|
VI TABLE"I, - Tangents and Externals.to' a 1° Curve.
<br />Chord=100 ft.)
<br />Angle
<br />Tangent
<br />External
<br />Angle
<br />Tangent
<br />External
<br />Angle
<br />'Tangent
<br />External
<br />45°.:
<br />.'5250.3
<br />2041.7{
<br />92°':
<br />5933.2
<br />2518:5
<br />99°-
<br />6708,6
<br />3092.7
<br />?.10'
<br />'526
<br />2052.1
<br />-10'
<br />5950.5
<br />2531,0
<br />10'
<br />G728,4
<br />3107.7
<br />20,
<br />5281.0
<br />2062.5
<br />20
<br />6967.9
<br />, 2543.5
<br />20.
<br />6748.2
<br />3122.9
<br />`'30.
<br />5290.4
<br />2073.0
<br />30
<br />5985:3
<br />2556,0
<br />30_
<br />G768,1
<br />3138.1
<br />.''40.
<br />"5311:9
<br />2083.5
<br />t40:
<br />6002.7
<br />2568,6
<br />2.20
<br />0788;1
<br />31'53.3
<br />7.A 50.
<br />5327.4
<br />2094.1
<br />_-•;50;
<br />6020.2
<br />i
<br />2581.3
<br />>40•
<br />„'50
<br />6308.2
<br />3168.7
<br />86 1
<br />5343:0
<br />2104:7
<br />j 93`.
<br />6037.8
<br />2594.0
<br />.100 ^::,
<br />G828:3
<br />3184.1
<br />10
<br />5358:6
<br />2115.3
<br />; ;10'
<br />6055:4
<br />2606.8
<br />10
<br />6848:5
<br />3199.6
<br />.20•
<br />5374.2
<br />2120.0'20
<br />j 3.61
<br />G073.1
<br />2619.7
<br />20r
<br />6868_.8
<br />3215.1
<br />30
<br />5389.9
<br />2136.7
<br />;;�,,30'
<br />G090.8
<br />.2032.6
<br />30-
<br />6889:2
<br />3230.8
<br />40'
<br />5405.6
<br />2147.5
<br />140:
<br />6108.6
<br />2645.5
<br />40,
<br />6909:6
<br />3246.5
<br />50,
<br />5421.4
<br />2158.4
<br />;50
<br />r
<br />6126.4
<br />{2658.5
<br />50,
<br />` 6930.1
<br />3262.3
<br />87
<br />5437.2
<br />2169.2
<br />94
<br />6144.3
<br />2671:6
<br />`101_••rc
<br />6950.6
<br />3278.1
<br />.10
<br />5453.1
<br />2180.2
<br />10`
<br />6,162.6
<br />2684.7
<br />10-
<br />6971.3
<br />3294A
<br />20
<br />5469.0
<br />2191.1
<br />'20'
<br />6180.2
<br />2697.9
<br />;,20:
<br />.6992.0
<br />3310.1
<br />..+30
<br />5484,9
<br />2202.2
<br />.•,30.
<br />6198:3
<br />2711.2
<br />30
<br />7012:7
<br />3326.1
<br />405500.9
<br />.938
<br />2213.2
<br />140'
<br />6216.4
<br />2724.5
<br />40_
<br />7033.6
<br />3342.3
<br />50.
<br />5517.0
<br />2224.3
<br />1, 50
<br />0234.6
<br />2737.9
<br />50.
<br />7054.5
<br />.3358.5
<br />88-,
<br />5533:1
<br />2235.5
<br />95'..•
<br />6252.8
<br />2751:3
<br />.102- -
<br />`..7075:5
<br />3374.9
<br />10'
<br />5549.2
<br />2246.7
<br />10'
<br />6271.1
<br />2764.8
<br />-10,
<br />7096.6
<br />3391.2
<br />2Q
<br />5565.4
<br />2258.0
<br />20
<br />.6289.4
<br />2778.3
<br />20•
<br />7117.8
<br />'3407.7
<br />:.30.
<br />+ 5581.6
<br />2269.3
<br />.30:
<br />6307.9
<br />27
<br />30'
<br />7139.0
<br />3424.3
<br />40
<br />5597.8
<br />2280.0
<br />40
<br />6320.3
<br />.92.0
<br />2805.6
<br />40
<br />7160.3
<br />3440.9
<br />50.
<br />5614.2
<br />2292.0
<br />,,-50,
<br />6344.8
<br />2819.4
<br />:' ,_50
<br />1 7181.7
<br />3457.6
<br />-89
<br />5630,5
<br />2303:5
<br />96'%
<br />6363.4
<br />2833:2
<br />:103.'
<br />7203.2
<br />3474.4
<br />10
<br />6646,9
<br />2315.0
<br />10•
<br />6382.1
<br />2847.0
<br />., 10:
<br />7224:7
<br />3491.3
<br />20
<br />56663.4
<br />2326.6
<br />20:,
<br />6100:8
<br />2861.0
<br />20
<br />,7246.3
<br />3508.2
<br />30'
<br />5679.9
<br />2338.2
<br />,30.
<br />6419.5
<br />2875.0
<br />30-
<br />7268.0
<br />3525.2
<br />- -'40
<br />5G96:4
<br />2340.8
<br />40'
<br />6438.4
<br />2889.0
<br />40'
<br />7289.8
<br />3542.4
<br />'c 50.
<br />5713.0
<br />2361.5
<br />- 50.
<br />.6457.3
<br />2903.4
<br />,•50:
<br />7311.7'
<br />3559.6
<br />90 rC'
<br />5729.7
<br />2373.3
<br />97,; "
<br />6476.2
<br />2917,3
<br />•104 "
<br />7333.6
<br />3576.8
<br />10
<br />:5746.3
<br />2385.1
<br />110
<br />6495.2
<br />2931.6
<br />10
<br />";7355.6
<br />3594.2
<br />20
<br />'5763.1
<br />2397.0
<br />-,;20'
<br />6514.3
<br />2945.9
<br />20
<br />' 7377.8
<br />3611.7
<br />30
<br />15779.9
<br />2108.9
<br />30
<br />'0533.4
<br />2960.3
<br />.30
<br />.7309.0
<br />3629.2
<br />40'
<br />5796:7
<br />2420.9
<br />:40,
<br />6552.0
<br />2974.7
<br />40.
<br />3646.8
<br />50
<br />5813.6
<br />2432.9
<br />50
<br />6571.9
<br />2989.2
<br />•. '50,
<br />.7422:2
<br />7444.6
<br />3664.5
<br />5830:5
<br />2444.9
<br />98„ '.
<br />6591.2
<br />:3003.8
<br />105.
<br />7467:0
<br />3682.3
<br />10
<br />5847.5
<br />2457.1
<br />:40
<br />• 6610.6
<br />= 3018.4
<br />7489:6
<br />3700.2
<br />20,
<br />':5864.6
<br />2469.3
<br />.20:
<br />6630.1
<br />3033.1
<br />-:':10.;
<br />! :.'20
<br />7512.2
<br />3718.2
<br />30:
<br />•.5881.7
<br />2481,5
<br />;30'
<br />6649:6
<br />3047:0
<br />i '-, 30.
<br />7534.9
<br />373G.2
<br />40
<br />5898.8
<br />2493:8
<br />40
<br />6669.2
<br />. 3062.8
<br />.'40'
<br />'.7557.7
<br />3754.4
<br />>...'b0
<br />5916.0
<br />2506.1
<br />50,
<br />: 6688.8
<br />3077.7
<br />_' 50.
<br />7580.5
<br />3772.6
<br />Corrections. to be Added (T Tangent. E.=External.),
<br />Int
<br />.Angle
<br />Curve 5�
<br />10°
<br />15°
<br />206
<br />'25°
<br />30°
<br />35°
<br />40°.
<br />45°.:
<br />50°
<br />-.55°
<br />60°'
<br />65°
<br />70°
<br />856
<br />T=.33
<br />.66
<br />1.00
<br />1.33
<br />1.68
<br />2.02
<br />2.38
<br />12.70
<br />13.05
<br />3.40
<br />3.77
<br />4.14
<br />4.55
<br />4.89
<br />20'
<br />E=:128
<br />.259
<br />.391
<br />.524
<br />.657
<br />.790
<br />.926
<br />1.06
<br />11.20
<br />1.34
<br />.1A7
<br />1.62
<br />1.76
<br />1.91
<br />90�
<br />T =•36 :
<br />-.72
<br />1.09
<br />4:45
<br />1.83
<br />2.20
<br />2.57
<br />2.94
<br />+.: 50">
<br />3.70
<br />4.10
<br />4.50
<br />4.91
<br />5.32
<br />50
<br />E =.149
<br />1.299
<br />.450
<br />.603
<br />.756
<br />'.910
<br />1.07
<br />1,22
<br />13.32
<br />-1.38
<br />1,54
<br />1.70
<br />1.87
<br />2.03
<br />2.20
<br />950;
<br />T=.39
<br />.79
<br />1.19
<br />1.55
<br />2.00
<br />2.40
<br />2.80
<br />13.20
<br />j 3.61
<br />4.02
<br />4.49
<br />4.08
<br />5.38
<br />5.83
<br />30•
<br />E =.174
<br />'.350
<br />.522
<br />.706
<br />.985
<br />1.06
<br />4:25
<br />11.43
<br />1 1.62
<br />1.80
<br />1.99
<br />2.18
<br />2.38
<br />2.58
<br />100o'
<br />T=.43
<br />.88
<br />1.30
<br />1,74
<br />2.18
<br />2.62
<br />3.06
<br />3.50
<br />3.95
<br />4.40
<br />4.88
<br />-5.37
<br />5.85
<br />6.34
<br />113, ..
<br />E =.200
<br />'.401
<br />.604
<br />.809
<br />1.01
<br />1,22.
<br />1,43
<br />1.64
<br />1,85
<br />2,06
<br />2.28
<br />2.50
<br />2.73
<br />2.98
<br />105°
<br />T=.46
<br />.94
<br />1.42
<br />1.90
<br />2.38
<br />2.87
<br />3.34
<br />3.84
<br />4.35
<br />4.84
<br />5.35
<br />5.87
<br />6.40
<br />6.93
<br />t-
<br />1
<br />E =230
<br />.470
<br />.700
<br />.938
<br />1.17
<br />1.42
<br />1.651
<br />1.90
<br />2.14
<br />1 2.39
<br />2.64
<br />2.00
<br />3.16
<br />3.41
<br />TABLE I. - Tangents and Externals to a 1° Curve. VII
<br />as a
<br />Chord =100 ft: '' , - .
<br />' Int+Tangent
<br />Aagle.
<br />Curve 5*
<br />External
<br />'Int,
<br />Angle"
<br />Tangent
<br />g
<br />Exteinal
<br />Int, '
<br />Angle
<br />Tangent
<br />External
<br />106°:;-,•
<br />'•7603:5
<br />3791,0
<br />1119 ..8336.7
<br />6�
<br />4386.1
<br />116°,
<br />9169.4
<br />5082.7
<br />10:
<br />'7626.6.
<br />3809.4
<br />10'
<br />8362.7
<br />'4407.6
<br />10'
<br />9199.1
<br />5107.9
<br />-•20'
<br />..,7649.7
<br />3827.9
<br />20'
<br />8388:9
<br />4429.2
<br />20
<br />9229.0
<br />5133.3
<br />30;
<br />:'.7672.9
<br />3846;5`30:
<br />8415.1'
<br />4450.9
<br />30
<br />9259.0
<br />' 5158.8
<br />40;;'7696.3
<br />T=.46
<br />3865.2
<br />40
<br />.8441.5,
<br />4472:7;
<br />40 "
<br />9289.2
<br />5184.5
<br />+.: 50">
<br />7719_7•
<br />3884,0
<br />50
<br />8468.0
<br />4494,6
<br />50
<br />9319.5.
<br />5210.3
<br />`107
<br />4743.2
<br />3902:9'
<br />112.
<br />8494.,6'
<br />4516.6_.117-
<br />9349.9
<br />5236.2
<br />--10
<br />'7766:8•
<br />3921.9
<br />10,
<br />8521.3,
<br />4538.8
<br />10
<br />0380.5
<br />5262.3
<br />20'
<br />7790'.5
<br />3940.9
<br />',20'
<br />8548'.1
<br />4561:1
<br />20
<br />9411:3
<br />5288.6
<br />30•
<br />7814.33.960:1
<br />..535
<br />30
<br />8575.0
<br />4583.`4'_
<br />30
<br />9442.2
<br />5315.0
<br />- ��40
<br />-7838.1
<br />3979.4
<br />40'
<br />8602.1
<br />4606.0
<br />40.
<br />9473.2
<br />5341.5
<br />• 50
<br />7862.1
<br />•3998.7''
<br />50
<br />8629.3
<br />4628.6
<br />50'
<br />•9504.4
<br />5368.2
<br />108."
<br />:,7886.2
<br />4018.21
<br />113, ..
<br />?8656.6
<br />4651.3
<br />118=
<br />9535.7
<br />5395.1
<br />4101
<br />1"
<br />:,,.7910. 4
<br />.4037:8'
<br />" 10
<br />8684.0
<br />4674.2
<br />10
<br />9567.2.
<br />5422.1
<br />20-
<br />='7934.6
<br />4057:4;
<br />20'
<br />8711.5
<br />4697:2
<br />20
<br />,0598.0
<br />5449.2
<br />3Q
<br />:7059.0'
<br />4077:2'
<br />130
<br />.8739.2;
<br />4720.3
<br />30
<br />,0630.7
<br />5476.5
<br />40'
<br />7983:5'
<br />4097:1',;'._
<br />2.20
<br />8767.0
<br />4743,6
<br />40
<br />9662.6
<br />5504.0
<br />r 50,
<br />:;8008. 0
<br />%4117.0
<br />,40'
<br />,' .50
<br />' 8794: 9
<br />4766.9
<br />50
<br />9694.7
<br />5531.7
<br />109,''•`,`.8032.7'.
<br />4137.1
<br />114
<br />8822.9
<br />4790.4
<br />119
<br />9727.0
<br />5559.4
<br />8057.44157.3
<br />10'
<br />.8851.0
<br />,4814.1
<br />10
<br />9759.4
<br />5587.4
<br />20`
<br />8082.3:
<br />4177.5'
<br />20
<br />8879.3"
<br />4837.8
<br />20
<br />9792.0
<br />5615.5
<br />�._ 30
<br />8107.3
<br />4197:9
<br />30
<br />8907.7
<br />4861.7
<br />30
<br />9824.8
<br />5643.8
<br />40 "•8132'3.
<br />'4218.4
<br />40
<br />8936.3
<br />4885.7
<br />40
<br />9857.7.
<br />5672.3
<br />= `•'50
<br />:8157:5.
<br />4239.0
<br />.50
<br />8965.0
<br />4909.9
<br />50
<br />9890.8•'
<br />5700.9
<br />110,
<br />'8182:8
<br />4259:7.
<br />115-
<br />8993.8
<br />4934.1
<br />120
<br />9924.0
<br />5729.7
<br />10
<br />8208:2
<br />4280.5
<br />•'_'10
<br />9022.7
<br />4958.6
<br />10
<br />9957,.5
<br />5758.6
<br />-20
<br />8233.7
<br />430I.A
<br />"20
<br />9051.7
<br />4983.1
<br />20
<br />9991.0
<br />5787.7
<br />30
<br />8259.3
<br />4322.4
<br />30
<br />9080.9
<br />5007.8
<br />'30
<br />10025.0
<br />5817.0
<br />•40
<br />8285.0.
<br />4343,6
<br />40
<br />9110.3•
<br />5032.6
<br />40
<br />10059.0
<br />5846.5,
<br />50
<br />8310.8
<br />4364.8
<br />50
<br />.9139.8
<br />5057.6
<br />50
<br />10093.0
<br />5876.1
<br />Corrections to be Added (T=Tangent.. E=External.)
<br />Int.
<br />Angle
<br />Curve 5*
<br />10°
<br />15°
<br />20°
<br />25°
<br />30°
<br />35°F4.63
<br />5°.
<br />50°
<br />55'
<br />60°
<br />6�
<br />70°
<br />100° '
<br />', T=.43
<br />.86
<br />1,30
<br />1.74
<br />2.18
<br />2.62
<br />3.0695
<br />4.40
<br />4:88
<br />5.37
<br />5.85
<br />6.34
<br />r=.200
<br />.401
<br />.604
<br />.809
<br />1.01
<br />1.22
<br />1.435
<br />2.06
<br />2.28
<br />2.50
<br />2.73
<br />MG
<br />T=.46
<br />1.42
<br />1.00
<br />2.38
<br />2.87
<br />3.3435
<br />4.84
<br />5,35
<br />5.87
<br />8.40
<br />8.93
<br />105°
<br />E=.230
<br />.94
<br />.470
<br />.700
<br />.938
<br />1:17
<br />1.42
<br />1,6514
<br />2.39
<br />2.64
<br />2.90
<br />3.16
<br />3.41
<br />1100 ;
<br />'•T=.50
<br />1.03
<br />1.55
<br />2.08
<br />2.60
<br />3.14
<br />3.6676
<br />5.31
<br />5,86
<br />6.43
<br />7.01
<br />7.59
<br />E=.260
<br />..535
<br />.808
<br />1.08
<br />1.36
<br />1.63
<br />1.019
<br />2.61
<br />3,05
<br />3.35
<br />3.65
<br />3.95
<br />✓
<br />.T=:54
<br />1.13
<br />1.70
<br />2.29
<br />2.86
<br />3.45
<br />4.0323
<br />5.83
<br />6,44
<br />7.07
<br />7.7 0
<br />8.35
<br />1150
<br />E =.307
<br />.624
<br />.939
<br />1.26
<br />1.57
<br />1.89
<br />2.21
<br />2.54
<br />2.87
<br />3.20
<br />3.53
<br />3.88
<br />4.23
<br />4.58
<br />120;,:
<br />T3..61
<br />1.25
<br />1.89
<br />2,52
<br />13.16
<br />3.81
<br />4.44
<br />5.11
<br />5.78
<br />6.44
<br />7,11
<br />7.80
<br />8.51
<br />9.21
<br />r..
<br />- E�-.339
<br />.720
<br />1.08
<br />1.45
<br />11.82
<br />2.20
<br />2.56
<br />2.95
<br />3.33
<br />3.72
<br />4,10
<br />4.50
<br />4.91
<br />5.32
<br />
|