|
:IZ! TABLE I..= Tangents and -Externals _to.a V. Curve.
<br />Chard =100 ft.
<br />Int.
<br />Angle
<br />Tangent
<br />External
<br />Int.
<br />Angle`
<br />Tangep External
<br />Int.,.
<br />Angle'
<br />Tgngent
<br />ExCernal
<br />W.
<br />2257.0
<br />428.5
<br />50' ..
<br />2671.8
<br />592.3
<br />57°'l
<br />+3110.9
<br />790.1
<br />IO'
<br />2266:6432.0`
<br />T=:15 .30
<br />• 10':
<br />2631.9
<br />596.6,
<br />10'
<br />3121.7
<br />-795.2
<br />20.
<br />2275;2
<br />`435.6'
<br />20
<br />2692?C
<br />600.9
<br />2U;
<br />.3132.6
<br />800.4
<br />30 -
<br />2285.9.'-439.2
<br />E=.037 _-075
<br />- ,?.30
<br />2702:.3
<br />;605.3
<br />30
<br />3143.4'
<br />805,6
<br />-40
<br />;229576.
<br />442.8?
<br />40
<br />12712,5.
<br />609.0
<br />40
<br />3154.2
<br />810.9
<br />50
<br />.2305:2
<br />'•446:41
<br />.-
<br />5D
<br />2
<br />27 17,,
<br />_
<br />f4]4,0
<br />b0.
<br />3165:1
<br />816.1
<br />i
<br />.23R .340 '.393 -457 -510 '•575
<br />.G3G .097 ,774
<br />^851
<br />65°
<br />{
<br />69 .93
<br />1-16 1.40 1.64 1.88 2.13 2.39
<br />2.63 2.88 3.13
<br />44'
<br />2314:9;
<br />450.0;
<br />,61^ ;.
<br />2732.9
<br />618.4
<br />.58,6"
<br />3176.0
<br />821.4
<br />10
<br />2324.fi
<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 i
<br />'
<br />;2753.4
<br />1627.2'
<br />20'
<br />3197.8
<br />:•832.0
<br />' --'80
<br />'2344:11
<br />4 461: U:
<br />r , 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 />401
<br />3219.7
<br />•842.7
<br />1 . 50 '
<br />' 2363.5
<br />468.4: ,
<br />, .50;
<br />2784. &
<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, S.
<br />•_r• .10 .
<br />2804.0
<br />.649.7
<br />10
<br />3252,7
<br />858A
<br />20
<br />2392:8'
<br />• 479.6,
<br />+ e 20
<br />2815.2
<br />454.3
<br />'20 t
<br />3263".7
<br />864.3
<br />30
<br />2402_6'
<br />x433.4•
<br />30
<br />2325.0.
<br />658.8
<br />30
<br />3274.8
<br />• 869.8
<br />;-;-40
<br />2412.4
<br />,487,2:
<br />'40
<br />t-
<br />2835:9
<br />663.4:
<br />40
<br />3285.8.
<br />.875.3
<br />50
<br />2422.34-491.0,
<br />3792.4
<br />50
<br />2846.3
<br />GGS.O
<br />5D_
<br />3296.9
<br />880:8
<br />1805.3
<br />2432.1
<br />494.8L3
<br />%
<br />2856 7
<br />672:7'
<br />68 -
<br />330S_0
<br />$86.4
<br />,10
<br />2441.9
<br />496.7,
<br />ib
<br />10
<br />2867.1•
<br />(677"3•
<br />10
<br />3319:1
<br />$92.0
<br />20
<br />2451,8
<br />502 6
<br />-
<br />2877.5
<br />(682-0
<br />• 20
<br />3330.3
<br />$97.5
<br />30 •
<br />2401-.7
<br />506.4.
<br />'; .30 '
<br />.2888 .0
<br />686.7
<br />-30
<br />3341:4.
<br />?. 903.'-'.
<br />40
<br />.2471.5
<br />•.510.3
<br />?,;•40 d
<br />2898:4
<br />1691.4
<br />-40
<br />3352.6
<br />908,8
<br />50
<br />:2481:4
<br />e514.3`50
<br />1181.6
<br />290$.9
<br />,696.1
<br />450
<br />3363.8
<br />: 914.5
<br />47"• -
<br />*2491:3
<br />518.21
<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 />2511:2
<br />526.1;
<br />2D
<br />29.10'.4
<br />710.5,
<br />•'.20
<br />3397.5
<br />••931.6
<br />-W
<br />2321,1
<br />530.1•
<br />30
<br />2951;0
<br />;715.3
<br />:30
<br />34081-8
<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 />-,9.43.3
<br />„•'f 5w
<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 />10j
<br />'2561.0
<br />;546.3.
<br />,, '•10
<br />2993=.3
<br />734-8
<br />10
<br />3454-1
<br />9GD.G
<br />20,
<br />2471-:0
<br />550.4 •
<br />; 20
<br />3003,9
<br />1739.7
<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 />,lA0
<br />2591.0
<br />?558.6
<br />•40
<br />3025:2
<br />749,6
<br />40
<br />3488.3
<br />979.3
<br />50
<br />2001.1
<br />562.8
<br />'510
<br />3035.8
<br />754.6
<br />50•
<br />;3499..7
<br />984.3
<br />-49
<br />2611.2
<br />566:9
<br />i
<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 />x'10
<br />3057.2.
<br />764.0
<br />10 '
<br />;3522.'6
<br />-,996.2
<br />20 '
<br />2631.3
<br />575.3
<br />"20
<br />30G7.9
<br />769.7
<br />20 !
<br />3534.-1'
<br />1002.3
<br />1-30
<br />2641.4
<br />.579.5
<br />1293.6
<br />3078.. Te
<br />.774.7
<br />30
<br />3345:6
<br />.1008.3
<br />40'
<br />2651.5
<br />583.8
<br />,:30
<br />;'40
<br />3`39.4
<br />779.8
<br />= •40
<br />;3557:2
<br />.1014.4
<br />Sol
<br />'2001.6
<br />588.0
<br />50
<br />3100.2
<br />7S4.9
<br />,;50 '
<br />3503;7
<br />1020.5
<br />Corrections-tobe'Added:(T=Tangent. E=Ezternal.p
<br />Angle
<br />cutoe S' 10°'
<br />15° 20° '
<br />25° 30° 35° 406 45° 50°
<br />55° 601 - 65°•
<br />70°
<br />40'
<br />T=:13 .26
<br />.40 .53
<br />.67 .30 .93 -106 1.20 1.34
<br />1,49 1.64 1.79
<br />1.94
<br />.-711t':
<br />E =.023 .046
<br />.070 .093
<br />.117 ,141 .172 .203 ,234 .265
<br />.277 .290 .315
<br />.341
<br />45'
<br />T=:15 .30
<br />.44 .60
<br />.76 .9l 1.06 1.21 1.37 1-52 11.70
<br />1,87 2.04
<br />2.21
<br />10,
<br />E=:030 .060
<br />.093 '.11.9
<br />.153 .184 ,210 '.254 .280 ;325
<br />.351 .378 .411
<br />.445
<br />50'
<br />,T=.I7. 34
<br />•.51 .68
<br />.85 1.02 1,19 1.36 1.54 1.72
<br />1.91 2-10 2.29
<br />2.48
<br />30 -
<br />E=.037 _-075
<br />.116 .151
<br />..189 .227 .250 .305 .345 .334
<br />.425 .407 .508
<br />.550
<br />55'
<br />T-19 33
<br />.57 1 .76
<br />.95 1.14 1.32 11.52 1.72 1,92
<br />2.14 2.35 2 S
<br />2.77
<br />40
<br />E=.046 1-.093
<br />.142 .138
<br />.235 .233 .221 3^81 .420 .479
<br />530 .5 21
<br />700
<br />60°
<br />T=,21 , .42
<br />•.63 .84 .1.05
<br />1.27 1.49 1:71 1-94 2.17
<br />2.38 2.00 2.33,
<br />3.07
<br />.50
<br />.112
<br />.163 .225
<br />.23R .340 '.393 -457 -510 '•575
<br />.G3G .097 ,774
<br />^851
<br />65°
<br />_1'`=.056
<br />T =;23 .46
<br />69 .93
<br />1-16 1.40 1.64 1.88 2.13 2.39
<br />2.63 2.88 3.13
<br />3.39
<br />10
<br />E=.007 .135
<br />.204 .273
<br />.343 .412 ,463 .554 ,625 ,697
<br />,711 .$45 .922
<br />1.01
<br />Rp
<br />TABLE I. - Tangents and ExternaIs`to a 1° -Curve:' 't'
<br />Clioid=1001t.
<br />Int.
<br />Angle
<br />Tangent
<br />External
<br />Int.
<br />'�ng15
<br />Tangent
<br />-
<br />External
<br />Int.
<br />'Angle
<br />Tangent
<br />External
<br />649.•
<br />'3580:3-,
<br />'1026.6
<br />.-711t':
<br />4056.9
<br />1308.2
<br />78°
<br />4630.8
<br />1G43.0
<br />HY
<br />3591.0,
<br />:1032.8
<br />10'
<br />4099.5
<br />1315.6
<br />10,
<br />4653.5
<br />1G51.7
<br />20,
<br />3603:5
<br />1039,0
<br />20
<br />4112.1
<br />1322.9
<br />20
<br />4567.4
<br />1660.5
<br />30 -
<br />3615:3
<br />1045.2
<br />'1051.4
<br />30'
<br />:4124.S
<br />1330.3
<br />30
<br />4581.3
<br />'1669.2
<br />40,
<br />3626'8'
<br />1.15 1.40
<br />40
<br />4137.4
<br />1337.7
<br />40
<br />4695:2
<br />1678.1
<br />J.50
<br />3635,5
<br />,1057.7
<br />j 50
<br />4150.1
<br />1345.1
<br />.50
<br />4709.2
<br />1686.9
<br />65 -f
<br />3650.2
<br />1063.9
<br />72
<br />4162.8
<br />1352.6
<br />; 79 --^
<br />4723,2
<br />1G95;S
<br />10
<br />30G1.9
<br />1070.2
<br />10
<br />4175"6
<br />1360.1
<br />1 '10
<br />4737.2
<br />1704.7
<br />20
<br />3673.7
<br />1076.6
<br />20
<br />4183.5
<br />1367.6
<br />j 20
<br />_
<br />4751 2
<br />1713.7
<br />30'
<br />3685:41082.9
<br />1.98
<br />'..30
<br />4''U1.2
<br />1375.2
<br />I 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 />3769.0
<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 i
<br />4239.7
<br />1393:0
<br />80 ',r
<br />4507.7
<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 />175550.0
<br />1 x:201
<br />3744"6
<br />1115.1'
<br />.^20.
<br />4265.6
<br />1413-5
<br />. '20
<br />483642
<br />1768.2
<br />30:
<br />3756:5
<br />1121.7
<br />.30
<br />4278.5
<br />1421-2
<br />30
<br />4950.5
<br />1777.4
<br />-40•
<br />3708.5
<br />1128.2'
<br />4.0
<br />4291.5
<br />•1429-0
<br />- 40
<br />4564.8
<br />1786.7
<br />50•
<br />3780:4
<br />1134^8
<br />."50
<br />4304.6
<br />1430.8
<br />50
<br />4879.2
<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 />4008.0
<br />1314.7
<br />20
<br />3910.4
<br />1154.7
<br />20
<br />1313.8
<br />1460.4
<br />.20
<br />4922,5
<br />1924.1
<br />i' x30!
<br />X3823.4
<br />•1161.3
<br />.-•30
<br />4356:9
<br />1468.4
<br />- 30
<br />4937.0
<br />1833.6
<br />0 '40
<br />3840.5"
<br />1165,1
<br />"40.
<br />1370.1
<br />1476.4
<br />40'
<br />4951.5
<br />1943.1
<br />:50'
<br />'3552..6
<br />.1174,8
<br />_50
<br />4383.3
<br />1484.4
<br />50
<br />4966.1
<br />1652.6
<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 />a10
<br />3876:3
<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 />Off
<br />3913.4
<br />-1209.9
<br />40
<br />4444,7
<br />1524.9
<br />40
<br />5039.5
<br />1900.9
<br />�50
<br />3925.6
<br />1215.8
<br />T 50.
<br />4463,1
<br />1533.1
<br />50
<br />5054.3
<br />1910.7
<br />769 --
<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 />t 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 />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 />19.70.3
<br />70 "
<br />1265.0'
<br />77
<br />4557,6
<br />1591.6
<br />845159.0
<br />1980:4
<br />- 10
<br />.4011.9
<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 />4,036;8
<br />1279.3
<br />20
<br />".4584.3
<br />1G08.6
<br />20
<br />5169.3
<br />" 2000.6
<br />30
<br />:4049.3
<br />1286.5
<br />30
<br />4598,5
<br />1G17.1
<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 lidded (T=Tangent. E=External.)
<br />gls Curve 5°
<br />10° 15°
<br />20°
<br />25° 30°
<br />35°
<br />1 40°
<br />1 45°
<br />50°
<br />55°
<br />60° 651
<br />701
<br />=A
<br />T=.21
<br />.42 ^63
<br />..8{
<br />1.05 1.27
<br />1.49
<br />1.71
<br />1.94
<br />2.17
<br />2,38
<br />2.60 2.83
<br />3.07
<br />60.,
<br />E =.056
<br />..112 ".168
<br />.225
<br />,283 .340
<br />.398
<br />.457
<br />.516
<br />.575
<br />.636
<br />.697 .774
<br />351
<br />65° T'-23
<br />.46 69 -
<br />.03
<br />1.15 1.40
<br />I.64
<br />1.88
<br />2.13
<br />2.38
<br />2.53
<br />2.83 3.13
<br />3.39
<br />r=.067
<br />.335 204
<br />.273
<br />.343 .412
<br />,4S3
<br />.554
<br />.625
<br />.697
<br />.711
<br />.845 .922
<br />1.01 .
<br />T�.25
<br />'.76
<br />1.02
<br />1.28' 1.54
<br />1^80
<br />2.06
<br />2.38
<br />2.60
<br />2-88
<br />3.16 3.44
<br />33.72
<br />70' E=.080
<br />.61
<br />'•.159 .240
<br />.321
<br />.403 AM
<br />.568
<br />.552
<br />.735
<br />.819
<br />.906
<br />,994 1.06 '1.17
<br />75° T=.27
<br />.56 '.83
<br />1.12
<br />1.40 1^60
<br />1.98
<br />2.27
<br />2.51
<br />2-87
<br />3.16
<br />3-47 3.78
<br />4.09
<br />E-.095
<br />'.182 .286
<br />.383
<br />.480 .578
<br />.078
<br />.777
<br />.877
<br />.077
<br />1.07.
<br />1.18 1-20
<br />1^39
<br />S9° •T-.30
<br />.61 .91:
<br />1.22
<br />1.53 1.84
<br />2.15
<br />2.46
<br />2.78
<br />3.10
<br />3.44'
<br />11.25
<br />3.78 4.12
<br />4.45
<br />E=.110
<br />.220 .332
<br />.445
<br />.558 .671
<br />.787
<br />.00311.o3
<br />1.13
<br />1-38 1.50 jL62
<br />T=.33
<br />.66 LOU
<br />1:33
<br />1-68 2.02
<br />2.36
<br />2.70
<br />13.05
<br />3.40
<br />4.14 4.55
<br />4,89.
<br />R-128
<br />.259 .391
<br />.524
<br />.657 .790
<br />.9261.06
<br />1.20
<br />1.34
<br />13.77
<br />1.47
<br />1"G2 1.75
<br />1.91
<br />MH
<br />
|