br />20
<br />873.35
<br />60.18
<br />30't'-175.00
<br />1235.3
<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 />119/
<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 />27.81
<br />10
<br />916.03
<br />72.7G
<br />20
<br />216.77
<br />4.10
<br />J 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 />28.07
<br />30
<br />933.13
<br />75.49
<br />40
<br />233.47
<br />4.76
<br />40
<br />585.36
<br />29.82
<br />40
<br />941.69
<br />76.86
<br />-50
<br />24 1. 81
<br />5.10
<br />50
<br />593.79
<br />30.68
<br />50
<br />950.25
<br />78.26
<br />5
<br />250.10
<br />5.46
<br />12
<br />602.21
<br />31,56
<br />19
<br />958.81
<br />79. G7,
<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 />260.8G
<br />6.21
<br />20
<br />619,07
<br />33.85
<br />20
<br />975.96
<br />82.53
<br />30
<br />275.21
<br />6.61
<br />30
<br />027.50
<br />34.26
<br />30
<br />984.53
<br />83,07
<br />40
<br />283.57
<br />7.,01
<br />40
<br />035.03
<br />35.18
<br />40
<br />993.12
<br />85.43
<br />69
<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 />30q.28
<br />7.86
<br />1.3
<br />G52.81
<br />37.07
<br />20
<br />1010.3
<br />8S.39•
<br />10
<br />308.64
<br />8.31
<br />10
<br />GGI.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 />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 />703.61
<br />43.03
<br />21.•-
<br />1061:0,
<br />97.57
<br />l0
<br />358.81
<br />11.22
<br />10
<br />711.97
<br />. 44.07
<br />10
<br />1070.6
<br />09.16
<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 />333.91
<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 />105.00
<br />Corrections -to be Added (T =Tangent. E=External.)
<br />Int,
<br />tingle
<br />Curve 50.
<br />10° 15° 2Q°
<br />25°
<br />30°
<br />351 40°
<br />45° W. 55° 1 60?
<br />60
<br />70°.'
<br />6°
<br />T=.02
<br />.03 .05 .06
<br />08
<br />I0
<br />.11 .13
<br />.15 .16.IB '.20
<br />.21
<br />23
<br />101
<br />E-.000
<br />.000..001 .001
<br />.002
<br />X02
<br />_.002 .003
<br />.003 .004 .004 .004
<br />.005
<br />,005
<br />1p°
<br />=.03
<br />.06 .09 .13
<br />.10
<br />'.007
<br />10
<br />.22 .25
<br />28 .31 .34 38
<br />. 2
<br />-AC
<br />�'.;iU
<br />E-.001
<br />•003 :004 .006
<br />30
<br />.008
<br />.009 .011
<br />,012 .014 .0I5 .017
<br />'.018
<br />'.020
<br />15°
<br />T =,04
<br />.10 14 .19
<br />24
<br />29
<br />:34' 99
<br />.45 .51 .53 .58
<br />.63
<br />.68
<br />5U
<br />E=.003
<br />1.007 .010 .014
<br />_018
<br />.32
<br />.023
<br />.39
<br />,027 .029
<br />.45 .61
<br />.032 .035 .039 .043
<br />.58 .0 .72 .79
<br />.047
<br />.84
<br />.051
<br />.90
<br />20° T= Op
<br />1.13 10 .26
<br />117.38
<br />E=:000
<br />'.011 .017 .022
<br />.028
<br />_034
<br />.038 .045
<br />.051 .057 :063 .070
<br />.076
<br />.083
<br />25°
<br />T=,08
<br />16 .24 .33
<br />.4Q
<br />49
<br />.58 .67
<br />.75 .83 .90 .99
<br />1.06
<br />1:14
<br />120.87
<br />E =.009
<br />.018 .027 .036
<br />.046
<br />.056
<br />.065 .074
<br />.083 .093 .1Q6 .120
<br />.127
<br />.135
<br />SGS
<br />T,61,i I. - Tangents and Externals to a 1° Curve. III
<br />Chord =100 f t,
<br />Int.,-
<br />Anglo
<br />Tangent
<br />External
<br />lilt.
<br />A�lsle
<br />Tangent
<br />External
<br />Int.
<br />Arigle,
<br />Tangent
<br />External
<br />22°
<br />1113.7
<br />107,24
<br />29°
<br />1481.8
<br />188.51
<br />36°
<br />1861.7
<br />294.0
<br />101
<br />1.122.4
<br />108.00
<br />40'
<br />1490.7
<br />190.74
<br />10'
<br />1870.9
<br />297.7
<br />:2U'
<br />11:1 L.0
<br />110.57
<br />2U
<br />1499:0
<br />192.99
<br />20
<br />1880.1
<br />300.5
<br />�'.;iU
<br />,1139.7
<br />112.25
<br />30
<br />1508.5
<br />195.25
<br />- 30
<br />1389.4
<br />303.5
<br />40'
<br />1148.'4
<br />113.95
<br />40
<br />1517.4
<br />107.53
<br />40
<br />1998.6
<br />305.4
<br />5U
<br />•1157.0
<br />115.06
<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 />2p
<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 />1.42
<br />1.54
<br />1.60
<br />E =-018
<br />.035
<br />.054
<br />.072
<br />.086
<br />2!
<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 />3Q
<br />124440
<br />133.50
<br />30
<br />1615.0
<br />223.5
<br />30
<br />2000.9
<br />339.3
<br />4U
<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 />343.6
<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 />_
<br />146,79
<br />_
<br />-40 _
<br />1679.1
<br />241.0
<br />40
<br />2066.6
<br />301.3
<br />50
<br />1314.0
<br />148.175
<br />50
<br />1G88.1
<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 />170G.3
<br />24S.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.G
<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 />$87.4
<br />16
<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 />269.0
<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 />3,5
<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 •`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 />-14G4.0
<br />184.08
<br />40
<br />1843.3
<br />289.2
<br />40
<br />2237.7
<br />50
<br />1472.9
<br />186.29
<br />30
<br />1852.5
<br />292.0
<br />50
<br />2247.3
<br />_421.4
<br />425.0
<br />Corrections to be.Added,(T=Tangent. E=External.)
<br />Int.
<br />Angle
<br />Curye 5°
<br />10°
<br />15°
<br />20 °
<br />25°
<br />30 °
<br />35 °
<br />40 °
<br />45 °
<br />-
<br />50°
<br />1 55°
<br />60°
<br />65°
<br />70°
<br />�26°
<br />T=.06
<br />.13
<br />.19
<br />:26
<br />'.32
<br />.30
<br />.45
<br />.51
<br />.58
<br />.65
<br />.72
<br />.79
<br />.$4
<br />.90
<br />E =.006
<br />.011
<br />.017
<br />.022
<br />.028
<br />.034
<br />.038
<br />.045
<br />.051
<br />.057
<br />.053
<br />.070
<br />.076
<br />.083
<br />25°
<br />T=.08
<br />.16
<br />.24
<br />.33
<br />.40
<br />• .49
<br />-.58
<br />.67
<br />.75
<br />.83
<br />.90
<br />.99
<br />1 06
<br />1.14
<br />E.6,091
<br />.018
<br />.027
<br />.036
<br />.016
<br />.050
<br />.055
<br />.074
<br />.083
<br />.093
<br />.106
<br />.120
<br />.127
<br />.135
<br />30*
<br />T-.10
<br />.19
<br />.29
<br />.39
<br />.49
<br />.59
<br />.69
<br />.79
<br />.89
<br />.99
<br />1.09
<br />L20-,
<br />1.29
<br />1.39
<br />E =.013
<br />.025
<br />.038
<br />.051
<br />.065
<br />.078
<br />.090
<br />.103
<br />.115
<br />.129
<br />.149
<br />.170
<br />.179
<br />.188
<br />35°
<br />=,I1
<br />.22
<br />.34
<br />A7
<br />58
<br />-.59
<br />.80
<br />.93
<br />1.05
<br />1.17
<br />1.29
<br />1.42
<br />1.54
<br />1.60
<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
<br />.247
<br />.264
<br />Opo
<br />T=.13
<br />.26
<br />A0
<br />.53
<br />.67
<br />.80
<br />.93
<br />1.06
<br />1.20
<br />1.34
<br />1.49
<br />1.64
<br />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 />205
<br />.217
<br />.290
<br />.315
<br />.34I
<br />45°
<br />T�.15
<br />.30
<br />.44
<br />.60
<br />.7fi
<br />.91
<br />1.06
<br />1.21
<br />I.37
<br />1.52
<br />1.70
<br />1.87
<br />2.04
<br />2.21
<br />E =.030
<br />GBO
<br />.093
<br />.219
<br />.153
<br />.184
<br />.216 254
<br />.289
<br />.325
<br />.351
<br />378
<br />.411
<br />.445
<br />
|