|
e
<br />El
<br />II TABLE I. - Tangents -and Externals to a 1° Curve?
<br />Chord =-100 ft.
<br />Angle
<br />Tangent
<br />External,
<br />A gle
<br />Tangent
<br />Exler,ial
<br />AngI6 ',
<br />Tangent
<br />External
<br />1"
<br />50.00
<br />•:22
<br />S'
<br />400.G6
<br />13.99
<br />15"
<br />754.32
<br />49:44
<br />10'
<br />53.34
<br />.30
<br />]0'
<br />409.03
<br />14.58
<br />10'
<br />762.80
<br />50.55
<br />20
<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 />.,49
<br />30'
<br />425.79
<br />15.8U
<br />30
<br />779.77
<br />52.52
<br />40
<br />83.34
<br />G1
<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 />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 />1.30
<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 />141.70
<br />1.75
<br />50
<br />492.88
<br />21.16
<br />50
<br />847.78
<br />62.38
<br />3
<br />1,0.04
<br />1.96
<br />10
<br />'501.28
<br />21.80
<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 />8G4.82
<br />64.90
<br />20
<br />1GG:72
<br />2.43
<br />20
<br />518.OS
<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 />=' 24.01
<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 />3.70 '
<br />110
<br />560.11
<br />27.31
<br />10
<br />•916.03
<br />72.7G
<br />•20
<br />216.77
<br />4,1020
<br />20
<br />568.53
<br />28.14
<br />20
<br />924.68
<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 />- i 40
<br />585.36
<br />29.82
<br />40
<br />941.69
<br />76.86
<br />'.5U
<br />241:81
<br />5.10
<br />/ 50
<br />593.79
<br />30.68
<br />50
<br />950.25
<br />78.2G.
<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 />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 />619.01
<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 />34.26
<br />30
<br />984.53
<br />83,97
<br />40
<br />233.57
<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 />30q. f8
<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 />G8G,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. OU
<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 />'338.81
<br />11.22
<br />10
<br />711.97
<br />44.07
<br />10
<br />1070.6
<br />99.16
<br />.
<br />20
<br />,367.17
<br />11.75
<br />20
<br />720.44
<br />45.12
<br />20
<br />1079.2
<br />100.7-55
<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 />1 392.28
<br />13.41
<br />50
<br />745,85
<br />48.34
<br />1 50
<br />1105.1
<br />105, GO
<br />Corrections to be Added- (T =Tangent. E=External.)
<br />Int, Curve 5°
<br />.Angle50
<br />10°
<br />15°
<br />20° 25°
<br />30°
<br />35°
<br />40°
<br />45°
<br />SV
<br />55°
<br />4113:7
<br />70°
<br />T=.02
<br />.03
<br />.05
<br />.06 .08
<br />.10
<br />.11 '
<br />.13
<br />.15
<br />.16
<br />.I8
<br />.21
<br />.23
<br />E=.000
<br />.000
<br />.001
<br />.001 .002
<br />.002
<br />.002
<br />.003
<br />.003
<br />.004
<br />]60*65°
<br />.004
<br />.005
<br />.005_o
<br />T=.03
<br />.08
<br />.09
<br />13 -.18
<br />.19
<br />.22
<br />25
<br />2B
<br />31
<br />34
<br />.d2
<br />'.4630
<br />E=.001
<br />.003
<br />.004
<br />008 .007
<br />,008
<br />.009
<br />All
<br />.012
<br />.014
<br />.015
<br />.018
<br />.020
<br />15oT=.04
<br />.10
<br />.14
<br />19 .24
<br />.29
<br />:34
<br />39
<br />.45
<br />.51
<br />,.53
<br />.83
<br />.68
<br />E=.003
<br />.007
<br />.010
<br />.014 .018
<br />.023
<br />.027
<br />d129
<br />.032
<br />.035.039
<br />20
<br />M7
<br />'.051_
<br />20° T=.06 .
<br />'.13
<br />84
<br />.90
<br />'.083
<br />.19
<br />.26 .32
<br />..39
<br />.45
<br />51
<br />.58
<br />.65
<br />.72 ".79
<br />E=.006
<br />.011_
<br />.017
<br />.022 .028
<br />.034
<br />.038
<br />.045
<br />.051
<br />.057
<br />.063 .070
<br />.07G
<br />324.1
<br />250 T=.08 f
<br />:I6
<br />.Z4
<br />33 .40
<br />.49
<br />..58
<br />1.08
<br />1.14
<br />87
<br />.75
<br />.83
<br />.90 .99
<br />E =.009
<br />.018
<br />.027
<br />.038 .048
<br />.056
<br />.085
<br />A74
<br />.083
<br />'.093
<br />.108 .120
<br />.127
<br />.135
<br />Znlii.>•: L`y Tangents iifid Externals to a 1' Curve. III
<br />Chord =100 f L.
<br />Int..,
<br />Angie`_
<br />Tatlkcnt
<br />IExte_rnal
<br />_ •
<br />.Angle ,1
<br />Tangent
<br />'External
<br />Int.
<br />Angle
<br />Tangent
<br />External
<br />45°
<br />4113:7
<br />107.24
<br />X29°
<br />1481.8
<br />188.51
<br />3G°
<br />1861.7
<br />294.9
<br />101
<br />11'='.•4
<br />108.90
<br />10'
<br />1490.7
<br />190.74
<br />10'
<br />1870:9
<br />297,7
<br />'2U
<br />1131.0
<br />110.57--
<br />` 20
<br />1409.6
<br />192.99
<br />20
<br />1880.1
<br />300.6
<br />•• 3U
<br />1139.7
<br />112.23
<br />30
<br />150S.5
<br />195.25
<br />30
<br />1889.4
<br />303.5
<br />414
<br />1148.4
<br />113.95
<br />40
<br />1517.4
<br />,197.53
<br />40
<br />1898.0
<br />306.4,
<br />`50
<br />1157.0
<br />115.60
<br />50
<br />1526.3
<br />199.82
<br />.50
<br />1907.9
<br />309.3
<br />23-
<br />1165:7
<br />117.33
<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 />5O
<br />1209,2
<br />126.20
<br />50
<br />1580.0
<br />213.86
<br />50
<br />1963.G
<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 />30
<br />1244.0
<br />133.50
<br />30
<br />1615.9
<br />223.5
<br />30
<br />2000.9
<br />339.3
<br />•10
<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 />1G33:9
<br />228.4
<br />50
<br />2019.G.
<br />345.5
<br />25
<br />1270.2
<br />139.11
<br />82
<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 />2U
<br />1287.7
<br />142.93
<br />20
<br />1661.0
<br />235.9
<br />20
<br />2047.8
<br />354.9
<br />3U
<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.G
<br />259.1
<br />50
<br />2132.7
<br />384,1
<br />27
<br />1375,6
<br />102.81
<br />34
<br />1751.7
<br />261".8
<br />41
<br />2142.2
<br />387,4
<br />90
<br />1334.4
<br />104.86
<br />10
<br />1760.8
<br />264.5
<br />10
<br />.2151'7,
<br />390,7
<br />20
<br />1393.2
<br />166195
<br />20
<br />1770. 0
<br />'267,2
<br />20
<br />210t: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 />85
<br />1800.6
<br />278.1
<br />42
<br />2199.4
<br />407.0
<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 />lot.
<br />Angle
<br />`200
<br />Curve S°
<br />10°
<br />15°
<br />20°
<br />25°
<br />30°
<br />35°
<br />40°
<br />45°
<br />50° 1 55°
<br />60°
<br />65°
<br />70°
<br />T=.06
<br />.13
<br />.10
<br />.28
<br />.32
<br />.39
<br />.45
<br />.51
<br />.58
<br />.65 .72
<br />.79
<br />.84
<br />.90
<br />E=.006
<br />.011
<br />.017
<br />.022
<br />.028
<br />,034
<br />,038
<br />.045
<br />.051
<br />.0571 .003
<br />.070
<br />.076
<br />,083
<br />-25°
<br />T=.OA
<br />.16
<br />.24
<br />.33
<br />,40
<br />.49
<br />.58
<br />.67
<br />.75
<br />.83- 90
<br />.99
<br />1.06
<br />1.14
<br />E =:009
<br />.018
<br />.027
<br />.03G
<br />.046
<br />.056
<br />.005
<br />.074
<br />,033
<br />.093 .106
<br />.120
<br />.127
<br />.135
<br />30°
<br />T=.10
<br />,1D
<br />.29
<br />,39
<br />A9
<br />.59
<br />.6979
<br />.E9
<br />99 1.09
<br />1.00
<br />1.29
<br />.39
<br />-
<br />E =.013
<br />.025
<br />.038
<br />.051
<br />.OG5
<br />.078
<br />,090
<br />,103
<br />.110
<br />.1291 .149
<br />,170
<br />,1791
<br />.188
<br />35°
<br />T =.11
<br />.22
<br />.34
<br />.47
<br />53
<br />.69
<br />SO
<br />.03
<br />1.05
<br />1.17 1,29
<br />1.42
<br />1.54
<br />1.66
<br />E=.019
<br />.035
<br />.054
<br />.072
<br />.086
<br />.1091
<br />.131
<br />.153
<br />.175
<br />.107 .213
<br />230
<br />.247
<br />.264
<br />40°
<br />T=.13
<br />^6
<br />.40
<br />.53
<br />.67
<br />,80
<br />.93
<br />1.06
<br />1.20
<br />1.34 1.49
<br />1.64
<br />1.79
<br />1,94
<br />F.=.023
<br />T=•15
<br />.046
<br />3D
<br />.070
<br />.44
<br />.093
<br />.GO
<br />.117
<br />.141
<br />I .172
<br />.203
<br />.234
<br />205 -.217
<br />.290
<br />.315
<br />,341
<br />45°
<br />.76,
<br />.91
<br />1 21
<br />1.37
<br />1.52 1.70
<br />1.87
<br />2.04
<br />2,21
<br />E =.030
<br />OGO
<br />.093
<br />.119
<br />.153
<br />.184
<br />11.08
<br />.216
<br />.254
<br />.289
<br />.325 .351
<br />.378
<br />.411
<br />.445
<br />b
<br />
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