|
II TABLE I. - Tangents and Externals to a 1 Curve,
<br />Chord= 100 ft.
<br />Angle
<br />Tangent
<br />External
<br />Angle
<br />Tangent
<br />External
<br />A, nngj
<br />Tangent
<br />External
<br />1°;-
<br />50.00
<br />.22
<br />8'
<br />400.6G
<br />13.99
<br />IS' - '
<br />754.32,
<br />49.44
<br />10`
<br />58.34
<br />.30
<br />10'
<br />409.03
<br />14.58
<br />10'
<br />702.80
<br />50.55
<br />20
<br />66.67
<br />.39
<br />20 ,
<br />417.41
<br />15.19
<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 />788.20
<br />53.97
<br />50
<br />91.68
<br />.73
<br />50
<br />442.55
<br />17.07
<br />50
<br />790,75-
<br />55.13'
<br />2
<br />100.01
<br />.87
<br />9
<br />450.93
<br />17.72 'x•16
<br />.070
<br />805.25
<br />56.31'
<br />10
<br />.108.35
<br />1.02
<br />10
<br />459.:32
<br />18.88
<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 />I0,
<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 />'60
<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.B9-
<br />17
<br />85G.30..
<br />03.63,
<br />10
<br />158.38
<br />2.19
<br />M.
<br />509,.68
<br />.22.62
<br />10
<br />864:82,
<br />64.90
<br />20
<br />106:72
<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 />60
<br />898.95
<br />70.09
<br />4
<br />.200.08
<br />3.49
<br />11
<br />551.70
<br />26,50
<br />28'
<br />907.49
<br />71.42
<br />10
<br />208.43
<br />3.79
<br />10
<br />560.11
<br />27,31
<br />30
<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 />924.68'
<br />74.12
<br />30
<br />225.12
<br />4.42
<br />30
<br />9576.95
<br />28.97
<br />30._
<br />933.13
<br />75.49
<br />40
<br />233.47
<br />-4.76
<br />40
<br />/ 535.36
<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 />..30.65
<br />50
<br />950,25
<br />78.26
<br />5
<br />250.10
<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 />266.866.21
<br />154.69
<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 />- a0
<br />627.60
<br />34.26
<br />30
<br />984.53
<br />83.97
<br />40
<br />293.57
<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 />300.28
<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 />651.25
<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 />678.13
<br />39.99
<br />30
<br />1036.1
<br />92.92
<br />40
<br />333.71
<br />9.71
<br />40
<br />680.60
<br />40.99
<br />40
<br />1044.7-
<br />94.46
<br />50
<br />342.08•
<br />10.20
<br />50
<br />695.00
<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 />367.1.
<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-.S,,l
<br />102.35
<br />40
<br />333.91
<br />'12.S5
<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 />Angie Curve 5° 101
<br />17 20° 25° 30°
<br />1 35° 1 40° 1
<br />45° 50°
<br />55°
<br />60°
<br />65°
<br />70°
<br />5° T=.02 .03
<br />.05 .06 .08 .10
<br />.11 .13.
<br />15 .16
<br />.18
<br />.20
<br />.21
<br />.23
<br />E=.000 .000
<br />.001 .001 .002 .002
<br />-.002 .003
<br />.
<br />- .003 004
<br />.Q04
<br />.004
<br />.005
<br />.005
<br />30° T=.03 A
<br />.09 .13 .16 19
<br />.22 .25
<br />28 .31
<br />.34
<br />.38
<br />.2
<br />•46
<br />E =.001 .003
<br />.004 .006 .007 008
<br />.009 .011
<br />.012 .014
<br />015
<br />.017
<br />-.018
<br />.020
<br />15° -Y-70i- .10.14
<br />.19 .24 29
<br />.34 39
<br />.45 .51
<br />.63
<br />-.b8
<br />.63
<br />.68
<br />E=M W7
<br />010 .014 .018 .023
<br />.027 .029
<br />.032 .035
<br />.039
<br />-.043
<br />.047
<br />.051
<br />20* T=.06 .18
<br />.19 2$. .82 89
<br />.45 51
<br />.5$ .&5
<br />.72
<br />.79
<br />.84
<br />.90
<br />E=.()05 '.011
<br />.077 .022 .028 .034
<br />.038 .045
<br />.0.51 .057
<br />.063
<br />.070
<br />.076
<br />.083
<br />fir° T=.O$ 16
<br />.24 .33 .40 40
<br />.58 .07
<br />.75 .83
<br />.90
<br />.99
<br />L.OB
<br />1.14
<br />E=.009 018
<br />.027 .038 .640 .656
<br />.065 .074
<br />.083 .093
<br />.106
<br />.i20
<br />.127
<br />.135
<br />TA71LE I. - Tangents and.Externals to a 1° curve.. III
<br />Chard =100 f t.
<br />Int.
<br />Angle
<br />-
<br />Tangent
<br />External
<br />Int.
<br />Angle
<br />- -
<br />Tangent I
<br />-
<br />External,
<br />Int.
<br />:.Angle
<br />Tangent
<br />External
<br />2P° :
<br />1113.7
<br />107.24
<br />29°1.
<br />1481.8.
<br />188:51
<br />36°
<br />1861.7
<br />294.9
<br />10"
<br />:1122.4
<br />108.90
<br />io''
<br />1490.7
<br />190.74
<br />10'
<br />1870.9
<br />297.7
<br />20
<br />1-131:0
<br />110,57
<br />4..20
<br />1499.6
<br />192.99
<br />20
<br />18S0.1
<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 />1167:0
<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 />37 •
<br />1917.1:
<br />312.2
<br />10
<br />1174.4,
<br />119.12
<br />10
<br />1544:2
<br />204.44 "
<br />I0
<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 />200.12
<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 />50 .'1209:2,
<br />126.20
<br />50
<br />1580.0
<br />213.86
<br />.50
<br />1963.6
<br />327.2
<br />24
<br />1217.9
<br />128.00
<br />31
<br />.1569:0
<br />216.3
<br />38""
<br />1972.0:
<br />330.2
<br />30
<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 />160G.9
<br />221.1 .
<br />20
<br />1991.5
<br />336.3
<br />20
<br />1244.0
<br />133.50
<br />30
<br />1015.9
<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
<br />: 40
<br />2010.2
<br />342.4
<br />50
<br />1261.5
<br />137.23
<br />SO
<br />1633.9
<br />228.4
<br />''50
<br />2010.6
<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 />^_0 `
<br />4287.7
<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 />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 />120
<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 />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
<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 />.30
<br />1402.0
<br />169.64
<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 />17BS.2'
<br />272.6
<br />40
<br />2180.3
<br />400.8
<br />50
<br />'1419.7
<br />1,73.27
<br />50
<br />1797.4
<br />275.3 ,
<br />50
<br />2189 9
<br />404.3
<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 />1824.9
<br />283.6
<br />20
<br />2218.6
<br />414.5
<br />30
<br />1456.1
<br />181.69
<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.b
<br />292.0
<br />50
<br />2247.3
<br />: 425.0
<br />Corrections to be Added •(T=Tangent. E=External,)
<br />Int.'
<br />Anglo
<br />Curve S° 19°
<br />IS-
<br />20°
<br />.25' 30°
<br />35° 40° 45° 50°
<br />55°
<br />60° 55° 70°
<br />20°
<br />T- M .13
<br />.19
<br />.25
<br />.32 .39
<br />..45 .51 .58 AS
<br />72
<br />.79 .84 .90
<br />E =.006 .011
<br />X17
<br />.022
<br />.023 .034
<br />.038 .035 .051 .057
<br />'.053
<br />.070 .076 .083
<br />25°"
<br />T=.06 .16
<br />.24
<br />.33
<br />.40 .49
<br />..58 .67 .75 .83
<br />.90
<br />.99 1.06 1.14
<br />E =.009 :018
<br />.027
<br />.036
<br />.016 .056
<br />.005 XM .0S3 .023
<br />.I06
<br />.120 .127 .135
<br />30°
<br />T =• 0 .19
<br />.29
<br />.39
<br />.49 .50
<br />69 :.79 .89 .99
<br />1.09
<br />L20 1.29 1.89
<br />E =,013 .025
<br />.038
<br />.051
<br />.065 .078
<br />.090 .103 .118 .129
<br />.149
<br />.170 .179 .188
<br />35°
<br />=•11 .22
<br />.34
<br />.47
<br />.58 .69
<br />.80 .93 1.05 1.17
<br />1.29
<br />1.42 !_54 1.68
<br />]E=.013 .035
<br />054
<br />.072
<br />.086 .109
<br />.131 .153 :175 .197..213
<br />230 -.247 .264
<br />40°
<br />T=.13 .26_T_.40
<br />.53
<br />.57 .80.93
<br />1,06 1.20 1.34
<br />1.49
<br />1.64 1.79 1.94
<br />E=.023 .048
<br />r=.15-.80 -
<br />.070
<br />.093
<br />.117 .141
<br />.172 ,203 .234 265
<br />.277
<br />.290 .315 .341
<br />4S°
<br />.44
<br />.60
<br />.76 .91
<br />1 06 1,21 1.37 1.52
<br />1.70
<br />1.87 2.04 2.21
<br />E-030 -.060
<br />..093
<br />.119
<br />.153 .184,
<br />.210 ,254 '.289 ,325
<br />.351
<br />.378 .411 .445
<br />\I
<br />
|