|
II TAeLa I. -,Tangents and External8 to a_19 Curve.
<br />Chord= 100 ft. I
<br />Int.
<br />Angle
<br />Tangent
<br />External
<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 />.101:
<br />53.34
<br />.30
<br />101
<br />409:03
<br />14.58
<br />10'
<br />762:80
<br />50.55
<br />110
<br />60.67
<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
<br />30
<br />779.77
<br />52.82
<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
<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 />.103.35
<br />1.02
<br />10
<br />439:32
<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 />1:30.
<br />30
<br />-476.10
<br />19.75
<br />30
<br />830.76
<br />1:08
<br />..40
<br />153.36
<br />•..1.55•.
<br />40
<br />484:49
<br />20.45'
<br />'40
<br />839.27
<br />_59.01
<br />G1.14
<br />50'
<br />141.70
<br />1.75
<br />50'
<br />492.88
<br />21.10
<br />50
<br />847.78
<br />62.38
<br />3'.
<br />150.04
<br />1.96
<br />10
<br />561.28
<br />21.89
<br />17
<br />856.30
<br />03.63
<br />1.0
<br />158,38
<br />2.19
<br />10
<br />509.68'
<br />22.62
<br />10'
<br />864'.82
<br />04.90
<br />20
<br />1GG,72
<br />2.43
<br />20
<br />518.08
<br />23.38
<br />20
<br />873.35
<br />¢6,18
<br />30
<br />175.OG
<br />2.67
<br />-30
<br />'526.48
<br />24.14
<br />30
<br />881.88
<br />'07.47
<br />40
<br />183.40
<br />.2,93
<br />40
<br />534.89
<br />.24.91
<br />40
<br />89041
<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 />25
<br />1270.2
<br />139.11
<br />32.
<br />1643.0
<br />230.9
<br />39 -
<br />2029.0
<br />348.6
<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 />500.11
<br />27.31
<br />10
<br />2047.8
<br />.72.7G
<br />- 20
<br />216.77
<br />4.10
<br />20
<br />508.53.
<br />28.14
<br />j 20
<br />,916:03,
<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 />535.36
<br />29.82
<br />40
<br />94t.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 />73.2G
<br />5
<br />250.1G
<br />5.46
<br />1.3
<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 />G10.64
<br />32.45
<br />.10
<br />.967,38
<br />81,09
<br />20
<br />206.SG
<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 />3U
<br />627.50
<br />34:26
<br />30
<br />984.53
<br />83.97
<br />40
<br />233.57
<br />7.01
<br />40
<br />635.93
<br />35.18
<br />50
<br />993.12
<br />85,43
<br />_50
<br />291.92
<br />7.43
<br />50
<br />644.37
<br />36.12
<br />.40
<br />50
<br />1001'.7
<br />$0.90
<br />6
<br />300.28
<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 />10
<br />G61.25
<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
<br />333.71
<br />9.71.
<br />40
<br />686.00
<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.S1
<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 />L087.8
<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 />13,411
<br />50
<br />745.85
<br />48.34
<br />50
<br />1105.1
<br />105.60
<br />Corec-tions to be Added (T =Tangent. E = External.)
<br />W.
<br />Angle. Curve 5° 10°
<br />i5° 20° •25°
<br />30°
<br />1 35° 40°
<br />45°
<br />50°
<br />1 550
<br />600
<br />650
<br />70°
<br />50 • T=.02 .03
<br />05 .06 .08
<br />.10
<br />.I1 .13
<br />.15
<br />.16
<br />.18
<br />.20
<br />21-
<br />.23
<br />S-.000 .000
<br />.001 .001 .002
<br />..032
<br />.002 .003
<br />.003
<br />.004
<br />.004
<br />.004
<br />.005
<br />.005
<br />l0' =.03 .O6
<br />.09 .13 .18
<br />.19
<br />.22 .25
<br />.28
<br />.31
<br />.34
<br />.38
<br />2_. .
<br />.46-
<br />is=.001 .003
<br />.004 .006 .007
<br />.008
<br />.009 .011
<br />.012
<br />.014
<br />.015
<br />.017
<br />.018
<br />`.020
<br />150 =.04 . .10
<br />.14 10 .24
<br />.29
<br />.34 ,89
<br />.45
<br />.51
<br />.53
<br />.58
<br />7 63
<br />-.M-
<br />9 =.003 .007
<br />.010 .014 .018
<br />.023
<br />A27 .029
<br />.032
<br />.035
<br />.039
<br />.043
<br />.047
<br />.051
<br />20-- T- O6 18
<br />19 26 .32
<br />39
<br />.45 .51
<br />.58
<br />10
<br />72
<br />.79
<br />.84--
<br />•.90
<br />];=.ODB 011
<br />017 X22 .028
<br />` .034
<br />.038 .045
<br />.051
<br />.65
<br />.057
<br />-063
<br />'.070
<br />.076
<br />.083
<br />250 TF+.OS 16
<br />.24 33 .40
<br />.49
<br />.d8 67
<br />1562.1
<br />209.12
<br />30
<br />1945.0
<br />1:08
<br />1.14
<br />E W.009 .018
<br />.027 .036 .046
<br />.056
<br />.065 X74
<br />.75
<br />.083
<br />.83
<br />.093
<br />.90
<br />.105
<br />.99
<br />.120,
<br />.127
<br />.135
<br />'TABLE I. Tangents n;nd"Externa.ls to a 1° Curve.. III'
<br />Chard =100 ft.
<br />i Angle ;
<br />Tangent
<br />[ xternal.
<br />Int.
<br />Aug1e
<br />Tangent
<br />External
<br />Int.
<br />Angle
<br />Tangcni
<br />External
<br />22°
<br />1113.7
<br />107:24
<br />29°
<br />1451:8
<br />188,51
<br />30°
<br />1861.7
<br />294..9
<br />r3 10'1122.4
<br />.90
<br />1U8.90
<br />10'
<br />1490.7
<br />190.74
<br />10'
<br />1870.9
<br />--297.7
<br />21)
<br />1131-0
<br />110.57
<br />20
<br />1409.6
<br />192.99
<br />20
<br />1880.1
<br />300.0
<br />3U
<br />1159.7
<br />112,2)
<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 />315, 0
<br />50
<br />1526.3
<br />199.82
<br />50
<br />1907,9
<br />309.3
<br />23 ,
<br />1165.7
<br />117.33
<br />30
<br />I535.3
<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 />1920.4
<br />315.2
<br />20
<br />11&3;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 />122.6330
<br />30
<br />1562.1
<br />209.12
<br />30
<br />1945.0
<br />'321.1
<br />' 40
<br />1200.6
<br />124.41
<br />- 40
<br />1571.0
<br />211.4S
<br />40
<br />1954.3
<br />324.1
<br />50
<br />1200,2
<br />126.20
<br />50
<br />1580.0
<br />213.56
<br />50
<br />1963.G
<br />327.1
<br />.24
<br />1217.9
<br />12S.00
<br />31
<br />1589.0
<br />216.3.
<br />,38-
<br />1972.9
<br />330.2
<br />10.1226.6
<br />.325 .35I
<br />129.52
<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 />iG15.9
<br />223.5
<br />30
<br />2000.9
<br />`339.3
<br />'40
<br />1252.8
<br />135.35
<br />40
<br />1G24.9
<br />226,0
<br />40
<br />2010.2
<br />:342.4
<br />-'50 -'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 />1052,0
<br />233.4
<br />10
<br />2038,4
<br />351,8
<br />20
<br />1287.7
<br />'142.93
<br />20
<br />1GG1.0
<br />235.0
<br />20
<br />2047.8
<br />354.9
<br />'30 .
<br />1298.5
<br />144,85
<br />30
<br />IG70.0
<br />238,4
<br />_
<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 />60
<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 />218.7
<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 />-
<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 />1360.8
<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 />341751.7
<br />281.8
<br />41
<br />.2142:2
<br />387.4
<br />10
<br />1334.4
<br />164.56
<br />10
<br />1760,8
<br />264.55
<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 />169.04
<br />30
<br />1779.1 '
<br />'269.9
<br />'SO
<br />2L70.8
<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 />1419.7.
<br />173.2 7
<br />50
<br />1797.4
<br />275,3
<br />50
<br />2189 9
<br />404,2
<br />28.,
<br />1428,0
<br />175.41
<br />36
<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 />1440.3
<br />179.72
<br />_
<br />2U
<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 />184,03
<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 />Int'
<br />Angle
<br />Curve 50 101
<br />I5°
<br />20°
<br />25° 300
<br />1 35',-40'
<br />45°
<br />50° 1 55°
<br />60° 65°
<br />70°
<br />Y0°
<br />T=.06 .13
<br />.19.26
<br />39
<br />.45
<br />.5i .58
<br />.65 .72
<br />.79 .84
<br />.90
<br />.011
<br />.017
<br />.022
<br />:12
<br />.028 .034
<br />,038
<br />.0151 ,051
<br />.057 .063
<br />.070 ,076
<br />.083
<br />25°
<br />-E=.006
<br />T=.08 .16
<br />24
<br />.33
<br />.40 .49
<br />.53
<br />.67 ,75
<br />.63 .90
<br />.99 1.06
<br />1.14
<br />E =.009 .018
<br />.027
<br />.036
<br />.046 .0.16
<br />.OGS
<br />.074 ,OS3
<br />.093 .106
<br />.120 .127
<br />.135
<br />goo
<br />T=.10 .12
<br />.29
<br />.39
<br />.49 .59
<br />89
<br />.79 .E9
<br />.% 1.09
<br />1,20 1.29
<br />1.39
<br />E =.013 .023
<br />.036
<br />.051
<br />.OG5 .078
<br />.000
<br />.1031 ,116
<br />.129 .149
<br />.170 .179
<br />.188
<br />350'
<br />T= -.Ii .22
<br />.34
<br />.47
<br />.58 .69
<br />80
<br />.93 105
<br />1.17 1.29
<br />1.42 154
<br />1.66
<br />E =.016 .035
<br />.0.54
<br />.072
<br />.066 .1091'.131
<br />.153 .175
<br />.197 .213
<br />.230 .247
<br />.264
<br />4a°
<br />T=.13 :'6
<br />.40
<br />.52
<br />-:67 .80
<br />.93
<br />1.06 1.20
<br />1.34 149
<br />1.64 1:79
<br />1.94
<br />E- .023
<br />.070
<br />.093
<br />117 .141
<br />1 .172
<br />- 203 .234
<br />265 217
<br />.290 .315
<br />.311
<br />49°
<br />_.046
<br />T=.1$ 30f
<br />,44
<br />.50
<br />76 91
<br />1.06
<br />1.21 1.37
<br />1.52 1.70
<br />1.87 2,04
<br />2 -21
<br />E=.030 X60
<br />.093
<br />.119
<br />.153 .184
<br />.216
<br />254 .289
<br />.325 .35I
<br />.378% .411
<br />.445
<br />I
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