|
IV TABLE I. - Tangents and Externals to a 1* Curve,
<br />Chord=100 it.
<br />Int.
<br />Angle
<br />Tangent
<br />External
<br />Int.
<br />Angle
<br />Tan ant External
<br />g-.
<br />Int.
<br />Angle
<br />aril
<br />Tan aril
<br />Tang
<br />F,xiernal
<br />External
<br />2257.0
<br />42S.5
<br />501
<br />2671:8
<br />592.3
<br />57°
<br />3110.9
<br />790.1
<br />10'
<br />2266.6
<br />432.0
<br />10'
<br />2681.9
<br />+ 596.6
<br />10'
<br />3121.7
<br />795.2
<br />20
<br />2276.2
<br />435.6
<br />20
<br />2692.1
<br />600,9
<br />20
<br />3132.6
<br />800.4
<br />30
<br />2285.9
<br />439.2
<br />30
<br />2702:3
<br />605.3
<br />30:
<br />3143.4
<br />805.6
<br />40
<br />2295.6
<br />442.8
<br />40
<br />2712.5
<br />609.6
<br />40
<br />3154.2
<br />810.9
<br />50
<br />2305.2.
<br />446.4
<br />50
<br />2722.7
<br />614.0
<br />50
<br />3165.1
<br />816.1
<br />44
<br />•2314.9
<br />450.0
<br />51 1
<br />2732.'0
<br />G18:4.
<br />58
<br />3176.0
<br />821.4
<br />.10
<br />2324.6
<br />453.6
<br />10 '
<br />2743:1
<br />.622.8
<br />10
<br />3186:9
<br />826.7
<br />'.20
<br />2334.3
<br />457,3
<br />20
<br />2753.4
<br />627_•:2
<br />20
<br />3197.8
<br />832.0
<br />30
<br />.2344.1
<br />461.0'
<br />30
<br />2763.7•
<br />631.7
<br />30
<br />3208:8
<br />837.3
<br />40
<br />2353.8
<br />464.6
<br />40
<br />2773.9
<br />636,2
<br />40
<br />3219.7
<br />842.7
<br />50
<br />2303.5
<br />468.4
<br />50
<br />2784,2
<br />640.7
<br />„ 50
<br />3230,7
<br />849.1
<br />45
<br />2373.3
<br />472.1
<br />52
<br />2794.5.
<br />645.2
<br />59
<br />.3241.7
<br />853.5
<br />10
<br />2383.1
<br />475.8
<br />10
<br />2804.9
<br />649.7
<br />10
<br />3252.7
<br />858.9
<br />- 20
<br />2392.8
<br />479.6
<br />20
<br />2815.2
<br />654.3
<br />20
<br />3263,7
<br />864.3
<br />30
<br />2402.6
<br />483.4
<br />30
<br />2825.6
<br />658.8
<br />.30
<br />3274,8
<br />. 869.8
<br />40
<br />2412.4
<br />487,2
<br />40
<br />2535.9
<br />663.4
<br />40
<br />3285:8
<br />875.3
<br />50
<br />2422.3
<br />491,0
<br />50/
<br />2846.3
<br />•668.0
<br />_ 4.50
<br />3296:9
<br />,.880.8
<br />1790.0
<br />67
<br />3792.4
<br />1141.4
<br />74
<br />4317.6
<br />1444.6
<br />81
<br />4893-6
<br />46-
<br />2432.1
<br />494:8•
<br />53, r/
<br />•2856.7
<br />072.7
<br />60
<br />3308:0
<br />836,4
<br />10
<br />2441.9.
<br />498.7
<br />10
<br />2867.1.
<br />677.3
<br />10 '
<br />3319.-1
<br />892.0
<br />20
<br />2451.8
<br />502,5
<br />:.-120
<br />2877.5
<br />682.0
<br />20
<br />3330.3
<br />897,5
<br />30
<br />2461-7.
<br />506.4
<br />'30
<br />2883.0
<br />686.7
<br />30
<br />3341.4
<br />903.2
<br />40
<br />2471-5'
<br />510.3
<br />40
<br />2898.4.
<br />691.4
<br />40
<br />3352.6
<br />903.8
<br />60
<br />2481.4
<br />.514.3
<br />50
<br />2908:0
<br />696.1
<br />50
<br />3363.8
<br />014.5
<br />47
<br />249E 3
<br />518.2,
<br />54
<br />2919.4
<br />700.9
<br />61 ?:W
<br />'3375.0
<br />920.2
<br />10
<br />2501•.2
<br />522.2
<br />10
<br />2929,9
<br />705.7
<br />10
<br />3386.3
<br />925,9
<br />20
<br />2511.2
<br />526.1
<br />20
<br />2940.4
<br />-710.5
<br />-20
<br />3397.5
<br />931.6
<br />30
<br />2521.1
<br />530.1
<br />30
<br />295 L 0
<br />715.3
<br />30
<br />3408.8
<br />037.3
<br />40
<br />2531.1
<br />134.2
<br />40
<br />2961.5
<br />720.1
<br />40
<br />3420:1
<br />943.1-
<br />50
<br />2541,0
<br />538.2
<br />50
<br />2972.1
<br />725,0
<br />50
<br />343114
<br />948.9
<br />46
<br />2551.0
<br />542.2
<br />55
<br />2982.7.
<br />729.9
<br />62
<br />3442.7,
<br />954.5
<br />10
<br />'256I.0
<br />546.3
<br />10
<br />2993.3
<br />734.8
<br />10
<br />3454.;
<br />960.6
<br />20,
<br />2571.0
<br />550.4
<br />20
<br />3003.9
<br />739.7
<br />20 .
<br />30
<br />966.5
<br />30
<br />2581.0
<br />554.5
<br />30
<br />3014.5
<br />744.6
<br />.�30
<br />,3465.4
<br />3476.8'
<br />972.4
<br />40
<br />2591.0•
<br />558.6•
<br />40
<br />3025:2
<br />749.6
<br />•;40
<br />3488.3'
<br />978.3
<br />50
<br />2601,1
<br />562.8
<br />50
<br />3035.8
<br />. 754.6
<br />,,50
<br />3499.7'
<br />- 984,3
<br />46
<br />2611.2
<br />566.9
<br />56
<br />3046.5
<br />7.59.6
<br />63 .•
<br />9511.1
<br />990.2
<br />10
<br />2621.2
<br />571.1
<br />10
<br />3057.2
<br />764.6
<br />10
<br />3522.6
<br />996.2
<br />20
<br />2631.3
<br />575.3
<br />20
<br />3067.9
<br />769.7
<br />20
<br />3534.1
<br />1002.3
<br />30
<br />2641.4
<br />570.5
<br />30
<br />3078.7
<br />774.7
<br />30
<br />3545.8
<br />1008.3
<br />40
<br />2651.5
<br />583.8
<br />40
<br />3089.4
<br />779.8
<br />40
<br />3557,2
<br />1014.4
<br />60 '
<br />2601.6
<br />588.0
<br />50
<br />3100.2
<br />784.9
<br />50
<br />3568:7
<br />1020.5
<br />TASLi.I. - Tangents a.id'£xternals to a 1° Curve: V
<br />Chord =100 ft.
<br />Int.
<br />Angle
<br />Corrections to be Added (T=Tangent. E=External.).
<br />Angle
<br />- Curva 5°
<br />10° 15° 20° '23° 30° 35° 40° 45° 50° 55° -60° 65° 70°
<br />40°
<br />T=.13
<br />.26 .40 .53 .67 .90 '-93 .106 1.20 1.34 1.49 1.64 1,79 1.94
<br />External
<br />E=.023
<br />.045 .070 .093 A17 .141 .172 .203 _,234 .265 .277 00 ..315 .341
<br />45°
<br />T=:15
<br />.30 .44 ..60 .76 .91 1.06 1.21 1.37 1.52 1.70 1.87 2.04 2.21.
<br />1308.2
<br />E=.030
<br />.060 .093 .119 .153 .184 .216 .254 .289 .325 -.351 .,378 .411 .445
<br />50°
<br />T=.17
<br />,34 '.51 .68 .85 1.02 1.19 1.36 1.54 1.72 1-91 2.10 2.29 2.48
<br />_
<br />E =.037'
<br />.075 .116 .151 .189 .227 .266 .305 .345 .384 .425 .467 .508 .550
<br />55°
<br />T=
<br />.57 .78 O5 1.19 1.32 1,52 L 2 1.92 2.14 2.35 2.58 2.77
<br />1651.7
<br />E-:0'4'6 .
<br />.093 .142 ,188 236 .283 .332 3.31 ,420 ..479 .530 .582 .641 .700
<br />6U°
<br />.T=,21
<br />.42 .63 .84 1.05 1.21 L49 1.7t '1.94 2,17 2.38�28 ,
<br />1322.9
<br />E =.056
<br />!112 .108 .225..283 .340 .398 .457 .516 .575 .6365°
<br />1660.5
<br />T=.23
<br />4G .G9 .93 1,18 L40 1.64 1,88 2,13 2.38 2,63E=.067
<br />1045.2
<br />30
<br />.135 .204 .273 .343' .412 .483 .554 .625 .697 .71
<br />TASLi.I. - Tangents a.id'£xternals to a 1° Curve: V
<br />Chord =100 ft.
<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 />64°
<br />3580.3
<br />1026.6
<br />71°
<br />4086.9
<br />1308.2
<br />78°
<br />4639.8
<br />1643.0
<br />to'
<br />3591.9'
<br />1032.8
<br />10'
<br />4099.5
<br />1315.6
<br />10'
<br />4353.6
<br />1651.7
<br />20
<br />3603.5
<br />1039.0
<br />20
<br />4112.1'
<br />1322.9
<br />20
<br />4367.4
<br />1660.5
<br />30
<br />3615:1
<br />1045.2
<br />30
<br />4124.8
<br />1'330.3
<br />30
<br />4081.3
<br />1669.2
<br />40-
<br />8626.8
<br />1051.4
<br />40
<br />4137.4
<br />1337.7
<br />40
<br />4695.2
<br />1678.1
<br />50
<br />3638.5
<br />1057.7
<br />60
<br />4150,1
<br />1345.1
<br />50
<br />4709.2
<br />1680.9
<br />6.r -
<br />'H50.2
<br />1063.9
<br />72
<br />4162,8
<br />1352.6
<br />79
<br />4723.2.
<br />1695.8
<br />10
<br />3661.9
<br />1070.2
<br />10'
<br />4175.6
<br />1360.1
<br />10
<br />4737.2
<br />1704.7
<br />20
<br />3673:7
<br />1076.6
<br />20
<br />41S8.5
<br />1367.6
<br />20
<br />4751.2
<br />1713.7
<br />30
<br />3685.4
<br />1082.9
<br />30
<br />4'201.2
<br />1375.2
<br />30
<br />4765.3
<br />1722.7
<br />40
<br />3697.2
<br />1089:3
<br />40
<br />4214.0
<br />1382.8
<br />40
<br />4779.4
<br />173 1. 7
<br />50
<br />3709.0
<br />1095.7
<br />50
<br />4226.8
<br />1390.4
<br />50
<br />4793.6
<br />1740.8
<br />66
<br />9720:9
<br />1102:2'
<br />73'.
<br />`4239.7.
<br />1.393:0
<br />80
<br />4807.7
<br />1749.9
<br />10
<br />3732•:7
<br />1108.6;
<br />10
<br />4252''G
<br />-1405.7
<br />10
<br />4822.0
<br />1759,0
<br />20
<br />3744.6;
<br />1115.1
<br />20
<br />4265.6
<br />1413.5
<br />20
<br />'4336.2
<br />•1768.2
<br />30
<br />37:;6.5
<br />1121.7
<br />30
<br />4278.5
<br />1421.2
<br />30
<br />4850.5
<br />1777.4
<br />40
<br />3768.5
<br />1128.2
<br />40
<br />4291.5
<br />1429.0
<br />40'
<br />.4864.8
<br />1780,7
<br />50
<br />37SO.4
<br />1134.8
<br />50
<br />4304.6
<br />1436.8
<br />50
<br />4379.2
<br />1790.0
<br />67
<br />3792.4
<br />1141.4
<br />74
<br />4317.6
<br />1444.6
<br />81
<br />4893-6
<br />1805.3
<br />10
<br />3804.4'
<br />114S. C'
<br />10
<br />4330.7
<br />1452.5
<br />10
<br />4908.0
<br />IS14.7
<br />20
<br />3316.4
<br />1154.7.
<br />20.
<br />4343.8
<br />1460.4
<br />20
<br />4922.5
<br />1824.1
<br />30
<br />3828.4
<br />1161.3
<br />30
<br />4350.9
<br />1408.4
<br />30
<br />4937.0
<br />1833.6
<br />40
<br />3840.5
<br />1168.1
<br />40
<br />4370.1
<br />1470.4
<br />40
<br />4951.5
<br />1843:1
<br />S0
<br />3852,6
<br />1174.8
<br />50.
<br />. 4383.3
<br />1484,4
<br />SO
<br />4066.1
<br />1852.6
<br />68
<br />2864'.7
<br />1181.6
<br />75
<br />4396.5
<br />1492.4
<br />82-
<br />4980.7
<br />1862.2
<br />10
<br />3876.8
<br />1188.4
<br />10
<br />4409.8
<br />1500.5
<br />10
<br />4995.4
<br />7871.8
<br />20
<br />3889.0
<br />1195.2
<br />20
<br />4423.1
<br />1503.6
<br />20
<br />5010.0
<br />1881.5
<br />30
<br />3901.2
<br />1202.0
<br />30
<br />4436.4
<br />1516.7
<br />30
<br />5024.8
<br />1891.2
<br />40
<br />8913.4
<br />1208.9
<br />..40.
<br />4449.;
<br />1524.9
<br />,,40
<br />5039.5
<br />1900.9
<br />50
<br />3925.6
<br />1215.8
<br />50:
<br />4463.1
<br />1533.1
<br />50
<br />5054.3
<br />1910.7
<br />69
<br />3937.0
<br />1222.7
<br />70
<br />4476.5
<br />1541.4
<br />83
<br />5069.2
<br />1920.5
<br />10
<br />'3950.2
<br />1229.7
<br />-10
<br />4489.9
<br />1549.7
<br />10
<br />5084.0
<br />1930.4
<br />20
<br />8962.5
<br />1.236.7
<br />20
<br />4503:4,
<br />1558.0
<br />20
<br />5099.0
<br />1940.3
<br />30
<br />3974.8
<br />1243.7
<br />30
<br />4516.9
<br />1566.3
<br />30
<br />5113.9
<br />1950.3
<br />40
<br />3987.2
<br />1250.8
<br />40
<br />4530.4
<br />1574.7
<br />40
<br />5128.9
<br />1960.2
<br />50
<br />3909.5
<br />1257.0
<br />50
<br />4514.0
<br />]583.1
<br />50
<br />5143.9
<br />1970.3
<br />TO
<br />4011.9
<br />1265.0
<br />72
<br />4557.6
<br />1591.6
<br />84
<br />5159.0
<br />1930.4
<br />10
<br />4024.4
<br />1272:1
<br />10
<br />4571.2
<br />1600.1
<br />10
<br />5174.1
<br />1990.5
<br />20
<br />.4036':S
<br />1279.3
<br />20
<br />4,584.8
<br />1608.6
<br />20
<br />5189.3
<br />2000.6
<br />30
<br />4049.3
<br />1286.5
<br />30
<br />9599.5
<br />1617.1
<br />30'
<br />5204.4
<br />2010.8
<br />40
<br />'4061.5
<br />1293.6
<br />40
<br />4012.2
<br />1025.7
<br />40
<br />5219.7
<br />2021.1
<br />50
<br />4074.4
<br />1300.9
<br />50
<br />4626.0
<br />1034.4
<br />50
<br />5234.9
<br />2031.4
<br />Corrections to be Added (T =Tangent. E = External.)
<br />Angle
<br />Curve 5°
<br />10° 15° 20°
<br />25'
<br />30°
<br />35°
<br />40°
<br />45°
<br />50°
<br />55°
<br />60° 65° 70°
<br />T=.21
<br />.42 :63 .84
<br />1.05
<br />l.21
<br />1.49
<br />1.71
<br />1.94
<br />2.I7
<br />2.38
<br />2.60 2.83 3.07
<br />r=.058
<br />.112 .168 .225
<br />.283
<br />.310
<br />.398
<br />.457
<br />.516
<br />.675
<br />.036
<br />,697 ,774 ,851
<br />65°
<br />T=.23
<br />.46 .69 .93
<br />1:16
<br />1,40
<br />1.64
<br />1,88
<br />2.13
<br />2.38
<br />2.63
<br />2.88 3.13 3.39
<br />:E -.067
<br />.135 .204 .273
<br />.343
<br />.412
<br />.483
<br />-.554
<br />.625
<br />.697
<br />.711
<br />.845 .922 1.01
<br />70°
<br />T =.25
<br />.51 .76 1,02
<br />1.28
<br />1.54
<br />1.80
<br />2.06
<br />2.33
<br />2.60
<br />2.68
<br />3.16 3.44 3.72
<br />E =.080
<br />.159 .240 .321
<br />AM
<br />.485
<br />.568
<br />.652
<br />.735
<br />.819
<br />.905
<br />AN 1.08 1.17
<br />750
<br />T-.27
<br />.56 .83 1.12
<br />1.40
<br />1.69
<br />1.98
<br />2.27
<br />2.57
<br />2.87
<br />3.16
<br />3.47 3.78 4.09
<br />E =.095
<br />.182 .286 .383
<br />ASO
<br />.578
<br />:678
<br />.777
<br />.877
<br />.977
<br />1.07
<br />1.18 1.20 1.39
<br />8o°
<br />7=30
<br />61 .91 1,22
<br />1-53
<br />1.84
<br />2-15
<br />2.46
<br />2.78
<br />3.10
<br />3.44
<br />3.78 4.12 4.46
<br />E=.110
<br />.220 .332 .445
<br />.658
<br />.871
<br />.787
<br />.903
<br />1.02
<br />1.13
<br />1.25
<br />1.38 1.50 1.62
<br />85.
<br />T=.33
<br />66 1.00 1.33
<br />1.68
<br />2,02
<br />2.36
<br />2.70
<br />3,05
<br />3.40
<br />3.77
<br />4-14 4.55 4.89
<br />E=-129
<br />.259 .391 .524
<br />.657
<br />.790
<br />.926
<br />11.06
<br />1.20
<br />1.34
<br />1.47
<br />'1.62 1.76 1.91
<br />uo a
<br />E
<br />yip
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