|
II TABLE 1. - Tangents and Externals to a V Curve.
<br />Chord=100 ft.
<br />Int.
<br />Angle
<br />Tangent
<br />Externa]
<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-,30-
<br />,012
<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 />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 />•a 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 />476.10
<br />19.75
<br />t30,:
<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 />8'
<br />150:04.
<br />1; 1.96
<br />10,501.28
<br />1589.0
<br />21.89
<br />17
<br />856.30.
<br />E63.63
<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 />74.761
<br />- 40 ,
<br />585.36
<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 />60
<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 />34.26
<br />.30-
<br />',984.53
<br />83.97
<br />40
<br />283.57
<br />7.01,
<br />40._635.93
<br />1733.5"
<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 />27
<br />1375.6
<br />.162.81 X34
<br />.1751.7_
<br />261:8.
<br />41' -
<br />2142.2
<br />387.4
<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;4
<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 />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 Curve 5°
<br />10° 15°
<br />20°;
<br />25°
<br />301
<br />35° 40°
<br />45°
<br />50° 55° 60° 65°
<br />70°
<br />bo T=.02
<br />.03 .05
<br />.06
<br />.08.
<br />-.10
<br />'.11` -..13.15
<br />36°
<br />.16 .18 .20 .21
<br />.23
<br />E=.000
<br />.000 .001
<br />.001
<br />.002
<br />.002
<br />.002 .003
<br />.003
<br />.004 .004 .004 .005
<br />.005
<br />10o T=.03
<br />.06 .09
<br />.13:
<br />.16.
<br />:19
<br />.22--.2528
<br />20
<br />,.31 .34 .38 .42
<br />.46
<br />E=.001
<br />.003 .004
<br />.006
<br />.007
<br />.008
<br />.009 .011
<br />,012
<br />.014 .015 .017 .018
<br />.020
<br />15° T=.04
<br />.10 .14"
<br />.19
<br />.24
<br />.29
<br />;'.34 .39
<br />.45
<br />:51, .53 .58 :63
<br />.68
<br />E=.003
<br />.007 •010
<br />.014
<br />.018
<br />'.023
<br />.027 .029
<br />.032
<br />.035 x.039 .043 .047
<br />.051
<br />20oIT=.06 <
<br />Y.13' .19
<br />.26
<br />. 32,
<br />.39
<br />.45 .51
<br />.58
<br />.65, .72 .79 .84
<br />.90
<br />=.006'
<br />.011 •.017
<br />.022
<br />.028
<br />.034
<br />.038 .045
<br />.051
<br />.057 .063 :070 .076
<br />.083
<br />25o 1 T=:08
<br />.16 1 .24.
<br />.33
<br />.40
<br />.49
<br />.58 .67
<br />.75
<br />.:83' .90 ' .99 1.06
<br />4.14
<br />'.135
<br />E,=.009
<br />.018 .027
<br />,.038
<br />.046
<br />.056
<br />.065 .074
<br />.083
<br />.093 .106 .120 .127
<br />321.1
<br />Test E L -Tangents and Externals to a 10. Curve.
<br />Chord=100 ft.
<br />Int'
<br />;. Angle
<br />Tangent
<br />External,
<br />_
<br />Int.
<br />Angle
<br />Tangent
<br />External
<br />Int.
<br />Angie
<br />Tangent
<br />External
<br />_
<br />;22°•
<br />1113.7
<br />107,24
<br />290
<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 />b0
<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 />r 20
<br />1553.1
<br />206.77
<br />.29 .39
<br />1935.7
<br />318.1
<br />30
<br />1191,8
<br />122.63
<br />.99
<br />1562,1
<br />209.12
<br />.20
<br />30
<br />1945.0
<br />321.1
<br />40
<br />4200.5
<br />124.41
<br />,130
<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 />33072 .
<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„30
<br />1.49
<br />.2000:9-
<br />339.3
<br />r"40
<br />1252.8'
<br />135.35
<br />"40
<br />1624.9
<br />226.0
<br />.141
<br />2010.2'
<br />342.4
<br />='50
<br />1261.5
<br />..
<br />137.23
<br />50
<br />'1633.9
<br />228,4
<br />..40
<br />'60
<br />2019.6
<br />i
<br />345.8
<br />:25.
<br />1270:2
<br />139.41
<br />32 -
<br />1643.0
<br />230:9
<br />39--,
<br />2029:0.
<br />348:0
<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 />1.20
<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 />b0
<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 -'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 />1374.2
<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 X34
<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 />r 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 />46
<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 />41824.9
<br />283.6
<br />20
<br />2218.6
<br />'414.5
<br />30
<br />1455.1
<br />181.89
<br />30'
<br />11834.1
<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 />2237.1
<br />421.4
<br />;'-b0
<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 5°•
<br />.10°
<br />15° 20°
<br />25°
<br />30°
<br />.35°
<br />40°
<br />45°
<br />50°
<br />5S°
<br />60°
<br />65'
<br />70° -
<br />,
<br />20°-
<br />' T=:06-
<br />.13
<br />-.19 .26
<br />.32
<br />":39.45
<br />.51
<br />.58
<br />.65
<br />.72
<br />.79
<br />.84
<br />.90
<br />E=.000
<br />_.011
<br />.017 .022
<br />.028
<br />.034
<br />.038
<br />.045
<br />.051
<br />.057
<br />.063
<br />.070
<br />.076
<br />.083
<br />250
<br />,T=.08
<br />.16
<br />.24` .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 =.009.
<br />.018
<br />.027 .036
<br />`.046
<br />.056
<br />.065
<br />".074
<br />.083
<br />.093
<br />.106
<br />.120
<br />.127
<br />.135
<br />300
<br />T=.10
<br />.19
<br />.29 .39
<br />':49
<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 .051
<br />.065
<br />.078
<br />.090
<br />.103
<br />.116
<br />.129
<br />.149
<br />.170
<br />.179
<br />.188
<br />350-
<br />• T=:11
<br />.22
<br />.34 .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 .072
<br />.086
<br />.109
<br />.131
<br />.153
<br />.175
<br />.197
<br />.213
<br />.230
<br />.247
<br />.264
<br />40°
<br />T=.13
<br />.26
<br />.46 .53
<br />.93
<br />1.06
<br />1.20
<br />1.34
<br />1.49
<br />1.64
<br />1.79
<br />1.94E=.023
<br />.046
<br />.070 .093
<br />.141
<br />.172
<br />.20324.265.277
<br />.290
<br />.315
<br />.341
<br />45°
<br />T=.15
<br />30
<br />.44 .GO
<br />�:67.80
<br />.91
<br />1.06
<br />1.21
<br />1.37
<br />1.521.70
<br />1.87
<br />2.04
<br />2.21
<br />E=,030
<br />.060
<br />.093 .119
<br />.184
<br />.216
<br />.254
<br />.289
<br />.325
<br />.351
<br />.378
<br />All
<br />.445
<br />
|