|
IV TABLE I. = Tangents'dnd Externals to a I' Curve.
<br />Chord= 100 ft.
<br />Int.
<br />Angie
<br />Tangent
<br />External
<br />Inc.Int.
<br />Angle
<br />Tangent
<br />External
<br />Angle
<br />Tangent
<br />External
<br />43°
<br />2257.0
<br />428.5
<br />50°
<br />2671.5
<br />592.3
<br />570
<br />3110.9
<br />790.1
<br />-1.0`
<br />2266.6
<br />432.0
<br />101
<br />2681_9
<br />596.6
<br />10'
<br />3121.7
<br />795.2
<br />20
<br />2270.2
<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 />440,4
<br />50
<br />2722.7
<br />614.0
<br />'50
<br />3165.1:
<br />816:1
<br />d4
<br />2314.9
<br />450,0
<br />51
<br />2732.9
<br />618.4
<br />58
<br />3170.0.
<br />S21.4
<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 />2363.5
<br />468.4
<br />50
<br />2734.2
<br />640.7
<br />50
<br />3230.7
<br />848.1
<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 />858.0
<br />•,•• 20
<br />2392.8
<br />-479.6
<br />20
<br />2815.2
<br />654.3
<br />20
<br />3263.7'
<br />804.3
<br />80
<br />2402.6
<br />453,4
<br />30
<br />2825.6
<br />658.8
<br />30
<br />3274.8
<br />860.8
<br />40
<br />2412.4
<br />487,2
<br />40
<br />2835.9
<br />663.4
<br />'4D
<br />3285.8
<br />875.3
<br />50
<br />2422.3
<br />491,0
<br />50
<br />2846,3
<br />668.0
<br />5D
<br />3206.9
<br />880,8
<br />46
<br />2432.1,
<br />494.8
<br />53
<br />2856.7
<br />672,7
<br />00
<br />3308.0
<br />886.4
<br />to
<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.S
<br />502.5
<br />20
<br />2877.5
<br />G82.0
<br />20
<br />.3330.3
<br />897.5
<br />30
<br />2461:7
<br />500.4
<br />:M
<br />28SS.0
<br />686.7
<br />30
<br />3341.4
<br />.903.2
<br />4.0
<br />2471.5
<br />51.0.3
<br />40
<br />2&98,4
<br />691.4
<br />40
<br />3352.6
<br />908.8
<br />50
<br />2481.4
<br />514.3
<br />50
<br />2908.9
<br />-696.1
<br />50
<br />3363.6
<br />914.5
<br />47
<br />2491.3'
<br />513:2
<br />54
<br />2910.4
<br />700.9
<br />61
<br />3375.0
<br />920.2
<br />10
<br />2501.2
<br />522.2
<br />10
<br />2029.9
<br />705.7
<br />10
<br />3386.3
<br />925.9
<br />20
<br />2511.2
<br />52G.1
<br />20
<br />2940.4
<br />710,5
<br />20
<br />3397.5
<br />931.G
<br />30
<br />2521.1
<br />530.1
<br />30
<br />2951.0
<br />715.3
<br />30
<br />3408.8
<br />937.3
<br />40
<br />2531.1
<br />534.2
<br />40
<br />29G1.5
<br />720.1
<br />40
<br />3420.1
<br />943.1
<br />50
<br />2541.0,
<br />533.2
<br />50
<br />2072.1
<br />725,0
<br />50
<br />3431.4
<br />948.9
<br />48
<br />2551.0
<br />542.2
<br />55
<br />2982.7
<br />729,9
<br />62
<br />3442.7
<br />054.8
<br />10
<br />2561.0
<br />546.3
<br />LO
<br />2993.3
<br />734,8
<br />10
<br />3454.1
<br />960.6
<br />20
<br />2571.0
<br />550.4
<br />20
<br />3003.9
<br />739.7
<br />20
<br />3465.4
<br />966.5
<br />30
<br />2581.0
<br />554.5
<br />30
<br />3014.5
<br />744,6
<br />30
<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 />084.3
<br />49
<br />2611.2
<br />566,9
<br />56
<br />3046.5
<br />759,6
<br />63
<br />3511.1
<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 />579.5
<br />30
<br />3078.7
<br />774.7
<br />30
<br />3545.6
<br />1008.3
<br />40
<br />2651.5
<br />583.8
<br />40
<br />3080.4
<br />779,8
<br />40
<br />3557.2
<br />1014.4
<br />50
<br />2661.6
<br />588.0
<br />50.
<br />3100.2
<br />7S4.9
<br />50-
<br />3563.7
<br />1020.5
<br />Corrections to be Added (T=Tangent.' E=External.)
<br />Angle
<br />Curve 5° 1
<br />10°
<br />la 20° 25° 30°
<br />35°
<br />40° 1 45° 50°
<br />1 55° 1 60°
<br />65° 700
<br />40°
<br />T=.13
<br />.26
<br />.40 ".53 .67 .80
<br />.93
<br />.106 1.20 1.34
<br />1.49 1.64,
<br />1.70 1.94
<br />4639.8
<br />E=_023
<br />_046
<br />.070 .093 .117 .141
<br />.172
<br />.203 .234 .265
<br />.277 299
<br />.315 .341
<br />45°
<br />T=.15
<br />.30
<br />.44 .60 .76 .91
<br />1.06
<br />1.21 1.37 1.52
<br />1.70 1.87'
<br />2.04 2.21
<br />1322.9
<br />E=.030
<br />.000
<br />.093 119 .153 .134
<br />.216
<br />.254 ,289 .325
<br />.351 .378
<br />.411 .445
<br />so.
<br />T-.17
<br />.34
<br />.51 .6S .85 1.02
<br />1:19
<br />'1.36 1.54 1.72
<br />1.91 2.10
<br />2.29 2.48
<br />40
<br />E =.037
<br />.075
<br />.116 .151 .169 .227
<br />.260
<br />.305 .345 .384
<br />.420 .467
<br />.508 .550
<br />55°
<br />T=19
<br />.38
<br />.57 .76 95 1.14
<br />132
<br />1.52 1.72 1.92
<br />2.14 2.35
<br />2.56 2.77
<br />3650.2
<br />E=.046.
<br />.093
<br />142 .188 236 .283
<br />.332
<br />3.31 .420 .479
<br />.530, .582
<br />.041 .700
<br />60°
<br />T=.21
<br />.42
<br />.63 84 1.05 1.27
<br />149•
<br />1.71 1.94 2.17
<br />2.38 2.60
<br />2.83 3.07
<br />1704.7
<br />1 =.056
<br />.112
<br />.168 .225 .283 .340
<br />.398
<br />.457 .515 .575
<br />MG -AW
<br />.774 .851
<br />6°
<br />T=,23
<br />.46
<br />89 93 1.16 1.40
<br />1.64
<br />1.88 2.13 2.38
<br />2.63 2.88
<br />3.13 3.39
<br />30.
<br />E=.OB7
<br />.135
<br />204 273 .343 .412
<br />.483
<br />.554 .625 .697
<br />.711 .845
<br />.922 1.01
<br />TAEL> I..- Tangents and E%ternals to a V 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 />780
<br />4639.8
<br />1643.0
<br />10'
<br />3591.9,
<br />10$2.8
<br />1.0'
<br />4099.5
<br />1315.6
<br />10'
<br />4653.0
<br />1651.7
<br />20
<br />3603.5
<br />1039.0
<br />20
<br />4112.1
<br />1322.9
<br />20
<br />4667.4
<br />1660.5
<br />30
<br />3615.1
<br />1045.2
<br />30
<br />4124.8
<br />1330.3
<br />30
<br />4681.3
<br />1669.2
<br />40
<br />3626.8
<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 />50
<br />4150.1
<br />1345.1
<br />50
<br />4709.2
<br />1686.9
<br />65
<br />3650.2
<br />1063.9
<br />72 '
<br />4162.8
<br />1352:6
<br />19
<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 />4188.5
<br />1367.6
<br />20,
<br />4751.2
<br />1713.7
<br />30
<br />3685.4
<br />1082.9
<br />30
<br />-4201.2
<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 />1731.7
<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 />3720.9
<br />1102.2
<br />73
<br />4239.7
<br />1398.0
<br />80,
<br />4807:7
<br />1749.9
<br />10
<br />3732.7
<br />110S.6
<br />10
<br />4252.6
<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 />4836.2
<br />1768,2'
<br />30
<br />3756:,5
<br />1121.7
<br />30
<br />4278.5
<br />1421,2
<br />3D
<br />4S50.5
<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 />1786.7
<br />50
<br />3780.4
<br />1134.8
<br />50_
<br />4304.6
<br />1436.8
<br />5'0
<br />4579.2
<br />1796.0
<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 />1148.0
<br />'10
<br />4330.7
<br />1452.5
<br />10
<br />4908.0
<br />1814.7
<br />20
<br />3816.4
<br />1 54.7
<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 />4356.9
<br />1463.4
<br />30
<br />4937.0
<br />1833.6
<br />40.
<br />3840.5
<br />1.168.1
<br />40
<br />4370.1
<br />1476.4
<br />40
<br />4951.5
<br />1843.1
<br />50
<br />3352.6
<br />1174.8
<br />50
<br />4383.3
<br />1484.4
<br />.50
<br />4966.1
<br />1852.0
<br />GS
<br />3864.7
<br />1181'.6
<br />75
<br />4396.5
<br />1492.4
<br />82
<br />4980.7
<br />£862.2
<br />10
<br />3876.8
<br />1188.4
<br />10
<br />4409.8
<br />1500.5
<br />10
<br />4995.4
<br />1871,8
<br />120
<br />3SS9.0
<br />1195,2-
<br />20
<br />.4423.1
<br />1508.6
<br />20
<br />5010.0
<br />1881.5
<br />30
<br />3901.2
<br />1202.0
<br />30
<br />4436.4
<br />1.516.7
<br />30
<br />5024.8
<br />1891,2
<br />40
<br />3913.4
<br />1208.9
<br />•40
<br />4449.7
<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 />G9
<br />3937.9
<br />1222.7
<br />76
<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 />3962.5
<br />1236.7
<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 />156B.3
<br />30
<br />5113.9
<br />1950.3
<br />40
<br />3997.2
<br />1250.8
<br />40
<br />4530.4
<br />1574.7
<br />40
<br />5123.9
<br />1960,2
<br />50
<br />3999.5
<br />1257.9
<br />50
<br />4544.0
<br />1583.1
<br />50,
<br />5143.9
<br />1970,3
<br />70
<br />4011.9
<br />1265.0
<br />77
<br />4557.6
<br />1591,6
<br />84
<br />5159.0
<br />1980.4
<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 />4036.8
<br />1273.3
<br />20
<br />4584.8
<br />160S.6
<br />20
<br />5189.3
<br />2000.6
<br />30
<br />4099.3
<br />1286.5
<br />30
<br />4598.5
<br />1617.1
<br />30
<br />5204.4
<br />2010,8
<br />40
<br />4061.8
<br />1293.6
<br />40
<br />4612.2
<br />1625.7
<br />40
<br />5219.7
<br />2021,1
<br />50
<br />4074.4
<br />1300.9
<br />50
<br />4626.0
<br />1634.4
<br />50
<br />5234.9
<br />'2031,4
<br />Corrections to be Added (T =Tangent, E = External.)
<br />Carve 5°
<br />10°
<br />15*
<br />20'
<br />25°
<br />30°
<br />35° 40°
<br />1 45°
<br />50°
<br />55°
<br />60°
<br />65° 701-
<br />4 qle
<br />600 T=.21
<br />42
<br />.63
<br />.84
<br />1.05
<br />1.27
<br />1.49 1.71
<br />194
<br />2.17
<br />2.38
<br />2 60
<br />2.83 U? --
<br />.07-`
<br />E =.056
<br />E=.056
<br />112
<br />.168
<br />225
<br />.283
<br />.340
<br />.398 .457
<br />.51$
<br />.575
<br />.636
<br />,697
<br />,774 ,851'
<br />65° T=,23
<br />.45
<br />.69
<br />.93
<br />L16
<br />1.40
<br />1.64 1.88
<br />2,13
<br />2.38
<br />2.63
<br />2.88
<br />3.13 3,39
<br />E =.067
<br />.13S
<br />.204
<br />.273
<br />.343
<br />.412
<br />.483 .554
<br />.025
<br />.697
<br />.711
<br />.845
<br />.922 1,01 .
<br />70° T=,25
<br />.51
<br />.76
<br />1.02'
<br />1.28
<br />1.54
<br />MO 2.06 "
<br />2.33
<br />2.60
<br />2.88
<br />3.16
<br />3.44 3,72
<br />E=.080
<br />.159
<br />.240
<br />.321
<br />,403
<br />.485
<br />.568 .652
<br />.735
<br />.819
<br />.905
<br />.9%
<br />1,08 1.17,
<br />15° T=.27
<br />.50
<br />.83
<br />1.12
<br />1.40
<br />1.69
<br />L(58 2.27
<br />2.57
<br />2.87
<br />3.16
<br />3.47
<br />3.78 4.09
<br />E=.09D
<br />.182
<br />.286
<br />.383
<br />.480
<br />.578
<br />.678 .777
<br />.877
<br />.977
<br />1.07
<br />1.18
<br />1.29 1.39
<br />80° T=.30
<br />.01
<br />.91
<br />1.22
<br />1.53
<br />1.84
<br />2.15 2.48
<br />2.78
<br />3.10
<br />3.44
<br />3.78
<br />4.12 4.45
<br />E =.110
<br />.220
<br />.332
<br />.445
<br />.558
<br />.671
<br />.787 .903
<br />1.02
<br />1.13
<br />1.25
<br />1.38
<br />1.50 1.62
<br />850 T=.33
<br />06
<br />1.00
<br />1,33
<br />1.68
<br />2,02
<br />2.36 2.70
<br />3.05
<br />3.40
<br />3.77
<br />4.14
<br />4.55 4.89
<br />E =.128
<br />.250
<br />.391
<br />.524
<br />.657
<br />.700
<br />.920 1.06
<br />1.20
<br />11.34 J1.47
<br />1.62
<br />11.76 1.91
<br />A
<br />
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