|
II TABLE I. - Tangents and Externals to a 1° Curve.
<br />,Chord =100, f t.
<br />Int.
<br />Angle
<br />Tangent
<br />External
<br />Ingle
<br />Angle
<br />Tangent
<br />fixten al
<br />✓Ink
<br />Angle
<br />Tangent
<br />External
<br />22°
<br />T=:02
<br />.03 .05
<br />.06- .08' .10-1
<br />-.11.
<br />.13' 1-.15.
<br />J
<br />.21
<br />23
<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 />" 301,
<br />' 101,
<br />409.01
<br />•, 14.58 4
<br />+ " 10'
<br />762.80
<br />50.55
<br />20
<br />66.67
<br />(--':39
<br />820'.
<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 />:-•60
<br />91:68
<br />-.73
<br />50
<br />"442:55'.
<br />`17:07'
<br />`50-
<br />796.75
<br />55.13
<br />T=.08
<br />.16 .24
<br />.33 .40 .49
<br />.58
<br />.87 .75 ,
<br />.83 .90 .99
<br />1.06
<br />1.14
<br />•.315.2
<br />2
<br />100.01
<br />'.S7
<br />'9 '
<br />450.93
<br />117:72-
<br />16 '' `
<br />.805.25
<br />.56.31'-
<br />10
<br />108.35
<br />1.02
<br />- 16
<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 />_�
<br />, 20
<br />822.25
<br />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 />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 />X856:30
<br />63.63
<br />10
<br />158.38
<br />2.19
<br />10
<br />509.68
<br />c 22,.62,'-10.:.864.82
<br />30
<br />2000.9
<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 />_
<br />5&5.36
<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 />266.8G
<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 />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 />300.29
<br />7.86
<br />13
<br />.652.81
<br />37.07
<br />•20""''
<br />1010.3
<br />88.39
<br />10
<br />1402.0
<br />8.31
<br />10
<br />.•661.25
<br />38.03-
<br />-10 ,
<br />1018.9'.
<br />89.89
<br />20
<br />.308.64
<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 />.703.51:•
<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 />105.60
<br />50
<br />392.28
<br />13.41,
<br />50
<br />745:85
<br />48.34•
<br />50
<br />1105.1
<br />Corrections to be Added-_(T=Tangent. E=External.)
<br />Int.Angle
<br />Curve 5°
<br />10° 150
<br />200 25� ' 30°,'
<br />35° •
<br />.400 45°
<br />50° 55° 600
<br />65°
<br />70°
<br />22°
<br />T=:02
<br />.03 .05
<br />.06- .08' .10-1
<br />-.11.
<br />.13' 1-.15.
<br />.16 .18 .20
<br />.21
<br />23
<br />5o
<br />E=.000
<br />:108.90'
<br />.001 .002 .002
<br />.002
<br />`:003 .,.003
<br />.004 .004 .004
<br />.005
<br />_005
<br />10°
<br />T=.03
<br />E=.001
<br />.000 .001
<br />.06 .09 .13 .16 .19
<br />.003 •.004 .006 .007 '`.008
<br />.22
<br />.009
<br />.25 .28-
<br />.011 .012
<br />.31 .34 8
<br />.014 .015 '.017
<br />.d2
<br />.018
<br />.46
<br />.020
<br />15°
<br />T=.04 -
<br />-.10 .14
<br />.19 .24 .29
<br />.34
<br />.39 .45
<br />.51 ' :53 .58
<br />.63
<br />.68
<br />303.5
<br />E =.003
<br />.007 -.010
<br />.014 .018 .023
<br />.027
<br />.029 .032
<br />.035 .039 x.043
<br />.047
<br />•051
<br />20o
<br />T=.06
<br />.13 .19
<br />.26 32 39
<br />.45
<br />.51 58 ,
<br />'.65 .72 .79
<br />.84
<br />•90
<br />309.3
<br />E=.006
<br />.011 .017
<br />.022 .028 .034
<br />.038
<br />.045 .051
<br />.057 .063 .070
<br />.016
<br />•0S
<br />25°
<br />T=.08
<br />.16 .24
<br />.33 .40 .49
<br />.58
<br />.87 .75 ,
<br />.83 .90 .99
<br />1.06
<br />1.14
<br />•.315.2
<br />E=.009
<br />.018 :027
<br />.038 .046 .056
<br />.065
<br />.074 .083
<br />.093 .106 :120
<br />.127
<br />.135
<br />4
<br />T"LiD I. = Tangents and Externals'to'A V Curve.' IhI
<br />Chord'=100 ft.
<br />Int;_
<br />Angle
<br />Tangent
<br />External
<br />Int.
<br />Angle
<br />Tangent
<br />External
<br />Int. _
<br />Angle .
<br />Tangent External
<br />22°
<br />1113.7
<br />-107.24
<br />-29°
<br />1481.8
<br />188.51'
<br />36°
<br />1861:7
<br />294.9
<br />101
<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 />31
<br />.1917.1
<br />. 312.2
<br />'10,,'1174.4;
<br />1.06
<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 1
<br />1553.1
<br />206.77 i
<br />;-20
<br />1935.7,
<br />1.318.1
<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 />213.48,
<br />-40
<br />1954.3
<br />324.1
<br />50
<br />1209.2
<br />126.20 !
<br />i
<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 1
<br />` " =10
<br />'.1982.2
<br />, 333.2
<br />20
<br />:1235.3
<br />131.65
<br />20
<br />1606:9
<br />221.1 r
<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 i
<br />40
<br />2010.2
<br />1342.4
<br />50 j
<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 p
<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 />.'.`,40
<br />'2057.2
<br />358.1
<br />40 •
<br />1305.3
<br />146.79 '
<br />40
<br />1670.1
<br />9
<br />241.0
<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 />1700.3
<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 />U.
<br />1751.7
<br />261.8
<br />41,
<br />'2142.2
<br />3874
<br />10
<br />.1384.4
<br />164.86
<br />10
<br />1760.8
<br />264.5
<br />10
<br />2151.7
<br />20
<br />1393.2
<br />166.95 .
<br />20
<br />1770:0
<br />267.2
<br />20
<br />2101.2
<br />(390.7
<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 />;t" 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 1
<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 />•
<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 />`14553;
<br />181.89
<br />'.30
<br />1834.1
<br />286.4
<br />30
<br />2228.1
<br />418.0
<br />40 '
<br />:7464.0.
<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 />188.29
<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 5'
<br />109
<br />15'
<br />20'
<br />25°
<br />30°
<br />35°
<br />40'
<br />45'
<br />50°
<br />554
<br />'60°
<br />65°,.700
<br />20°
<br />T=.06
<br />..13
<br />.19
<br />.26
<br />.32
<br />.39
<br />.45
<br />.51
<br />.58
<br />.65
<br />.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 />.057
<br />.063
<br />-,.070
<br />.076
<br />.083
<br />256
<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=.0 09
<br />=.009
<br />.018
<br />.027
<br />.036
<br />.046
<br />.056
<br />:065
<br />.074
<br />.083
<br />.093
<br />.106
<br />.120
<br />.127
<br />.135
<br />30°
<br />T=.1
<br />.19
<br />.29
<br />.39
<br />.40
<br />.59
<br />.69
<br />.79
<br />.89
<br />:99
<br />1.09
<br />1.20
<br />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
<br />.179
<br />.180
<br />35° •
<br />T=.11
<br />.22
<br />.34
<br />.47
<br />.58
<br />.69
<br />..80
<br />.93
<br />1.05
<br />1.17
<br />1.29
<br />1.42
<br />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
<br />•247
<br />,.264
<br />q0o
<br />T=.13
<br />.26
<br />.40
<br />:53
<br />.67
<br />.80
<br />.03
<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 />.265
<br />.277
<br />.290
<br />.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
<br />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
<br />.411
<br />.445
<br />
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