|
VY TABzm L -,Tangents and: Externals to a-,1* Curve.
<br />Chord =100. ft.
<br />Angle
<br />Tangent
<br />g
<br />External
<br />Int.
<br />Angle
<br />Tangent
<br />g
<br />External
<br />Int'
<br />Angle
<br />Tangent
<br />g
<br />External
<br />'85°• '
<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 />'5265.6
<br />2052.1
<br />10'
<br />5950.5
<br />2531.0
<br />10'
<br />6728.4
<br />3107.7
<br />s>.•-20
<br />5281.0
<br />2062.5
<br />20
<br />5967.9
<br />2543.5
<br />20
<br />.6748:2.
<br />3122.9
<br />30
<br />5296.4
<br />2073.0
<br />'30
<br />5985:3
<br />2556.0
<br />30
<br />6768•.1
<br />3138.1
<br />40
<br />5311.9
<br />2083.5
<br />40
<br />6002'7
<br />2568.6
<br />40
<br />.6788.1
<br />3153,3
<br />50
<br />5327,:4
<br />2094.1
<br />50
<br />6020.2
<br />2581.3
<br />50
<br />6808.2
<br />3168.7
<br />86',
<br />5343.0
<br />2104.7
<br />93 -
<br />6037.8
<br />2594.0
<br />100
<br />6828:3
<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 />2126.0
<br />' 20.
<br />6073.1
<br />2619.7
<br />20
<br />6868.8
<br />3215.1
<br />30
<br />5389.9
<br />2136.7
<br />.30,
<br />6090.8
<br />2632.6
<br />30
<br />6889.2
<br />3230.8
<br />40
<br />5405.6
<br />2147.5
<br />40.
<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 />6126.4
<br />2658.5
<br />:.50
<br />6930.1
<br />3262.3
<br />187 `'t
<br />5437.2
<br />2169.2
<br />94 -:',
<br />6144.3
<br />2671:6
<br />101
<br />6950.6.
<br />3278.1
<br />16
<br />5453.1
<br />2180.2
<br />10':
<br />6162.6
<br />2684.7
<br />i•,. 10
<br />6971.3'
<br />3294.1
<br />L" 20
<br />5469.0
<br />2101.1
<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 />n,J 40
<br />5500.9
<br />2213.2
<br />..40-,
<br />6216.4
<br />2724.5
<br />40.
<br />.7033.6:
<br />3342.3
<br />50
<br />'5517.0
<br />2224.3
<br />;50:
<br />6234.6
<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 />.70N A'
<br />3391.2
<br />20
<br />55,35.4
<br />2258.0
<br />..20,
<br />6289:4
<br />2778.3
<br />(. 20
<br />7117.8
<br />3407.7
<br />30
<br />5531.6
<br />2269.3
<br />30
<br />6307.9
<br />2792.0
<br />30
<br />7139.0
<br />3424.3
<br />:40
<br />5597:8
<br />2280.6
<br />40•
<br />632ot3
<br />2805.6
<br />40
<br />7160.3
<br />344.0.9
<br />_ 50
<br />5614.2
<br />2292.0
<br />_50'
<br />6344.8
<br />2819.4
<br />,'50:
<br />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 />5646.9
<br />2315.0
<br />10'
<br />6382.1
<br />2847.0
<br />10
<br />7224.7
<br />3491.3
<br />20
<br />5663.4
<br />2326.6
<br />20
<br />6400:8
<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 />7268.03525.2
<br />5787.7
<br />40
<br />5696.4
<br />2349.8
<br />:40'
<br />6438.4
<br />2889.0
<br />40
<br />7289.8
<br />-3542.4
<br />50
<br />5713:0
<br />2361.5
<br />_50'
<br />6457.3
<br />2903.1
<br />50.
<br />7311.7
<br />3559.6
<br />,90 '
<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 />10
<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 />5779.9
<br />2408.9
<br />,30'
<br />6533:4
<br />2960.3
<br />30.
<br />7399:9
<br />3629.2
<br />P 40
<br />5796:7
<br />2420.9
<br />.,,40.
<br />6552.6
<br />2974.7
<br />'40'
<br />.7422.2
<br />3646.8
<br />i .(''50.
<br />5813.6
<br />2432.9
<br />_ ,50:,
<br />6571.9
<br />2989.2
<br />i,. 50
<br />7444.6
<br />3664.5
<br />61- '
<br />5830:5
<br />2444.9
<br />98'
<br />6591:2
<br />3003.8
<br />.105 '
<br />7467.0
<br />3682.3
<br />^.t 10.
<br />5847.5
<br />2457.1
<br />P.'101
<br />6610.,6
<br />3018.4
<br />i..10
<br />7489.6
<br />3700.2
<br />20:
<br />5864:6
<br />2469.3
<br />20
<br />6630.1
<br />3033.1
<br />.20.
<br />7512.2
<br />3718.2
<br />f;...30.
<br />5881.7
<br />2481.5
<br />30
<br />6649.6
<br />3047.9
<br />30
<br />7534:9
<br />3736.2
<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 />`. '50;
<br />5916.0
<br />2506.1
<br />b0
<br />6688.8
<br />3077.7
<br />C 50.
<br />7580.51
<br />3772.6
<br />i
<br />i
<br />4 Corrections to be Added (T= Tangent. - E:=External.)
<br />Angle
<br />e_
<br />-6,u,e 5°-_'.10°
<br />15°. .20° 25° 30° 350 40° 45° ' 50
<br />55°I 60° .65° 70°
<br />85°
<br />T=.33
<br />.66 L00 1.33 J1.68 2.02' 2.36 2:70 3.05 3:40
<br />-3.77
<br />'4.14 4.55 4.89
<br />166°
<br />E =.128
<br />.259 .391 .521 .657 .790 .926 1.06 1.20 LU
<br />1.47
<br />1.62 1.76 1.91
<br />;90°'
<br />' T=.36
<br />.72 1.09' 1.45 11.83 2:20 2.57- 2.94 3.32 3.70
<br />4.10
<br />4.50, 4.91 5.32
<br />7626.6_
<br />E=.149
<br />.299 .450 .603 .756 .910 1:07 1.22 1.38 1.54
<br />1:70
<br />1.87 2.03 2.20
<br />95°
<br />T=.39
<br />.79 1.19 L55 2.00 2.40 2.80 3.20 3:61 4.02
<br />4.49
<br />4.98 5.38 5.83
<br />3827.9
<br />E =.174
<br />.-.350..522 .706 .985 1.06 1.25 1:43 1.62 1.80
<br />1:99
<br />2.18 2.38 2:58
<br />100° `
<br />T=-43 .
<br />' •.86 1.30 1.74 2,18 2.62 ' 3.06 3.50 3.95 4.40
<br />'4.88
<br />5.37 5.85 6.34
<br />30
<br />E=.200
<br />.401 .604 .809 1.01 1.22 1.43 1.64 1.85 2.06
<br />2.28
<br />2.50 2.73 2.96
<br />105°
<br />T=.46
<br />.94 1.42 1.90 2.38 2.87 3.34 3.84 4.35 4.84
<br />5.35 5.87 6:40 6.93
<br />40
<br />E-.230
<br />..470 .700 .938 1.17 1.42 1.65 1.90 2:14 2.39
<br />2.64 2.90 3.16 3:41
<br />c�
<br />TABLE I. - Tangents,and Externals to a-1° Curve. Vil
<br />Chord= 100 ft.
<br />-int. '
<br />Angle _
<br />Tangent
<br />g .
<br />External
<br />Int.
<br />Angle
<br />Tan ent
<br />g
<br />External
<br />int.
<br />Angle.
<br />,Tan Tangent
<br />g
<br />Ezternal
<br />166°
<br />7603:5
<br />3791.0
<br />111°
<br />8336.7
<br />14386.1
<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
<br />30
<br />8415.1
<br />,4450.9
<br />30 "
<br />9259.0'.5158.8
<br />2.96
<br />40
<br />7696.3
<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 />7743.2.
<br />3902.9
<br />112 -
<br />8494.6
<br />4516.6
<br />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 />9380.5
<br />5262.3
<br />„
<br />1'.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 />7814.3
<br />3960.1
<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 />4018.2
<br />113'.
<br />8656.6.
<br />4651.3
<br />118'-
<br />9535.7
<br />5395.1
<br />10•
<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 />7034:6
<br />4057.4
<br />20
<br />8711.5
<br />4697.2
<br />'20
<br />9598.9
<br />.5449.2
<br />?..30:
<br />.7959.0
<br />4077.2
<br />.' 30
<br />'8739.2
<br />4720.3
<br />"30
<br />•9630.7
<br />5476.5
<br />..40
<br />'7983.5
<br />4097.1
<br />40
<br />8767.0
<br />4743.6
<br />40
<br />9662.6.
<br />5504.0
<br />50
<br />8008.0
<br />4117.0
<br />50
<br />8794.9
<br />'4766.9
<br />50
<br />9694.7
<br />5531.7
<br />109'
<br />8032.7
<br />4137.1
<br />114
<br />8822.9
<br />4790.4
<br />.119
<br />9727:0.5559.4`
<br />10-
<br />8057.4
<br />4157.3
<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
<br />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 />4301:4
<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 />d.- 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 />-
<br />10°
<br />15°
<br />20°
<br />25°
<br />30°
<br />35°
<br />40°
<br />45° 1
<br />50°
<br />55°
<br />60°
<br />65°
<br />70°
<br />100°
<br />T=.43
<br />.86
<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 />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 />2.96
<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 />E =.230
<br />.470
<br />.700
<br />.938
<br />1.17
<br />1.42
<br />1.65
<br />1.90
<br />2.14
<br />2.39
<br />2.64
<br />2.90
<br />3.16
<br />3.41'
<br />110°
<br />T=.50
<br />1.03
<br />1.55
<br />2.08
<br />2.60
<br />3.14
<br />3.66
<br />4.21
<br />4.76
<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 />1.91
<br />2.19
<br />2.49
<br />2.61
<br />3.05
<br />3.35
<br />3.65
<br />3:95
<br />115°
<br />1.13
<br />1.70'
<br />2.29
<br />2.86
<br />3.45
<br />4.03
<br />4.63
<br />5.23
<br />5.83
<br />6.44
<br />7.07
<br />7.70
<br />8.35
<br />E =.307
<br />.62.4
<br />.939
<br />1.28
<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 />458
<br />�Bq '
<br />T=.61
<br />1.25
<br />2.52
<br />3.16
<br />3.81
<br />4.44. 5.11
<br />5.78
<br />6.44
<br />7.11
<br />7.50
<br />8.51
<br />9.2i
<br />E =.339
<br />11.89
<br />.720.1.08
<br />1.45
<br />1.82
<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 />5.82
<br />I
<br />
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