|
IV TAatEJ.,- Tangents and. Externals to.a 1° Curve.
<br />• I Chord .=100 ft.
<br />Angle
<br />Tangent
<br />External
<br />Int:Int.
<br />Angle*
<br />Tangent External
<br />Angle
<br />Tangent
<br />External
<br />43°
<br />2257.0
<br />428.5,
<br />.50°
<br />2671.8
<br />592.3
<br />57°
<br />3110.9
<br />790.1
<br />10'',,2266.6
<br />50°
<br />432.0:
<br />'• 10'
<br />2681.9.
<br />596.6
<br />-•'.10'
<br />3121.7
<br />795.2
<br />cr
<br />20
<br />2276.2
<br />ti 435.6,
<br />•.20
<br />.2692.1
<br />600.9.
<br />`_ 20
<br />`3132.6
<br />800.4
<br />30
<br />2285. 9;
<br />=.067 135 .204 .273
<br />30
<br />'2702.3
<br />.605.3
<br />-30
<br />3143.4
<br />805.6
<br />40 '
<br />"2295.6'
<br />,439.2:
<br />,442.8`
<br />40 I
<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,
<br />2732.9;
<br />618.4'
<br />58
<br />3176.0
<br />821.4
<br />10
<br />-2324.6,
<br />453:8
<br />-'.10;i
<br />,2743.1
<br />622.8,
<br />`627:2.
<br />10 '
<br />:3186.9
<br />826.7
<br />.20
<br />2334:3
<br />,457.3.
<br />'20'.
<br />2753.4
<br />4183.5
<br />20
<br />3197.8
<br />832.0
<br />1713.7
<br />2344:1,
<br />'461.0'
<br />.30.
<br />2763.7'
<br />631.7
<br />30 '
<br />3208.8
<br />837.3
<br />,30
<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 />f 50
<br />2363.5
<br />488.4;
<br />'. ,' a0',
<br />.2784.2
<br />,640.7
<br />':'50 v
<br />. 3230.7
<br />543.1
<br />1740;8
<br />66' • _ .
<br />3720.9
<br />1102.2'
<br />73- 7
<br />; 4239.7
<br />' 1398.0
<br />80
<br />4807.7
<br />45
<br />2373.3'
<br />472.11
<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 1
<br />'2402.6
<br />483.4-
<br />30
<br />'2525:6
<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 />50
<br />3296.9
<br />' 8S0.8
<br />46 .
<br />2432.11.
<br />494.81
<br />53
<br />2856.7'
<br />672.7
<br />60
<br />3308.0
<br />886.4
<br />10
<br />20
<br />498.7,
<br />10
<br />'2867.1•
<br />677.3-
<br />10
<br />3319.1
<br />892.0
<br />20
<br />.2441.9
<br />`2451.8
<br />;502.5
<br />1161;3
<br />2577.5
<br />682.0
<br />20 ,
<br />-3330.3
<br />897.5
<br />30
<br />'2461.7
<br />506.4
<br />r20
<br />30
<br />2SSS.0
<br />686.7
<br />30 ;
<br />3341.4
<br />903.2
<br />40
<br />2471.5
<br />3852:6
<br />40
<br />2893.4
<br />691.4;
<br />40
<br />3352.6
<br />908.8
<br />1852.6
<br />2481.4
<br />.510:3
<br />514.3
<br />50
<br />2908.9,
<br />696.1
<br />50
<br />3383.8
<br />914.5
<br />47. .
<br />2491.3
<br />518.2.
<br />54
<br />2919.4
<br />700.9'
<br />61
<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 />2511.21
<br />526.1
<br />'.20
<br />2040.4
<br />710.5
<br />- -20
<br />',3397.5
<br />931.6
<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 />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 />'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 />954.8
<br />10
<br />2561.0
<br />546.3
<br />"10
<br />2993.3
<br />734.8;
<br />`. 10 ,
<br />.3454.1
<br />060.6
<br />`20
<br />2571.0
<br />550:4-
<br />20
<br />3003.0
<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 />t;,
<br />30
<br />3476.8
<br />972.4
<br />40
<br />2591.0
<br />3999.5
<br />40
<br />3025.2
<br />749.6'
<br />40 .
<br />'3488.3.
<br />978.3
<br />50
<br />-2601'.1
<br />•558.6=
<br />562.8
<br />50
<br />3035.8
<br />754.6.
<br />: "50
<br />3499.7`
<br />984.3
<br />1980:'4
<br />2611.2
<br />566.9
<br />56
<br />3046.5
<br />759.6
<br />63
<br />3511.1
<br />990.2
<br />-49
<br />10
<br />2621.2
<br />571.1
<br />._
<br />10
<br />3057.2
<br />764.6
<br />'10 .
<br />3522.6
<br />996.2
<br />20
<br />30
<br />575.3.
<br />20
<br />3067.9
<br />769.7-
<br />20
<br />3534.1
<br />1002.3
<br />30
<br />.2631.3
<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 />2851.5-
<br />`553.8
<br />40
<br />3089,.4
<br />779.8.
<br />40
<br />3557.2
<br />1014.4
<br />1020.5
<br />50
<br />2681.6
<br />11588.0
<br />50
<br />3100.2
<br />734.9
<br />50
<br />3563.7
<br />Corrections to be ;Added- (T = Tangent. E = External.)
<br />Tmm ' - Tangents and Externals to a 1'5Curve. V
<br />Chord =100 f t. -
<br />Angle
<br />Curve 5° 109 15° 20°
<br />25° 309 35° 40° 45o 500 -55° 60° 65° 70°
<br />Angle
<br />Tangent
<br />External
<br />40°
<br />T=13 .26 .40 -.53
<br />E=.023 .046 .070 .093
<br />'.67 .80 .93 .106 1.20 1.34 1.49 1.64 1.79 1.94
<br />.117 .141 .172 .203 .234 .265, .277 ' 290 .315 .311
<br />64°
<br />3580:3
<br />.21 1 .37 1 ,21
<br />.87 2.411 .04 2.445
<br />.52 1.351 1
<br />.91 1.216 1
<br />45'
<br />E=.030 119
<br />103 .134 254 289 325 378
<br />78°'
<br />.:080 .093
<br />T=.17 .34 .51 .68
<br />.85 1:02 1.19 1.36 T. 1.72 ' 1'.91 2.10 2.20 2:590
<br />50°
<br />E=.037 .075 -.116 .151
<br />.189 .227 .266 .305 .345 .334 .425 .467 .509
<br />'• 10'
<br />4099.5
<br />3-5
<br />-92 2.530 2
<br />-52 1.420 1
<br />1.233 1.332 .32 13
<br />2.641 .56 2.700
<br />'E=.046 - 142 .138
<br />.236 81 479 582
<br />20:
<br />.093
<br />T=.21 .42 63 .84 '
<br />1.05 1.27 1.49 1.71 1.94 2.17. 2.38 2.60 2.83 3.07
<br />600
<br />E=.056 .112 ;225
<br />7133' .340 .398 '.457 .516 ,.575 .636 .697 .774 •851
<br />65-TT=.23
<br />.168
<br />.46 .69 .93
<br />'E
<br />1_.16 1.40 1.64 1.88 2"13 2.38' 2.83 2.88 3.13 3.39
<br />':554 1.0
<br />30
<br />=.067 135 .204 .273
<br />.343 .412 .483 .625 .697 -.711 ,.845 .922
<br />Tmm ' - Tangents and Externals to a 1'5Curve. V
<br />Chord =100 f t. -
<br />Angle
<br />Tangent
<br />External
<br />` `Angle
<br />Tangent
<br />External
<br />Int.,
<br />n je
<br />Tangent
<br />External
<br />64°
<br />3580:3
<br />1026:6
<br />s 71°"
<br />4086.9
<br />1308.2
<br />78°'
<br />4639:8
<br />1643:0
<br />10'
<br />3591.9
<br />.1032.8
<br />'• 10'
<br />4099.5
<br />10'
<br />4653.6
<br />1651.7
<br />20:
<br />3603.5
<br />'1030:0
<br />; 20
<br />4112-1
<br />,1315.6
<br />1322.0
<br />.20
<br />4667.4
<br />1660"5
<br />30
<br />3615.1
<br />1045:2
<br />30
<br />4124:81330.3
<br />2,38
<br />,30
<br />4681.3
<br />1660.2
<br />40:
<br />3626:8
<br />;1051.4
<br />40-
<br />4137.4
<br />1337.7
<br />40
<br />4695.2
<br />1676.1
<br />50
<br />3638.5
<br />1057.7
<br />'. 50.
<br />4150;1
<br />;1345.1
<br />7
<br />50
<br />4709.2
<br />1686.9
<br />65 "
<br />3650`.2
<br />'1063-9-
<br />72" -'
<br />4162:8
<br />'1352A
<br />` '79' ..
<br />4723.2
<br />1695.'8
<br />10;
<br />3661.9
<br />,1070.2
<br />X10
<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 />4183.5
<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- 7
<br />; 4239.7
<br />' 1398.0
<br />80
<br />4807.7
<br />1749.9
<br />10
<br />3732.7
<br />1108.6
<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 />120
<br />4836:2
<br />1768.2
<br />30,
<br />3756.5
<br />1121.7
<br />: 30
<br />4279.5
<br />1421.2
<br />..'30
<br />4850.5
<br />1777.4
<br />40
<br />3768.5
<br />1123.2
<br />�40
<br />;4291:5
<br />1429:0
<br />:.;40
<br />4864.8
<br />1786.7
<br />80-
<br />3780.4
<br />.1134.8
<br />�50'
<br />:4304.6
<br />1436.8
<br />r b0•
<br />4879.2
<br />1798.0
<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 />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 />'4356.9
<br />1468.4
<br />-30-
<br />4937.0
<br />1833.6
<br />40•
<br />3840:5
<br />1168,1
<br />40
<br />4370:1
<br />11476.4
<br />40'
<br />4951.5
<br />1843.1
<br />:'50
<br />3852:6
<br />:1174.8
<br />50
<br />4383:3
<br />,1484.4
<br />50
<br />4966.1
<br />1852.6
<br />68
<br />3804.7
<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 />1871.8
<br />20
<br />3889.0
<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 />1516:7
<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 />69 -"
<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 />1230.7
<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 />3999.5
<br />1257.9
<br />50:
<br />4514.0
<br />'1583.1
<br />50
<br />'5143.9
<br />1970.3
<br />70.-L',
<br />4011.9
<br />1265.0
<br />77
<br />4557``"61591.6
<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 />1279.3
<br />20.
<br />4584".8
<br />1608.6
<br />20:
<br />5189.3
<br />2000.6
<br />30
<br />4049.3
<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 />-482810
<br />1834.4
<br />.50.
<br />5234.9
<br />2031.4
<br />Corrections to be Added (T =Tangent. E=External.)
<br />Inc.
<br />Curve 5°-,
<br />10°
<br />IS°
<br />20°
<br />25°
<br />30°
<br />35°
<br />40°
<br />45°
<br />50°
<br />55°
<br />60°
<br />65°
<br />70°
<br />'Angle ,
<br />.
<br />-
<br />60o
<br />-T:F.21
<br />.42
<br />.,63
<br />:.84
<br />1.05
<br />1.27
<br />1.49
<br />1:71
<br />1.94
<br />2,17
<br />2,38
<br />2.60
<br />2.83
<br />3.07
<br />E=.056
<br />.112
<br />,168
<br />.225
<br />..283
<br />.340
<br />.398
<br />.457
<br />.516
<br />.575
<br />.638
<br />.691
<br />.774
<br />,851
<br />65°.
<br />T=.23
<br />.46
<br />.69-
<br />..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
<br />3.13
<br />3.39
<br />E=.067
<br />.135
<br />.204
<br />.273
<br />.343
<br />.412
<br />;483
<br />.554
<br />.625
<br />.697
<br />,711
<br />.845
<br />.922
<br />1.01
<br />170;
<br />T=.25
<br />.51
<br />76'
<br />1.02
<br />1.28
<br />1:54
<br />1.80
<br />2.06
<br />2.33
<br />2.60
<br />2.88
<br />3:18
<br />13.44
<br />3.72
<br />E=.080
<br />.159
<br />.240
<br />,321
<br />.403
<br />.485
<br />.568
<br />.652
<br />.735
<br />.819
<br />.906
<br />.9941.08
<br />1.17
<br />75°
<br />T=.27'
<br />.56
<br />83
<br />1.12
<br />1.40
<br />11.
<br />1.98
<br />2.27
<br />2.57
<br />2.87
<br />3.16
<br />3.47
<br />3.78
<br />4.09
<br />E =.095
<br />.182
<br />.480
<br />.578
<br />.678
<br />.777
<br />.877
<br />.977
<br />1.07
<br />1.18
<br />1.29 .1.39
<br />800
<br />=.30
<br />.61
<br />1.53
<br />1.84
<br />2.15
<br />2.46
<br />2.78
<br />3.10
<br />3.44
<br />3.78
<br />4.12
<br />4.46
<br />E =.110
<br />'.220
<br />T_332.445
<br />.558
<br />.671
<br />.787
<br />.903
<br />1.02
<br />1.13
<br />1.25
<br />1.38
<br />1.50
<br />1.62
<br />8SoT=.33.
<br />66
<br />1.68
<br />2.02
<br />2;36
<br />2.70
<br />3.05
<br />3.40
<br />3.77
<br />4.14
<br />4.55
<br />4.89
<br />E =.128
<br />.259
<br />.657
<br />.790
<br />.920
<br />1.06
<br />1.20
<br />1.34
<br />1.47
<br />1.62
<br />1.76
<br />1.91
<br />
|