|
N TAnI,E I. - Tangents and Externals to a 1* Curve.
<br />Chord =100 it:
<br />Int.
<br />Angle '
<br />Tangent
<br />External
<br />Ini.
<br />Angle
<br />Tangent
<br />g
<br />External
<br />lnt.--
<br />angle
<br />Tangent
<br />External
<br />43°
<br />2257.0
<br />423.5
<br />50°
<br />2671.8
<br />592.3
<br />570
<br />3110.9
<br />790:1
<br />1011
<br />2266.6
<br />432,0
<br />I0"
<br />2681.9
<br />596,6,
<br />"10'
<br />3121.7
<br />795.2
<br />20 :
<br />2276.2
<br />435.6
<br />20
<br />2692:1
<br />Goo. 9.
<br />20
<br />3132.6,
<br />800.4
<br />_30
<br />.2285.9
<br />439.2
<br />'442.8
<br />1 30
<br />2702.3
<br />G05.3
<br />30
<br />3143.41
<br />.805.5
<br />40 '
<br />2295.6
<br />.30
<br />40
<br />2712.5
<br />600.6
<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 />!4
<br />10 ;''2324.6•
<br />2314.9:
<br />450.0
<br />51
<br />2732.0
<br />618.4
<br />58-
<br />3176.0.
<br />821.4
<br />.378
<br />.411
<br />453.6
<br />'457.3
<br />30
<br />2743.1
<br />022,8
<br />10
<br />3186.9
<br />826.7
<br />20
<br />2334.3
<br />1.36
<br />20
<br />2753.4
<br />627.2
<br />20
<br />3197.8
<br />832.0
<br />30
<br />'40
<br />2344.1.
<br />461.0
<br />30
<br />2763.7
<br />031.7
<br />30
<br />.200
<br />1.32
<br />-837.3
<br />.345
<br />1.72
<br />2353.8:
<br />464.6
<br />40
<br />2773.9
<br />_
<br />636,2.
<br />40
<br />.3208.8
<br />3219.7
<br />842,7
<br />-50 ..2363.5
<br />1.
<br />.093
<br />468.4
<br />50:
<br />2784.2
<br />640,7
<br />50
<br />3230.7
<br />.848.1
<br />i5
<br />2373,3
<br />472.1
<br />52
<br />2794.5
<br />645.2
<br />69
<br />3241.7
<br />553.5
<br />10
<br />`
<br />2383.1'
<br />475.8
<br />10
<br />2SU4,9
<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 />8614.3
<br />30
<br />2402,6,
<br />483.4
<br />30
<br />2825,0
<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 />830.8
<br />;d6
<br />2432.1
<br />494.8
<br />53
<br />.2856.7
<br />672.7
<br />G0
<br />3308.0'
<br />886.4
<br />10
<br />2441.9
<br />493.7
<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 />30 `
<br />.40
<br />2461-:7;
<br />505.4
<br />30
<br />2833.0
<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 />908.8
<br />50 i
<br />,2481.4
<br />514.3
<br />50
<br />2908.9
<br />696.1
<br />50
<br />3303•.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 />29213,9
<br />705.7
<br />10
<br />.3336.3
<br />925.0
<br />20 -
<br />2511.2.
<br />526.1
<br />20
<br />2940.4
<br />710.5
<br />20
<br />.3397.5
<br />031.G
<br />30
<br />2521.1
<br />5;0.1
<br />30
<br />2951.0
<br />713.3
<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 />72.5,0
<br />50
<br />3431.4
<br />' 948.9
<br />418
<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 />1930.4
<br />20
<br />2571.0
<br />550.4
<br />20,
<br />3UO3.9
<br />739.7
<br />20
<br />3465.4-
<br />.60.6
<br />966.5
<br />30
<br />2581.0
<br />554.5
<br />30
<br />3014,5
<br />714.6
<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 />2001.1„
<br />562.8
<br />50
<br />3035,8
<br />754.6
<br />50
<br />3499.7
<br />984.3
<br />&.9
<br />2611.2
<br />566.9
<br />56
<br />3046.5
<br />759.6
<br />63
<br />3511.1
<br />090.2
<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 />3067.0
<br />760.7
<br />20 .
<br />3534.5
<br />1002.3
<br />30
<br />264t.4
<br />579.5
<br />.30
<br />3075.7
<br />774.7
<br />30
<br />3545.6
<br />LoU8.3
<br />40
<br />2651_5
<br />583.8
<br />'40
<br />3059.4
<br />770.8
<br />40
<br />3557.2
<br />1014.4
<br />50
<br />.2661. 6
<br />583.0
<br />50
<br />3100.2
<br />754.9
<br />50
<br />3568.7
<br />1020.5
<br />Corrections to be Added (T=Tangent. E=External.) -
<br />Int.
<br />Angle
<br />p�sye 5°
<br />10°
<br />15° 120°
<br />an
<br />Tangent
<br />25°
<br />A, t'
<br />gle
<br />35°
<br />40°
<br />45°
<br />50°
<br />5"a°
<br />60°
<br />63°
<br />7U°
<br />40°
<br />T-.13 ,
<br />.26
<br />.40
<br />.53
<br />fi7
<br />10'
<br />:93
<br />.106
<br />1.20
<br />1.34
<br />1.40
<br />1.64
<br />1.79
<br />1.94
<br />20
<br />E=.023
<br />.046
<br />.0701
<br />A93
<br />.117
<br />30
<br />.172
<br />.203
<br />.234
<br />265
<br />.277
<br />90
<br />.315
<br />.341
<br />45°
<br />T=.15
<br />.30
<br />.44
<br />.60
<br />.761.06
<br />r.141
<br />4695.2
<br />121
<br />1.37.
<br />1.52
<br />1.70
<br />1.87
<br />2.04
<br />2.21
<br />50
<br />E=.030
<br />,060
<br />.093
<br />.119
<br />.153
<br />72
<br />.216
<br />254
<br />.289
<br />.325
<br />.351
<br />.378
<br />.411
<br />.445
<br />50°
<br />T=.17
<br />.34
<br />.51
<br />.68
<br />.85
<br />20
<br />119
<br />1.36
<br />1.54
<br />1.72
<br />1.9I
<br />2.10
<br />2.29
<br />2.48
<br />30
<br />E=.037
<br />.075
<br />.116
<br />.151
<br />.189
<br />1.14
<br />.200
<br />1.32
<br />.305
<br />i.52
<br />.345
<br />1.72
<br />.384
<br />1.92
<br />.425
<br />2.14
<br />AN
<br />2.35
<br />.508
<br />2.56
<br />.550
<br />2.77
<br />$5° ' T=19
<br />.38 .57 .76' .05
<br />1731.7
<br />E=,046
<br />.093
<br />.142
<br />.188
<br />.236
<br />.283
<br />1.27
<br />.332
<br />1:19
<br />3,81
<br />1.71
<br />,420
<br />1.94
<br />.479
<br />2.1711:6331,12.60
<br />.530
<br />.582
<br />.641
<br />2.83
<br />.700
<br />3.07
<br />60° T=.21'
<br />.42 .63 .84 1.05
<br />4807.7
<br />E=.056
<br />.112
<br />.168
<br />.225
<br />.283
<br />.340
<br />1.40
<br />.398
<br />1.64
<br />.457
<br />1.88
<br />..516
<br />2.13
<br />.575
<br />2.38
<br />2.63
<br />.697
<br />2.88
<br />.774
<br />3.13
<br />.851
<br />3.39
<br />65° T=.23
<br />.46' 69 93 1.16
<br />20
<br />E=,007
<br />'.135
<br />.204
<br />273
<br />.343
<br />.412
<br />.463
<br />.554
<br />.625
<br />.697
<br />.711
<br />.845
<br />.922
<br />1.01
<br />u
<br />TABLE I. - Tangents and Externals to a 1° Curve: -V
<br />Chord= 100 It.
<br />Int.Tangent
<br />Angle
<br />100 150
<br />erna
<br />External
<br />Int'
<br />Angle
<br />an
<br />Tangent
<br />External
<br />A, t'
<br />gle
<br />Tangent
<br />External
<br />G4°
<br />3580.3
<br />1026.6
<br />71°
<br />4086.9
<br />1308.2
<br />78°
<br />4639.8
<br />1643.0
<br />lot
<br />3591.9
<br />1032.8
<br />10'
<br />4099,5
<br />1315.6
<br />10'
<br />4653.6
<br />1051.7
<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 />36$8.5
<br />1057.7
<br />50
<br />411,0.1
<br />1345.1
<br />50
<br />4709.2
<br />1680.9
<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 />10
<br />3661.9
<br />1070.2
<br />10
<br />4175.E
<br />1860_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 />3085.4
<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.G
<br />1740.8
<br />GG
<br />372D.0
<br />1102.2
<br />73 '
<br />4239.7
<br />1398.0
<br />80'
<br />4807.7
<br />.1740.9
<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 />20
<br />48361.2
<br />1768.2
<br />30
<br />3756.5
<br />1.121.7
<br />30
<br />4276.5
<br />1421.2
<br />30
<br />48:10.5
<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 />3730.4
<br />1134.8
<br />50
<br />4304.6
<br />1436.8
<br />0
<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 />1145.0
<br />10
<br />4330.7
<br />1452.5
<br />10
<br />4908.0
<br />1814.7
<br />20
<br />3816.4
<br />1154.7
<br />20
<br />4343.8
<br />14G0.4
<br />20
<br />4922.5
<br />1824.1
<br />30
<br />3828.4
<br />11G1.3
<br />30
<br />435G.9
<br />1.4.65.4
<br />30
<br />4937.0
<br />1833.6
<br />40
<br />3840.5
<br />1168.1
<br />40
<br />4370.1
<br />1.47G.4
<br />,¢0
<br />4951.5
<br />1843.1
<br />,50
<br />3852.6
<br />1174.8
<br />50.
<br />4383.3
<br />14S4.4
<br />50
<br />4966.1
<br />1852.6
<br />GS
<br />3804.7
<br />1181.6
<br />75
<br />4396-5
<br />'1493.4
<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 />1508.0
<br />20
<br />5010.0
<br />1881.5
<br />3U
<br />3901.2
<br />1202,0
<br />30
<br />4436.4
<br />1510.7
<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 />5060.2
<br />1920.5
<br />10
<br />3950.2
<br />1229.7 '.I
<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 />30
<br />4516.9
<br />1566.3
<br />30
<br />5113.9
<br />1950.3
<br />40
<br />3987.2
<br />_1243.7
<br />1250.8
<br />40
<br />4530.4
<br />1574.7
<br />40
<br />5128.0
<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 />7Q
<br />4011.9
<br />1255.0
<br />77
<br />4557.6
<br />1591.G
<br />84
<br />5159.0
<br />1980.4
<br />10
<br />4024.4•
<br />1272.1
<br />10
<br />4571.2
<br />1000.1
<br />10
<br />5174.1
<br />1990.5
<br />20
<br />4030.8
<br />1279.3
<br />20
<br />4584.8
<br />1308.6
<br />20
<br />5189.3
<br />'2000.6
<br />30
<br />4049-3
<br />1236.5
<br />30
<br />4598.5
<br />3617.1
<br />30
<br />5204.4
<br />2010.8
<br />40
<br />4061.8
<br />1293.G
<br />40
<br />4612.2
<br />3.025.7
<br />40
<br />5219.7
<br />2021.1
<br />50
<br />4074.4
<br />1300.9
<br />50
<br />4626.0
<br />1,634.4
<br />50
<br />5234.9
<br />2031.4
<br />Correctior_s to be Added (T =Tangent. E External.)
<br />Curva 5°
<br />100 150
<br />20°
<br />25°
<br />30°
<br />3S1
<br />401
<br />451 50°
<br />55°
<br />60° 65°
<br />70°
<br />Angle
<br />T=.21
<br />.42 .03.
<br />.84
<br />1.05
<br />1.27
<br />1.49
<br />1.71
<br />1.94 2.17
<br />2.38
<br />2,60 2.83
<br />3,07
<br />80° E=.056
<br />.112 .168
<br />.225'.283
<br />.340
<br />.308
<br />.457
<br />.516 .575
<br />.036
<br />,697 .774
<br />.851
<br />T=.23
<br />.46 .69.
<br />93
<br />1.16
<br />1.40
<br />1.69
<br />1,88
<br />2.13 2.38
<br />2.63
<br />2.88 3.13
<br />3.39
<br />E=.067
<br />.135 .204
<br />273
<br />.343
<br />.412
<br />.483
<br />.554
<br />.625 .097
<br />.711
<br />.845 .922
<br />1.01 .
<br />T=.261
<br />.76
<br />1.02
<br />1.28
<br />1.54
<br />1.80
<br />2.06
<br />2.33 2.60
<br />2.88
<br />3.16 3.44
<br />3.72
<br />701 E=.080
<br />.159 .240
<br />.321
<br />,403
<br />.485
<br />.508
<br />.652
<br />.735 .819
<br />.906
<br />.994 1.08
<br />1.17
<br />T=27
<br />.56 .83
<br />1.12
<br />1.40
<br />1.69
<br />1.98
<br />2.27
<br />287 2.87
<br />3.16
<br />3.47 3.78
<br />4.09
<br />E =.095
<br />.182 .286
<br />.383
<br />. 480
<br />.578
<br />.678
<br />.777
<br />.877 .977
<br />1.07
<br />1.18 1.29
<br />1.39
<br />T=.30
<br />.61 .91
<br />1.22
<br />1.53
<br />1.64
<br />2.15
<br />2.46
<br />2.78 3.10
<br />3.44
<br />3.78 4.12
<br />4.45
<br />80° E=.110
<br />.220 .332
<br />.445
<br />.558
<br />.671
<br />.787
<br />903
<br />1.02 1.13
<br />1.25
<br />1.38 1,50
<br />11.62
<br />85° T 33
<br />.6G 1.E10
<br />1.33
<br />1.68
<br />2.02
<br />2.36
<br />2.70
<br />3.05 3.40
<br />3.77,
<br />4.14 4.55
<br />4.99.
<br />E=.129
<br />.259 .351
<br />.524
<br />.657
<br />.790
<br />.026
<br />1.06
<br />1.20 1.34
<br />1.47
<br />1.02 1.76
<br />1.01
<br />
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