|
II TABLE I. - Tangents and Externals to a_1° Curve.
<br />Chord =100 ft:
<br />fit'
<br />Angle
<br />Tangent
<br />External
<br />_
<br />Int:' %
<br />Angle
<br />Tangent
<br />ri
<br />)✓xteral.
<br />Y:Angaint.
<br />Angle
<br />Tangent
<br />External
<br />1°
<br />50.00
<br />.�.t. .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 />r •20-
<br />'d
<br />417.41-
<br />c 15•18
<br />-20
<br />771.29
<br />51.68
<br />30 .
<br />75.01
<br />=::49:.1
<br />:30'1
<br />1425,79'.:
<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 />, p1Z.07
<br />50;
<br />1798.75,
<br />, 55.13
<br />t
<br />`Ol
<br />J
<br />.39
<br />.93
<br />.51 .58
<br />.65 .72
<br />657
<br />'.79
<br />.84 .90
<br />2
<br />100
<br />87
<br />9
<br />450
<br />17 72
<br />.1G •
<br />805 25.
<br />66.31
<br />10
<br />.108'35
<br />1 02'
<br />' 10
<br />459M
<br />J18 38
<br />16
<br />813 75
<br />57.50
<br />20-i
<br />••116:68
<br />-=; 1.19'..
<br />.: ':20
<br />•467':.71-
<br />+ '19.'OGs
<br />=20-822125
<br />.120
<br />%58.70
<br />'30••
<br />-•125.02
<br />1.36
<br />;30:
<br />:476.10
<br />119,75
<br />30 :
<br />1945.0,
<br />.59.91
<br />1. 40 '.
<br />-:133.36
<br />'.1:55 j.
<br />x'40
<br />484:49
<br />20.45.
<br />•v. 40
<br />_830.76
<br />839.27
<br />, 61.14
<br />50'
<br />';141:70
<br />'< 1:75--'',"'50
<br />;
<br />",492,88,"=2116-'
<br />213.86
<br />150"
<br />'847:78�"
<br />62.38-
<br />24 -':1
<br />`1217.9
<br />128.00
<br />31.: '
<br />1589.0
<br />`
<br />38.
<br />1972.9
<br />330.2
<br />3' ""
<br />150.04
<br />196
<br />:"10
<br />501:28
<br />21:80
<br />17 ' . '
<br />' 856.'30'
<br />63.63
<br />:. 10 '
<br />1'158.38
<br />J "2.19, i
<br />.:; 10,
<br />::'509:6&
<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 />e 523.38 ,
<br />_:
<br />L";; 20 ..
<br />2000'.9
<br />;•66'.18-
<br />30
<br />175.06
<br />2.67
<br />30.
<br />„526.48.';_24.14
<br />f534.89
<br />226.0
<br />30
<br />___873.35'
<br />881.88
<br />67.47
<br />40
<br />183.40
<br />2.93
<br />0-.
<br />1633.9
<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 />89.8.95
<br />.70.09
<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 />4
<br />:'200:08
<br />'1-3.49'
<br />11'-
<br />551.70
<br />-` 26150'
<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 ,'916'.03.
<br />2057.2
<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 />..s '30
<br />933.13
<br />75.49
<br />40
<br />233.47
<br />4.76 •
<br />`5.10'
<br />< 40:.
<br />4
<br />-.-585.36
<br />29,.82_
<br />40
<br />941.69
<br />76.86
<br />50
<br />241.81
<br />152:69
<br />50'-
<br />593.79'
<br />30:68
<br />`50
<br />950.25
<br />78.26
<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 />5
<br />250.16
<br />5.46
<br />1211`(
<br />1602:21
<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 />`"2033.35,
<br />1742.6
<br />.33.35'
<br />' ---,20 ;r
<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 />- 1 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 />c 36:12 .
<br />.. 50
<br />1001.7
<br />86.90
<br />SBO j
<br />1402;0 .
<br />169.04
<br />'..30
<br />1779.1'
<br />269.9
<br />x.'30
<br />2170.8
<br />397.4
<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 />1036.1
<br />92.92
<br />40:333:71
<br />'
<br />" 9.71
<br />40
<br />686.60,
<br />40.99'-
<br />40
<br />1044;7
<br />94.46
<br />50 '342:08
<br />1455,1
<br />?•10.20
<br />50
<br />695.06
<br />42.00_.
<br />50
<br />1053.3,
<br />96.01
<br />40.'
<br />1464.0 ,
<br />134.08
<br />'.(40
<br />1843.3
<br />289.2.,
<br />40
<br />2237.7
<br />421.4
<br />7
<br />350.44
<br />10.71
<br />.-14
<br />703.51'''-43.03
<br />292.0
<br />21
<br />1061.9
<br />97:57
<br />104
<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 />30
<br />-375764;:.='1229-.'`
<br />, 30 .'
<br />728.90
<br />46.18'
<br />- :30!
<br />.1087.8
<br />,100.75
<br />X102.35
<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 />56--
<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
<br />Curve 5°
<br />10° 15° 20° 1 25°
<br />30°
<br />_35-,
<br />40°. 45°
<br />50° 55°
<br />60°
<br />65° 70°
<br />5°
<br />T=.02.03
<br />.05 .06 '.08
<br />.10
<br />.11
<br />:13., .15
<br />.16 .18
<br />.20
<br />.21 .23
<br />'101
<br />E=.000
<br />.000 .001 .001 '.002
<br />..002
<br />..002
<br />;003 -.003
<br />.004 .004
<br />,004
<br />,
<br />.005 ..005
<br />10°
<br />T=.03
<br />.06 .09.::13' .16
<br />.19
<br />.22.25
<br />-' .28,,
<br />.31 '.34
<br />.38
<br />.42 .46
<br />30
<br />E=.001
<br />.003 .004 .006 .007
<br />.008_
<br />:.009
<br />.011 .012
<br />:014 .015
<br />.017
<br />.618 .020
<br />15o
<br />T=.04
<br />.10-1 .14 .19 .24
<br />.29
<br />.34
<br />.39 .45
<br />.51 - p.53
<br />_.58
<br />.63 :.68
<br />'50
<br />E =.003
<br />,:.007 '.010 .014 .018
<br />.023
<br />.027
<br />.029 .032
<br />.035 ;:039
<br />.043
<br />.047 :051
<br />200
<br />1 T=.06'
<br />.13 .119 .26 .32
<br />.39
<br />'.45
<br />.51 .58
<br />.65 .72
<br />657
<br />'.79
<br />.84 .90
<br />23-- �i11G5:7
<br />=.006
<br />A=
<br />.011 `.017 .022 .028
<br />.034
<br />.038
<br />.045 .051
<br />; .063
<br />.070
<br />-.076 .083
<br />25°
<br />T=.08
<br />.16 .24,..33 .40
<br />.49
<br />..58
<br />.67 .75
<br />83 .90'
<br />.99
<br />1.06 1.14
<br />.'1174.4
<br />20
<br />� E=.009
<br />.018 .027 .036 .046
<br />.056
<br />.065
<br />.074 .083
<br />-.093 .106
<br />.120
<br />.127 .135
<br />i
<br />TAnLE<L Tangents and,I;xternals to a.I'"Curve:, III
<br />Chnrd =1-00 ft
<br />Int
<br />' Angle
<br />-
<br />Tangent
<br />External
<br />Int.
<br />Angle '
<br />Tangent
<br />External::
<br />Int:..
<br />Angle'
<br />Tangent
<br />Eictemal
<br />45°
<br />'1113.7
<br />107.24
<br />:291'
<br />1481.8
<br />188.51
<br />3G°:•:
<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 />140
<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 />o, 50
<br />1526.3.
<br />199.82 i
<br />50
<br />`.1907.9
<br />:309.3
<br />.027
<br />•036
<br />.046
<br />{
<br />.065
<br />.074
<br />.083
<br />.093
<br />.106
<br />23-- �i11G5:7
<br />.127
<br />117:38
<br />30'
<br />3535.3
<br />202.12:
<br />37t:'
<br />4917.1-
<br />312:2
<br />'10
<br />.69
<br />119.12.
<br />10
<br />1544.2.
<br />204.44
<br />10
<br />J.l-20
<br />1926.4
<br />0315.2
<br />.'1174.4
<br />20
<br />1183.1
<br />120.87
<br />20
<br />155311
<br />206.77
<br />.078
<br />11935.7
<br />'318.1
<br />c30
<br />1191:8'
<br />122:63 -
<br />`x.130
<br />1562"1
<br />209.12 '.
<br />:30
<br />1945.0,
<br />321.1
<br />.34
<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 />11209.2 '
<br />126,20 !
<br />`':50
<br />1580.0
<br />213.86
<br />.50
<br />•1963.6
<br />327.1
<br />24 -':1
<br />`1217.9
<br />128.00
<br />31.: '
<br />1589.0
<br />216:3
<br />38.
<br />1972.9
<br />330.2
<br />1
<br />1226.6'
<br />129.82
<br />10
<br />1598iO
<br />218.7 ;
<br />10
<br />1982.2
<br />333:2
<br />_10
<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 />1244:01
<br />133.50 (
<br />..:30
<br />1615:9
<br />223.5
<br />30
<br />2000'.9
<br />339.3
<br />40 1
<br />1252.8.
<br />135.35 r
<br />:40
<br />1624.9
<br />226.0
<br />,.:'40
<br />2010:2
<br />342.4
<br />;.0.50
<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 />10
<br />2038.4
<br />351,8
<br />120 .
<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 />x.'30
<br />1670.0
<br />238.4
<br />30
<br />2057.2
<br />358.1
<br />-40 1
<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 />1322.81
<br />i
<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 />253.91
<br />a},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 i
<br />'.:. i 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 1
<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 />SBO j
<br />1402;0 .
<br />169.04
<br />'..30
<br />1779.1'
<br />269.9
<br />x.'30
<br />2170.8
<br />397.4
<br />0.40 :
<br />1410'.9'
<br />171.15
<br />'40
<br />1788.2
<br />272.6
<br />'.x: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 />j
<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 />, 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 />134.08
<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 />Angle
<br />-,Curve 5°;
<br />-10°,
<br />15°
<br />,20°,
<br />25°;
<br />30°
<br />35° 1
<br />40°
<br />45°
<br />50°
<br />-55°
<br />.60°
<br />65°
<br />700
<br />200
<br />T=:06
<br />:13
<br />..19,.26
<br />'.32
<br />.39
<br />.45
<br />.51
<br />.58
<br />.65
<br />.72'
<br />'.063
<br />.79
<br />.84
<br />.90
<br />E=.006 ••.011
<br />.017
<br />:022
<br />,028
<br />:034
<br />.038
<br />.045
<br />.051
<br />.057
<br />.070
<br />.076
<br />.083
<br />- 250,
<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 7.009
<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 />°
<br />T=:10
<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 />+•
<br />f 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 />.188
<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 />1.421.54
<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 />40°•
<br />T=.13
<br />.26 ,
<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
<br />1.79
<br />1.94
<br />'
<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 />40
<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 />
|