|
II TABLE I. -Tangents and Externals to a 1° Curve.
<br />Chord= 100 ft.
<br />lnt• Tangent External
<br />Angle
<br />35°
<br />40° 450
<br />Ent.
<br />Angle
<br />:Tangetit
<br />External
<br />tot'
<br />Ansle
<br />Tan ent
<br />g
<br />External
<br />r.
<br />1.
<br />50.00
<br />`- .22 '
<br />!8'.
<br />400.G5
<br />'13.99
<br />Is'
<br />754.32
<br />49.,44
<br />LO'
<br />58.34
<br />.30 .
<br />10'
<br />409.03
<br />14.58
<br />30'
<br />762.60
<br />50,55
<br />2U66.67
<br />.018
<br />89,
<br />20
<br />417.41
<br />15:18
<br />20
<br />771.29
<br />51.68
<br />30
<br />75.01
<br />49 •
<br />M.
<br />425,79.
<br />15:84
<br />;- 30'
<br />779:77
<br />52.92
<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 r
<br />10..
<br />.492.55
<br />12,07 :
<br />50
<br />796.75
<br />55.1
<br />12,
<br />100.01.
<br />.87:
<br />9 .:_.
<br />,.#50.93
<br />17.72
<br />16,,, -
<br />805.25
<br />56.31
<br />10
<br />108.3.5'
<br />•'1':02 :
<br />' 10'
<br />459.32'
<br />1838
<br />10
<br />813:75
<br />'57.50
<br />20•
<br />116168
<br />1.19
<br />-20
<br />467.71
<br />--19.00".
<br />` 20.'
<br />-622.25
<br />.58.70
<br />-M
<br />'125.02.
<br />1.36
<br />_ 30..'..476:10,
<br />1562.1
<br />200.12
<br />,• 30
<br />830:76
<br />59.91
<br />-•40
<br />1133.30
<br />- 1.55'
<br />40
<br />484.49
<br />_19.75
<br />20.45
<br />40
<br />839:27
<br />61,14
<br />50
<br />741'.70.
<br />1.75
<br />,50
<br />492.88
<br />- 21.16',
<br />,? 50
<br />'847178.
<br />62:38
<br />3`,•'
<br />130 04
<br />1.96
<br />-10;
<br />501.28'
<br />'.21:89
<br />17 '-:
<br />"856,30•
<br />63.63
<br />10
<br />15838
<br />72119
<br />-.10
<br />509.68
<br />22:62
<br />10 ,.864.82
<br />1982:2
<br />"64:90
<br />20
<br />'.106:72,
<br />2,43
<br />20
<br />518.08
<br />23.38
<br />_1`20,'
<br />•873:35
<br />66,18
<br />30
<br />-175.66
<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 />!
<br />200.08
<br />3.49
<br />11
<br />551:70
<br />2Q,50-
<br />18
<br />907,49
<br />71.42
<br />to
<br />208.43'.,
<br />3.79.'
<br />-10
<br />560, 1t
<br />27.3L
<br />-
<br />10
<br />•916.03
<br />72.76
<br />20
<br />216,77
<br />'. 4.10
<br />20568.53
<br />1661.0
<br />28.14
<br />20 :
<br />024.58
<br />74.12
<br />30
<br />225.12
<br />,- ',421
<br />"4
<br />-1.30 ,"
<br />576.95
<br />28:97',
<br />` .30.
<br />933.13
<br />'75.40
<br />40
<br />233.47
<br />4,7G
<br />40
<br />585.36
<br />29.82
<br />;.;40
<br />•941:69
<br />76.80
<br />50
<br />241.81
<br />5.10
<br />50
<br />•593.79
<br />30,68'
<br />50
<br />950,25
<br />78.20
<br />.5
<br />250,16
<br />5.46
<br />12 " .
<br />602,2t
<br />31.55
<br />19
<br />058.81
<br />79,67
<br />LO
<br />258,51
<br />5:83
<br />10
<br />610.64
<br />32.45
<br />10
<br />067.38
<br />81.09
<br />20
<br />256,80
<br />.._ 0,21
<br />20
<br />619.07,
<br />33.35
<br />- 20
<br />:975.96
<br />82.53
<br />30
<br />275,21
<br />0.61
<br />30•
<br />62.7.50
<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 />150
<br />291,92
<br />7.43.
<br />50
<br />644.37
<br />38.12
<br />50
<br />1001.7
<br />. 86.90
<br />6
<br />30q.a
<br />7.86
<br />13
<br />G52:81
<br />37.07
<br />20
<br />1010.3.
<br />88.39
<br />10•
<br />308.64
<br />8.31
<br />LO
<br />601.25
<br />38.03
<br />10
<br />1018.9
<br />89.89
<br />20 '
<br />316.90
<br />8.76'
<br />20
<br />659.70
<br />89.01
<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 />'90.01
<br />7
<br />350,44
<br />10.71
<br />14
<br />703.'51
<br />43.03x,'
<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 />311
<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 />.59
<br />745.85'
<br />48.34
<br />50 '
<br />1105.1
<br />105.60
<br />Corrections to be Added (T=Tangent. E=External.) _..
<br />AngleCurve 5° .10° 15° 20° 25° 30° '
<br />Acgle
<br />35°
<br />40° 450
<br />° °
<br />50 55 60°
<br />65 °
<br />70°
<br />5°T=.02 .03 .05 .06 03 .10.'.11
<br />Tangent
<br />:13 at
<br />18 .18 .20
<br />.2t
<br />.23
<br />E=.000 .000 .001 .001 002 .002
<br />.002
<br />,003 .003
<br />.004 .004 .004
<br />..005
<br />.005
<br />10° =•03 06 09 ..13 .I0 .IB
<br />22
<br />.25 28
<br />.3t .34 .38
<br />.2
<br />A6
<br />E=.001 MS ':004 .000 .007 _008
<br />,009
<br />Alt .012
<br />.014 ,016 .017
<br />.018
<br />'.020
<br />ip : =.04 10 14 _:19 24 ,29
<br />.31
<br />39 .45
<br />51 .53 -.58
<br />1880.1
<br />:300,6
<br />E=.003 ,007 .010 .014 .019 .023
<br />.027
<br />:45
<br />.029 .032
<br />6l S8
<br />,035 ,039 .09
<br />,85 .12 ,79
<br />.047
<br />.$4
<br />.051
<br />.9U
<br />p 28 .32 38
<br />A6- ]N11
<br />E =,006 .022 .028 .034
<br />.038
<br />.035 ..051
<br />.057 .063 .070
<br />'.07Q
<br />'.083
<br />25° T 14 .4 49
<br />1.06
<br />1:14
<br />58
<br />.87 75
<br />.83.80,99
<br />E=,009 A27 .036 ,046 058
<br />.065
<br />.674 083
<br />.093 .108 .121}
<br />.127
<br />:135
<br />K
<br />TAimn I:`-- Tangents and Externals to ail° Curve. III
<br />Chord =100 it.
<br />r' Int.:
<br />_Angle:
<br />Tangent
<br />Extental
<br />Int.-
<br />Angle
<br />Tangent
<br />External
<br />Int.
<br />Angle
<br />Tangent
<br />External
<br />.32 •.39,45
<br />ll13:7
<br />-167.24
<br />29°:
<br />14S1.8
<br />188.51
<br />36°
<br />1861.7
<br />294.9
<br />lot'
<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 />310.57
<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:,1148.4
<br />.80L,19131:05 1.17 1.29
<br />113.95
<br />40
<br />'1517.4
<br />197.53
<br />,
<br />,' 40
<br />1898:8
<br />306.4
<br />50 '
<br />1157,0
<br />115.06
<br />50
<br />1528,3
<br />199.82
<br />-50
<br />-1907:9
<br />309.3
<br />2
<br />1105.7.
<br />117.38
<br />80 ';
<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 .:1935.7
<br />318.1
<br />'•30
<br />;1101.8
<br />122.63,.
<br />30
<br />1562.1
<br />200.12
<br />''30
<br />1945'.0
<br />321.1
<br />405
<br />124.41
<br />40 j
<br />-1571.0
<br />211.48.
<br />'40
<br />1954':3
<br />324.1
<br />50
<br />.1209:2
<br />126.20 .
<br />-so
<br />1580.0
<br />213.86
<br />` 50
<br />1963.6
<br />327.1
<br />21 `'
<br />1217.9
<br />.128.00
<br />31. -
<br />1589:0
<br />216:3
<br />38'
<br />1472.9
<br />'330.2
<br />10 .;1228.8'
<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 />160G:9
<br />221.1
<br />20
<br />1991.5
<br />336,3
<br />1244.0
<br />133.50
<br />30
<br />1615.0
<br />223,5 t,
<br />,.'30
<br />2000.9
<br />339.3
<br />40
<br />1252.8
<br />,135,35
<br />40
<br />1024.0
<br />220.0
<br />40
<br />.2010.2
<br />342.4
<br />50
<br />1261:5
<br />137.23
<br />50
<br />3G33,9
<br />228,4
<br />50..
<br />2019:G,
<br />' 345.5
<br />26'
<br />1270:2',
<br />139.11
<br />32 .'
<br />1043,0
<br />230.9 `
<br />:39'
<br />2029.0
<br />348.6
<br />'-YO
<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 />j20
<br />2047:8
<br />354.9
<br />30
<br />.1296,'5
<br />144.85
<br />30
<br />1670.0
<br />238.4'
<br />X30
<br />2057.2
<br />358.1
<br />140
<br />-1305,3•
<br />146.79..-
<br />40
<br />'1679:1
<br />241.0.
<br />`,-40
<br />2660.6
<br />361.3
<br />50
<br />-1314,0
<br />148.75 '
<br />60
<br />1888,1
<br />243.5
<br />- 50
<br />2078:0
<br />364.5
<br />28 __:
<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 />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 />150:70
<br />30
<br />1724.4 :'•253:9
<br />-,30
<br />2113.8
<br />377.5
<br />40
<br />'1358.0
<br />158.72
<br />40
<br />1733.5
<br />250.5 ;
<br />40
<br />2123.8
<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 />'Z7 :.
<br />1375.6
<br />182.81.
<br />8!.
<br />1751.7
<br />261.8 -
<br />41 "
<br />2142.2
<br />387.4
<br />10
<br />'1384.4
<br />264.86
<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.'U
<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 />-40
<br />1788.2
<br />272.6
<br />40
<br />.2180.3
<br />400.8
<br />^' 50 ;
<br />1479:7
<br />173.27 :
<br />50.
<br />1797.4
<br />275.3.
<br />50
<br />2189 9
<br />404.2
<br />,28
<br />1'42816
<br />175.41
<br />36 =-
<br />1806,'0 ,
<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 />283,8 .
<br />20
<br />2218.6
<br />414.5
<br />30
<br />1455.1
<br />181.89
<br />30
<br />1834.1
<br />280.4
<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 />166.29
<br />50
<br />1852.5
<br />292.0
<br />60
<br />-2247.3
<br />425.0
<br />Corrections to be Added- (T =Tangent. E --=External.)
<br />lat
<br />Angle Curve5' 10'
<br />15°
<br />20°
<br />�75° 30°
<br />35° 40° 45° 50° 551
<br />60° 651.j 70°
<br />T-mM • .13
<br />.19
<br />.26
<br />.32 •.39,45
<br />.51 .58 .65 .72
<br />.79 ,84 .90
<br />E=.008_- _.011
<br />.017
<br />.022
<br />.028 .034
<br />.036 .015 .051 .057 .003
<br />.070 ,078 033
<br />25° T=.08 .16
<br />.24
<br />.33
<br />.40 .49
<br />58 .67 .75 ' .83 .90
<br />.99 1.06 1.14
<br />E =.009 018
<br />_.027
<br />,036
<br />.048, .056
<br />:005 ,074 -ON .093 .106
<br />.120 .127 .135
<br />T=.10 ,19
<br />,29
<br />.39
<br />,49 ,59.69
<br />.79 .89 .90 1,09
<br />1.20 1,29 L_39
<br />E=.013 .025
<br />.038
<br />.051
<br />.065 .078
<br />,000 .103 .110 .129 .149
<br />.170 .179 .188
<br />35° T=•11 .22
<br />.34
<br />.47
<br />58 •69
<br />.80L,19131:05 1.17 1.29
<br />1'.92 1.54 1.86
<br />E =.018 -.035
<br />',054
<br />.072
<br />.086 .109
<br />:131 ,175 .107 ,213.230
<br />247 204
<br />40°13 26
<br />.40
<br />53
<br />.67 .80
<br />.93 1.20 1.34 1.49
<br />1.64 1.79 1.99
<br />E=.02'16
<br />.070
<br />.093
<br />.117 .141
<br />.172 .234 265 .277
<br />,290 .3I5 .341
<br />T=.15. ,3U
<br />.44
<br />_80
<br />_78 ,OI
<br />1 0& 1.37 1.52 1.70
<br />1.87' 2,04 221
<br />E=.030093
<br />_119
<br />_153 ,184
<br />.210 .289 _325 .351
<br />.378 .411 A45
<br />
|