|
IV TA13LE I. - 'Tangents:aiid.Externals'to a10:Curve.
<br />Chord=100.ft.
<br />Angie
<br />Tangent
<br />External
<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'
<br />+2266.6
<br />432.0
<br />10'
<br />2631.9•
<br />'596.6
<br />10''
<br />:3121.7
<br />795.2
<br />G.+ 20
<br />2276:2
<br />435.6
<br />20-
<br />2692.1
<br />600.9,
<br />20
<br />:3132.6•
<br />800.4
<br />i 30
<br />-,"40
<br />2285.9
<br />'.2295-.6
<br />439.2:
<br />30
<br />2702.3
<br />605.13
<br />"..'30
<br />3143.4
<br />;805.6
<br />fi
<br />50
<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 />sic). 1
<br />1695.8
<br />1704:7
<br />2314.0
<br />450;0
<br />51.'_
<br />2732.9
<br />618.4
<br />'58
<br />3176.0
<br />821:4
<br />::,C 10
<br />2324.6
<br />453.6
<br />'. 10'
<br />'2743.1:
<br />622.8:
<br />10
<br />3186'.9
<br />826.7
<br />1_n'20
<br />2334:3
<br />457.3 ,
<br />20.
<br />2753-4
<br />627.2
<br />20
<br />31978.
<br />832.0
<br />!.i'30
<br />2344.1
<br />461,0 •
<br />';;.30_
<br />2763:7
<br />631.7
<br />'30•3208'.8
<br />50
<br />4793;6
<br />F 40
<br />2353.8
<br />464,6
<br />_`;.40'
<br />2773.9
<br />636.2
<br />40
<br />.3219.7
<br />.837.3
<br />.842.7
<br />i•'i.50 ;.2363.5.
<br />66-
<br />468.4
<br />.;'50;
<br />2784.2
<br />640.7
<br />'50"
<br />3230.7;
<br />_848.1
<br />35 .:-'
<br />237313
<br />472;1.'
<br />52:" .
<br />2794.'5
<br />645.2
<br />59 '
<br />8241.7
<br />853.5
<br />40
<br />12383.1
<br />475.8
<br />.,.10
<br />`_
<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 />F;. .30
<br />2402.6
<br />433.4.
<br />30
<br />2825.6
<br />658.8
<br />:301
<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 t
<br />50
<br />2S46.3
<br />668.0 '
<br />.50'
<br />3296.9
<br />SS0.8
<br />1814.7
<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 />2867.11
<br />677.3
<br />',la
<br />'3319.1.
<br />892.0
<br />C. ;20
<br />2451.8
<br />502.5 i
<br />;.-20
<br />2877:5
<br />682.0
<br />.20
<br />3330.3
<br />897.5
<br />7.'30
<br />2461:7
<br />506.4
<br />30
<br />2388.0'
<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 />...r-'50
<br />2481.4
<br />514.3 -
<br />.'..50
<br />2903.9 -
<br />696.1
<br />.'.'.50
<br />3363.8
<br />914.5
<br />'47;.':
<br />2491.3
<br />518:2.
<br />54,-
<br />2919.4
<br />700.9:
<br />61
<br />._.10
<br />3375.0
<br />920.2
<br />;! 2'10 f
<br />' 2501:2
<br />522.2
<br />; .
<br />2929.9
<br />705.7 i
<br />i. i0i
<br />3386.3 '
<br />925.9
<br />,'20
<br />251112
<br />526.1
<br />;. 20
<br />2940.4
<br />710.5 ,
<br />20'
<br />3397.5
<br />931.6
<br />i,.'c`30
<br />2521t1
<br />530.1
<br />;. 30
<br />2951.0
<br />715.3
<br />30
<br />3408.8;
<br />937.3
<br />:•.1' 40 1
<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 />1930'.4
<br />2551.0
<br />542:2 i
<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 />960.6
<br />i.- 20 !
<br />2571.0
<br />5 50.4
<br />.'20
<br />3003.9
<br />739.7 '
<br />, 20"=
<br />3465.4
<br />966.5
<br />,i 30
<br />2581.0
<br />554.5
<br />;. 30
<br />3014.'5
<br />744.6
<br />-'.30
<br />3476.8
<br />972.4
<br />L1970.3
<br />2591.0
<br />558.6
<br />-40,
<br />3025.2
<br />749.6
<br />:',40.
<br />3488.3
<br />978.3
<br />2601:1
<br />502.8 '
<br />-`50.
<br />3035.8
<br />754.6
<br />50:
<br />3499.7
<br />984.3
<br />49„`
<br />2611.2
<br />1
<br />566:9
<br />56",,
<br />3046.5
<br />759:6
<br />63,,'
<br />3511.1
<br />,
<br />990.2
<br />I,7:10 .'2621.2
<br />20 .
<br />571A
<br />:I, 10
<br />3057.2
<br />764.6
<br />10':
<br />3522.6
<br />996.2
<br />4,r 20 !
<br />2631.3
<br />575.3i
<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 />` 80
<br />3078.7
<br />774.7
<br />130",
<br />3545.6
<br />1008.3
<br />1:40
<br />2651.5
<br />583.8 :
<br />:2, 40
<br />3089.4;
<br />779.8 ;
<br />40•
<br />3557.2
<br />1014.4
<br />£;.c:50
<br />2601.6
<br />588.0:
<br />t,`50
<br />3100.2,
<br />754.9
<br />50.
<br />356S.7
<br />1020.5
<br />a
<br />TABLE I. -'Tangents and Externals to a, V Curve. -V
<br />Ch ord.=100 f t,
<br />Int.
<br />-'Angle
<br />Corrections to be Adde"d (T = Taligelit '- Z E ="D, giern:dL)-
<br />Ant a
<br />�Cuive 5°�35°:30°
<br />35° a, ' 45° 50° 55° 600 - 65° 70°
<br />40° -
<br />T=`.13
<br />.26' -.40: .53 .67. .80 .93 .106 1.20 1.3.1 1.49 1.64-' 1.79 1.94
<br />a .
<br />External
<br />E=.023_.'---
<br />.070 • .093 .117 .141 .172 -.203 .234 .265 .277 290 .315 .341
<br />1026.6
<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 .5L .68 .85 1.02 1:19 1.36 1_..54 1.72 1.91 2.10 2.29 2.48
<br />'.-116:151_
<br />1032.8
<br />1039.0
<br />E=.037
<br />.075 _.189 .227 .266 .305 .345 .384 -:425 .467 .508 .550
<br />55°"-
<br />- T=,19
<br />.38 57" •.76 95. 1.14 1.32 1.52 1.72 1.92 2.14 2.35 ' 2.56 2.77
<br />1660.5
<br />E=.046
<br />-:093 '.142 :188 .236 .283 .532 3.81 .420 .479 .530 .582 .641 .700
<br />60°
<br />''T=.21
<br />42 .63. .84 1.05 1:27 1:19 1.71 1.94 2.17: 2.33 2.60 2.83 3.07
<br />1330.3
<br />E =.056
<br />112 .168 .225 =.283 .340 .398 .457 .516 .575 .636 %.697 .774 .851
<br />1660.2
<br />IT=. -23
<br />, .46, .69 1 .93 1.16 1.40 1.64 1.88 2.13 2.38 2.63' 2.88 3.13 3.39
<br />1051.4
<br />..E =.067
<br />-.135 .204 .273 .343 -:412 383 .554 .625 .697 .711 -:845 .922 1.01
<br />a
<br />TABLE I. -'Tangents and Externals to a, V Curve. -V
<br />Ch ord.=100 f t,
<br />Int.
<br />-'Angle
<br />Tangent
<br />Extern
<br />Tangent
<br />External'
<br />Int.
<br />Angle
<br />Tangent
<br />a .
<br />External
<br />640 -.
<br />'3580.3
<br />1026.6
<br />71°
<br />4086.9
<br />1308.2
<br />78°,•.
<br />10'
<br />4639.8
<br />4353.6
<br />1643.0
<br />1051:7
<br />10'
<br />3591.9
<br />1032.8
<br />1039.0
<br />10'
<br />20
<br />4093.5
<br />4112.1
<br />1315.6
<br />1322.9:
<br />t 20
<br />4667.4
<br />1660.5
<br />20
<br />30
<br />3603.5
<br />3615.1
<br />1045..2
<br />30
<br />.4124.8
<br />1330.3
<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; ',4695.2
<br />65°
<br />1678.1
<br />1686.9
<br />50
<br />3638.5
<br />1057 7
<br />-50;
<br />4150.1
<br />1345.1
<br />56
<br />.4709.2
<br />'T=.25
<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 />8661:9
<br />1070.2 .
<br />10,
<br />4175.6
<br />1360.1
<br />10
<br />20
<br />4737.2
<br />4751,2.
<br />1713.7
<br />20
<br />3673.7
<br />'3685.4
<br />1076.6
<br />20
<br />30,
<br />41S3.5
<br />1367.6
<br />1375.2
<br />30
<br />4765.3
<br />1722.7
<br />30
<br />'40 ',
<br />3697.2
<br />1082.9 .
<br />1089:3
<br />40-
<br />.4201.2
<br />4214.0
<br />1382.8 1
<br />40
<br />4779.4
<br />'.1731.7
<br />50
<br />3709:0
<br />1095.7 ;
<br />,.
<br />56
<br />4226.8
<br />1390.4 i
<br />50
<br />4793;6
<br />1740.8
<br />..220 .33
<br />.558
<br />.671 .787
<br />.903 1.02
<br />1.13 1.25 1.38 1.50
<br />1.62
<br />T=.33
<br />66-
<br />`3720.9
<br />1102.2j
<br />73 ;.
<br />4239.7
<br />1398."0 i,
<br />:
<br />80_.+
<br />-4807.7
<br />4822.0
<br />1749.9
<br />1759.0
<br />10
<br />20
<br />3732.7
<br />;3744.6
<br />1108:6
<br />1115.1 ;
<br />_;10; 1.4252.6
<br />20:
<br />'4265.6
<br />1405.7
<br />1413.5 i
<br />-10..
<br />;20
<br />4836.2
<br />1768.2
<br />30
<br />3756.5
<br />1121.7
<br />30
<br />4278.5
<br />1421.21
<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 />'
<br />40
<br />50
<br />4864.8.
<br />4870:2
<br />1786.7
<br />1796.0
<br />50
<br />3780.4
<br />1134.8
<br />;50
<br />4304.6
<br />1436:8
<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 />,
<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 />3516.4
<br />1154.7
<br />20
<br />4343.8
<br />1460.4 ,
<br />+. _20
<br />4922.5
<br />1824.1
<br />30
<br />1161.3
<br />3Q ',4356.9
<br />1468.4 i
<br />30
<br />4937.0,
<br />:1833.6
<br />40
<br />.3828.4
<br />8340.5
<br />1168.1"
<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 />4333.3
<br />1484.4'
<br />`•_50
<br />-.4966.L
<br />1852.6
<br />-68,.,-
<br />3364:7
<br />1181.6 ''
<br />75 -
<br />4396:5
<br />1492.4
<br />82 - '
<br />-4980.7 �
<br />1862: 2
<br />10
<br />'387G.8•
<br />1188:4
<br />-- IQ
<br />:4409.8
<br />1500.5;
<br />10
<br />.4995.4'
<br />3871.8
<br />20
<br />3S89.0
<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 />:443G.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 />3937.91
<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 />3962.5.
<br />1236.7
<br />n 26
<br />4503.4
<br />1558.0+
<br />20
<br />5099.0
<br />-1940.3
<br />,'20
<br />1-30
<br />3974.8'
<br />1243.7
<br />30 ',
<br />; 4516.9
<br />1566.31
<br />30
<br />- 5113.9
<br />'5128.9
<br />+1950.3
<br />40 1';3987.2
<br />1
<br />1250.8r
<br />•40
<br />4530.4
<br />1574.7.
<br />40 '
<br />1960.2
<br />50 ;
<br />1257.9'
<br />.50
<br />4514.0
<br />1583.1'
<br />-, 50 '
<br />'5143.9
<br />L1970.3
<br />;3999.5,
<br />70
<br />4011.9
<br />1265:01
<br />77
<br />•4557.6
<br />1591:61
<br />••84-.
<br />x5159.0
<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 />;80
<br />4049.3
<br />128G.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 />14612:2
<br />1625.7'
<br />40
<br />-5219.7
<br />'5234.,9
<br />2021.1
<br />_ b0 ,
<br />4074.4;
<br />1300.9
<br />50
<br />4626 0
<br />1634.41
<br />_.50
<br />2031.4
<br />Corrections to be Added (T =Tangent. E=External.)
<br />Int.
<br />Curve 5°
<br />10° '15°
<br />20°
<br />'25
<br />30° 35
<br />"40° 45°
<br />50° '55° 60°- 65°
<br />70°
<br />Angle-
<br />., _
<br />_
<br />_, ..
<br />.- .-
<br />, -. _ .
<br />__, -
<br />,
<br />T=.21
<br />.42' .63
<br />.84
<br />1.05.
<br />1.27 1.49
<br />1.71 1.94
<br />2.17 2.38- 2:60 2.83 -
<br />8:07
<br />60'
<br />E =.056
<br />-.112 .168
<br />_225_
<br />.93
<br />.283
<br />.
<br />.340 -.398
<br />.457 .516
<br />'.575 .636 .697 .774
<br />..851
<br />T=.23'
<br />.46 .69
<br />1.16`
<br />1.40 1.64.
<br />1.88- 2.13.
<br />2.38 2.63 2.88 ' 3:13 .3.39
<br />65°
<br />E =.067
<br />.135 :204
<br />.273
<br />.343
<br />.412 -.483
<br />.554 .625..697
<br />.711 .845 .922
<br />1.01
<br />'T=.25
<br />.76
<br />1.02
<br />1.28.1.54
<br />1.80
<br />2.06 2.33
<br />2.60 2.88 3.18 3.44.3.72
<br />70°
<br />E=.080
<br />.51,
<br />.159 :240
<br />.321
<br />:403
<br />.485 .568
<br />•.652 ..735
<br />.819 .908 :994 1.08
<br />1.17
<br />ri
<br />T=.27
<br />.56- '.83f21445
<br />12-
<br />1.40
<br />1.69 1.98
<br />2.27 2.57
<br />2.87. 3.16 3.47 3.76 -
<br />4 09
<br />:.�5°
<br />E =.095
<br />.182 .2883
<br />.480
<br />.578 .678
<br />.777 .877
<br />.977 1.07 1.18 1.29
<br />1.39
<br />-T=.30
<br />Al -.912
<br />1.53
<br />1.84 2.15
<br />2.46 2.78
<br />3.10 3.44 3.78, 4.12.
<br />4.46
<br />E =.110
<br />..220 .33
<br />.558
<br />.671 .787
<br />.903 1.02
<br />1.13 1.25 1.38 1.50
<br />1.62
<br />T=.33
<br />66 1.00
<br />1433
<br />1.68'
<br />2.02 2.36
<br />2.70 3.05
<br />3.40 3.77 4.14 4.55
<br />4.89
<br />�rO
<br />E =:128
<br />.259'•;.301
<br />1.524
<br />.657
<br />.790 .926
<br />1.06. 1.20:
<br />1.34. 1.47 1.62 1.76
<br />1.91
<br />
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