|
N- TAtLE_I.-.Tangents.aild Externals to a 1°:Curve.
<br />Chord= Inn ft -
<br />`Angle
<br />Tangent
<br />External
<br />_ogle..
<br />.Tangent External
<br />.Angle.
<br />.Tangent
<br />Extern
<br />External
<br />'2257.0
<br />428.5 ]
<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 />` " IV
<br />2681:9
<br />-596.6 .
<br />10' '
<br />3121.7
<br />795.2
<br />:20
<br />2276.2
<br />435.6 i
<br />,. .20
<br />2692.1
<br />600.9
<br />20
<br />3132.,6
<br />800.4
<br />•L.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 t
<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 />-
<br />-".50-
<br />'2722.7
<br />'614,0`
<br />i
<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 />453.6 ;
<br />;. ,10-
<br />2743.1
<br />622.8 %
<br />>i .30,
<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 />337.3
<br />10
<br />2353.8
<br />464, 6 ,
<br />.. , 40-.
<br />2773.9
<br />636.2
<br />10
<br />3219.7 `
<br />842.7
<br />-•:50
<br />2363:5
<br />.468.4
<br />i
<br />.'- 50::
<br />2784:2-
<br />640.7.
<br />'50
<br />3230.7
<br />,•848.1
<br />45 "'
<br />237373
<br />472.1 j
<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 />2315.2
<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 />2835.9
<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 />850.8
<br />'46 -
<br />2432.1
<br />494.8
<br />53
<br />2856.7'
<br />672:7,:
<br />60._.:
<br />3308.0
<br />886.4
<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 />20
<br />2877:5
<br />682.0 '
<br />20,
<br />3330.3
<br />897.5
<br />730
<br />2461:7
<br />506.4 .
<br />30
<br />2888.0
<br />686,7
<br />30
<br />3341.4
<br />903.2
<br />40
<br />2471.5
<br />510.3
<br />40
<br />2S98.4
<br />691.4 40'
<br />1508.6
<br />3352.6
<br />903.8
<br />50
<br />2481.4
<br />514,3
<br />"50
<br />2908.9
<br />696.1
<br />50.
<br />3363.8
<br />.914.5
<br />`47. r
<br />2491.3
<br />518,2
<br />54"
<br />2919.4
<br />700:9
<br />61
<br />3375.0
<br />920:2
<br />8`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.A
<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 />4$
<br />2551.0
<br />542:2 '
<br />55
<br />2982.7
<br />I
<br />729:9 1
<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 />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 />V30 (
<br />2581.0
<br />554.5
<br />30.
<br />3014.5
<br />744.6
<br />` 30 !
<br />,
<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 />6:50
<br />2601.1
<br />5G2,8 :
<br />•. .50
<br />3035.8
<br />754.6 ;
<br />,50',
<br />3499.7
<br />984.3
<br />48-.>
<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 />3089,4 !
<br />779.8 -
<br />.40,
<br />3557.2
<br />1014.4
<br />.50
<br />2661.6
<br />588,0 ;
<br />•...5Q
<br />3100,2:
<br />784.9
<br />50'.
<br />3568.7
<br />1020.5
<br />TABLE L_= Tangents-and'Externals to a V Curve:
<br />('h nrc9'=100 ft.
<br />V
<br />Int.
<br />' Angle .
<br />Corrections to be=Added• (T=Tangent. 'E=External.)
<br />`
<br />Int
<br />Angle-
<br />Curve 5
<br />-,-
<br />10°, 15° 20° 25° 30° '35° 40° 45° 50° 55° 60°' 65° 70°
<br />40° !
<br />T=:13
<br />-.26. -.40 53 .67 .8o .93 :106 1.20- 1.34 1.49 1.64 1.79 1.94
<br />External
<br />E=.023
<br />046 .070 .093 .117 .141 -.172 ".203 .234 .265 .277 390 .315 .341
<br />450 ;:
<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 />E=.030:
<br />'.060 .093 .119 .153 ,.184 .216 .254 .289 .325 .351 .378 .411 .445
<br />50'
<br />"T=.17`
<br />.34 .51 GS ..85 1.02 1.19 1.36 1.54 _1.72` 1.01 2.10 2.29 2.48
<br />3591.9
<br />-E=.037,
<br />:075 '.116 .151 '.189 .227 .266 .305 .345 ..384 .425 .467 .508 .550
<br />55.:T=.19
<br />1315.6
<br />1322.9 ,
<br />.38 .57 .76 .95 1.14 1.32 1.52 1.72 1 92 2.14 2.35 - 2.56 2.77
<br />•1353.6
<br />46G7.4
<br />E=,046
<br />.093 .142 .188 .236 ,.283 .332 3.81 •,420 .479 .530 ".582 .641 .700
<br />60°
<br />T=.21f
<br />,:42 .63- • .84 1.05 1.27 1.49 1.71 _1.94 2.17 2.38 2.60 2.83 3.07
<br />4124.8
<br />E =.056-
<br />.112 ,168 .225 ..283..340 .398 .457 -.516 .575 .636 :697 :774 .851
<br />65°
<br />T=.23
<br />.46, -.69 .93 1.16 .40. 1.64 1.88 2,13 2.38 2.63 2.88" 3.13 3.39
<br />'3626',8
<br />E=.067
<br />.135 .204 .273 .,343 .412 .483 ..554 .625697 .711 .845 .922 1.01
<br />TABLE L_= Tangents-and'Externals to a V Curve:
<br />('h nrc9'=100 ft.
<br />V
<br />Int.
<br />' Angle .
<br />Tangent
<br />External
<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 />784
<br />4639.8
<br />1643.0
<br />1651.7
<br />10'
<br />3591.9
<br />1032.8 :
<br />.:10'
<br />20
<br />4099.5
<br />4112.1
<br />1315.6
<br />1322.9 ,
<br />10'
<br />20
<br />•1353.6
<br />46G7.4
<br />1660.5
<br />20
<br />30
<br />3603.5
<br />-3615.1
<br />1039:0
<br />1045.,2
<br />36
<br />4124.8
<br />1330.3 '
<br />30
<br />4681:3
<br />1689.2
<br />40
<br />'3626',8
<br />1051.4
<br />40�
<br />•4137•.4
<br />I337.7
<br />.- 40
<br />4695..2
<br />4709.2
<br />1878.1
<br />1686.9
<br />--.60
<br />3638.5'
<br />1057:7
<br />_ 507
<br />4150..1
<br />1345.1
<br />5Q
<br />3,44' 3.72
<br />70°
<br />65-
<br />3650.2
<br />1063.9 +
<br />'72
<br />4162.8
<br />1352.6 !,
<br />79
<br />4723.2'
<br />1695.8
<br />1704.7
<br />-10
<br />3661:9
<br />1070.2
<br />- 10
<br />20
<br />4175.6
<br />4183.5
<br />1360.1
<br />1367.6
<br />10
<br />20
<br />4737:2
<br />4751:2
<br />1713.7
<br />20
<br />30
<br />3673:7
<br />3685.4
<br />1076.6 :
<br />1082.9
<br />30.
<br />4201.2
<br />1375.2
<br />30
<br />4765.3
<br />1722.7
<br />1731.7
<br />40
<br />3697.2
<br />1089.3
<br />40
<br />.4214.0
<br />1382.8
<br />40
<br />50
<br />4779.4
<br />1740.8
<br />50
<br />3709:0
<br />1095.7'
<br />-50.
<br />4226.8
<br />1390.4
<br />.
<br />.4793:6
<br />gg,:
<br />3720.9
<br />1102.2'
<br />73-;
<br />4239,7
<br />1398.0
<br />80
<br />16
<br />"4807.7
<br />4822.0
<br />1749:9
<br />1759.0
<br />10
<br />3732.7
<br />1108.6
<br />:10-
<br />20
<br />4252.6
<br />'4265,6
<br />1405.7
<br />1413.5.
<br />20
<br />.4836.2
<br />.1768.2
<br />20
<br />30
<br />8744.6
<br />3756.5
<br />1115.1
<br />1121.7
<br />30
<br />4278.5
<br />1421.2 '
<br />30
<br />4850.5
<br />1777.4
<br />40
<br />37G8.5
<br />1128.2
<br />40
<br />4291,5
<br />1429. .0
<br />1436.8
<br />40
<br />50
<br />4864.8
<br />4879.2
<br />1786.7
<br />1796.0
<br />50
<br />3780.4
<br />1134.8
<br />50
<br />4304.6
<br />67
<br />3792.4
<br />1141.4
<br />'74
<br />431T.6
<br />1444.6.
<br />81
<br />10
<br />4893.6
<br />'4908.0
<br />1805.3
<br />1814.7
<br />10
<br />3804:4
<br />1148.0:
<br />1154.7
<br />10'
<br />20.
<br />4330.7
<br />4343,8
<br />1452.5 •
<br />1460:4
<br />-
<br />20
<br />4922:5
<br />3824.1
<br />20
<br />30
<br />3316.4
<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 />1476.4
<br />40
<br />50
<br />4951.5
<br />4966,1.
<br />1843.1
<br />1852.6
<br />" 50 :
<br />3852:6'
<br />1174.8
<br />50
<br />4383.3
<br />1484.4'
<br />68 -
<br />3864.7
<br />1181.6
<br />75 :
<br />4396.5
<br />1492.4`
<br />'82 - ?
<br />-4980.7.
<br />1862:2
<br />10
<br />1188.4
<br />10
<br />4409.8
<br />1500.5
<br />110
<br />4995:4
<br />. 1871.8
<br />20
<br />.3376.8
<br />•3889.0
<br />1195.2•
<br />20
<br />4423.1
<br />1508.6
<br />20
<br />5010.0,
<br />5024,.8.
<br />1881.5
<br />1891.2
<br />30
<br />3901:2
<br />1202.0,
<br />30
<br />40
<br />-4136.4
<br />1516.7
<br />1524.9
<br />30
<br />40
<br />5039.5
<br />1900.9
<br />40
<br />-'50
<br />.3913.4
<br />3925.6
<br />1208.9
<br />1215.8
<br />50
<br />.4449.7
<br />4463.1
<br />1533.1
<br />.50
<br />5054.3
<br />1910.7
<br />68:
<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 />4159:9
<br />1549.7',
<br />10
<br />20
<br />-•5054.0
<br />:5099.0
<br />1930.4
<br />1940.3
<br />20
<br />3962.5
<br />.1236.7'
<br />20
<br />30
<br />4503.4
<br />4516.9
<br />1558.0'
<br />1566.3:
<br />30
<br />5113.9
<br />1950.3
<br />30
<br />40
<br />3974.8
<br />3987.2
<br />1243.7
<br />1250.8
<br />40
<br />4530.4
<br />1574.71
<br />:40 ';
<br />5128:9'
<br />•1960.2
<br />50
<br />3999.5,
<br />1257.9
<br />50
<br />4514.0
<br />1553.115143.9
<br />11970.3
<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 />-
<br />10
<br />4024.4
<br />1272.1•
<br />lQ
<br />4571.2
<br />1600.1'
<br />10
<br />•5174.1
<br />%1990.5
<br />20'
<br />403G.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 />3.0
<br />5204.4
<br />2010.8
<br />40
<br />-4011.8
<br />1293.6.
<br />- 40
<br />4612.2
<br />1625.7
<br />40
<br />5219.7
<br />2021.1
<br />'2031:4
<br />50
<br />.4074.4
<br />.1300.9
<br />50
<br />4626.0
<br />1634.4`
<br />•, .,50
<br />5234.9
<br />Corrections to be Added (T=Tangent. E=External.)
<br />Int.
<br />Curve 5°
<br />10° 15°
<br />20°
<br />256 "30° '35°
<br />406
<br />45° 50°
<br />55° 60°
<br />65° 70°
<br />Angle •
<br />T=,.21
<br />'.42`.`.63
<br />8
<br />.05 1.27 1_.49
<br />1.71
<br />I.R. 2.17
<br />2.38- 2.60
<br />. -_ . ...
<br />2.83 •3:07
<br />60°
<br />E =.056
<br />:112 .168
<br />:24251'
<br />.283 .340 .398
<br />.457
<br />.518 .575
<br />.636 .697
<br />.774 •,851
<br />1.88
<br />2:13 2:38
<br />2.63 2.88
<br />3.13 3.39
<br />T=.23
<br />.69
<br />.93
<br />1.16 1.40 1.84 -
<br />65°
<br />E =.067
<br />.46
<br />135 .204
<br />.273
<br />_-.343 .412 .483
<br />..554
<br />..625 .697_
<br />.711' .845
<br />.922 1.01
<br />T=,25.
<br />.76
<br />1,02
<br />1.28 1.54 1.80
<br />2.06
<br />2.33 2.60
<br />2.88 3.18
<br />3,44' 3.72
<br />70°
<br />E=.080
<br />.51
<br />.159 .240
<br />.321
<br />'.403 .485 .568
<br />.652
<br />.735 ..8 19
<br />.906 .994'1,08
<br />1.17
<br />. .83
<br />1.12
<br />1.40 1.69 1.98
<br />2.27,'
<br />2.57 2.87.'
<br />3.16 3.47
<br />3.76 4.09
<br />1.39
<br />75°
<br />.286
<br />.383
<br />.480 .578 .678
<br />.777
<br />.877 .977
<br />1.07. 1.18
<br />1.29
<br />.91
<br />1.22
<br />1.53 1.84 2.15
<br />2.46'
<br />2.78 3.10'
<br />3.44 3.78
<br />4.12 4.46
<br />80°
<br />A8.25
<br />.332
<br />.445
<br />.558 .671 .787
<br />..903
<br />1.02 1.13
<br />1.25 1.38
<br />1.50 1.62
<br />1.00
<br />1.33
<br />1.68 2.02 2:36
<br />2.70
<br />3.05 3.40.
<br />3.77 4.14
<br />4.55.4.89
<br />89°
<br />..391
<br />.524
<br />.657 .790 .920
<br />1.06
<br />1.20 1.34.1.47
<br />- '1.62
<br />1.76 1.91
<br />
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