|
VI
<br />Teai.E I, - Tangents and•Extei`nals to,a� Curve.
<br />Chnrd=100 ft_
<br />' Int,
<br />Anglc
<br />Tangent
<br />External
<br />Int.
<br />Angle
<br />Tangent
<br />-
<br />1;xternal
<br />Int.
<br />Angle
<br />Tangent
<br />External
<br />85°
<br />5230.3
<br />204,1.7
<br />021
<br />5933.2
<br />2518.5
<br />99°
<br />G708.6
<br />3092.7
<br />30'
<br />5265.6
<br />2052.1
<br />10'
<br />•5950,5
<br />2531.0
<br />- LO`
<br />6728.4
<br />3LO7.7
<br />20
<br />6281.0
<br />2062.5
<br />20
<br />5967.9
<br />2543.5
<br />20
<br />6748.2
<br />3122.9
<br />30
<br />529G.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 />0020.2
<br />2581.3
<br />50
<br />6SO8.2
<br />3168.7
<br />86
<br />5343.0
<br />2104.7
<br />93
<br />G037.9
<br />2594.0
<br />100
<br />682S.3
<br />3164.1
<br />10
<br />5358.6
<br />2115.3
<br />10
<br />6055.4
<br />2606.S
<br />10
<br />G848.5
<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 />5359.9
<br />2136.7
<br />.30
<br />6090.8-
<br />2632.6
<br />30
<br />6589.2
<br />3230.3
<br />40
<br />5405.6
<br />2147.5
<br />40
<br />6108.6
<br />2545.0
<br />40
<br />6909.6
<br />3246.5
<br />50
<br />5421.4
<br />2153.4
<br />50
<br />6126.4
<br />2658.5
<br />50
<br />G930.1
<br />3242.3
<br />87
<br />5437.2
<br />2160.2
<br />94
<br />6144.3
<br />2671.0
<br />101
<br />6950.6
<br />3275.1.
<br />10
<br />5453.1
<br />2180.2
<br />10
<br />6162.6
<br />2684.7
<br />10
<br />6971.3
<br />3294.1
<br />20
<br />5469.0
<br />2101.1
<br />20
<br />6180.2
<br />2697.0
<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 />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 />27-01.3
<br />102
<br />7075.5
<br />3374.9
<br />• 10--5.549.2
<br />S057.4
<br />2246.7
<br />40
<br />6271.1
<br />2764,8
<br />10
<br />7096.6
<br />3391.2
<br />20
<br />5565.4
<br />2258.0
<br />20
<br />6289.4
<br />2778,3
<br />20
<br />7117.8
<br />3.107.7
<br />30
<br />5.581.6
<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 />6326.3
<br />2305,6
<br />40
<br />7160.3
<br />3440.9
<br />60
<br />5614.2
<br />3292.0
<br />50
<br />6344,8
<br />2319.-1
<br />50
<br />7181.7
<br />3457.6
<br />89
<br />5630.5
<br />2303.5
<br />D6
<br />6363.4
<br />2S33.2
<br />103
<br />7203.2
<br />3474.4
<br />10
<br />5646.9
<br />2315.0
<br />10
<br />0382.1
<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 />350S.2
<br />30
<br />5679.9
<br />2338.2
<br />30
<br />6419.5
<br />2S75.0
<br />30 '
<br />7268.0
<br />3525.3
<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 />733.1.6
<br />3576.8
<br />10
<br />5746.3
<br />2385.1
<br />10
<br />-6495.2
<br />2031.6
<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 />40
<br />5796.7
<br />2420.9
<br />40'
<br />6552.6
<br />2974.7
<br />40
<br />7422.2
<br />3646.8
<br />50
<br />5813.6
<br />2432.9
<br />50
<br />6571.0
<br />2959.2
<br />50
<br />7444.6
<br />3664.5
<br />91
<br />5&30.5
<br />2444.9
<br />98
<br />6591.2
<br />3003.5
<br />105
<br />7467.0
<br />3682.3
<br />10
<br />584.7.5
<br />2457.1
<br />10
<br />6610-6
<br />3018.4
<br />10
<br />74S9.6
<br />3700.2
<br />20
<br />58&1,.6
<br />2469.3
<br />20
<br />6630.1
<br />3033.1
<br />20
<br />7512.2
<br />3718.2
<br />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 />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. Carve 5°'
<br />Angle
<br />10° 15° 1 211° 25° j' 30° 350 _40°
<br />45`..
<br />56°
<br />55°
<br />60° 65° 7
<br />8S' T=.33
<br />.65 1.00 1.33 1.68 2.02 2.36 2.70
<br />3.053-40
<br />106'
<br />3.77
<br />4.14 4x5 4-
<br />E-.128
<br />.259 ,391 .524 .657 .790 .926 1.06'
<br />1.20
<br />1.34
<br />1.47
<br />1.62 1.76 I.
<br />90°- T=.36
<br />.72 1.09 1.45 1.83 2.20 2.57 2.94
<br />8.33
<br />3.70
<br />4.10
<br />4.50 4.91 5.
<br />I;=.149
<br />.299 .450 .603 .750 .010 1.07 1.22
<br />1.33
<br />1.64
<br />1.70
<br />1.87 2.03 2•
<br />45° T =.39
<br />.79 .1.10 1.55 2.00 2.40 2.80 3.20
<br />3.61
<br />4.02
<br />4.49
<br />4.98 5.38 5.
<br />E=.174
<br />.350 .522 .706 .985 1,06 1.25 1.43
<br />1.62
<br />1.80
<br />1.99
<br />2.18 2.3S 2.
<br />100° T =.43
<br />.86 1.30 1 74 2.18 2.62 3.06 3.50
<br />3.95
<br />4.40
<br />4.88
<br />5.37 5.85 6.
<br />E =.200
<br />.401 .604 .809 LO1 122 1.43 1.64
<br />1.85
<br />2.00
<br />2.28
<br />2.50 2.73 2•
<br />105° E=230
<br />42 MU 3.34
<br />1 $2
<br />CSS
<br />14.84
<br />5.35
<br />6.87 640 V
<br />50
<br />12,381334
<br />.470 700 1 11 65 1..90
<br />1 2.14
<br />1 2.39
<br />2.64
<br />2.90 3.16 3:
<br />0°
<br />89
<br />32•
<br />20
<br />638
<br />3"
<br />96
<br />93^
<br />�41
<br />TABLE I. -- Tangents and Externals to a V Curve, jTII
<br />Chord =100 ft.
<br />Int,
<br />Angle'
<br />I Tangent
<br />External
<br />Int.
<br />Angle
<br />Tangent
<br />External
<br />Int.
<br />Angle
<br />Tangent
<br />External
<br />106'
<br />•7603.5
<br />'3791.0
<br />111°
<br />S336.7
<br />4386.1
<br />196°
<br />9169.4
<br />5082.7
<br />I0'
<br />7626.6
<br />3809.4
<br />10'
<br />5362.7
<br />4407.6
<br />10'
<br />9199.1
<br />5107.9
<br />20-
<br />7649.7
<br />3S27.0
<br />20
<br />S388.9
<br />4429.2
<br />20
<br />9229.O\
<br />5133.3
<br />30
<br />7672.9
<br />3846.5
<br />30
<br />5415.1
<br />4450.9
<br />_ 30
<br />9259.0
<br />y, 5158.8
<br />�}O
<br />7696.3
<br />3SG5,2
<br />40
<br />8441.5
<br />4472.7 I
<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 />5310.3
<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 />.5203.3
<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 />7814,3
<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 />5629.3
<br />4623,6
<br />50
<br />9504,4
<br />'5368.2
<br />109
<br />7886.2
<br />.4018,2
<br />113
<br />116513 1)
<br />4.G5I:1
<br />318
<br />953.1.7
<br />5395,1.
<br />10
<br />7910.4
<br />4037.8
<br />10
<br />S6S4.0
<br />4G74..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 />9598.9
<br />54.19 .2
<br />30
<br />7959.0
<br />4077.2
<br />.30
<br />.373'9,2
<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 />474,3.6
<br />40
<br />9652.6
<br />5504,0
<br />50
<br />8008.0
<br />4117.0
<br />50
<br />8794.9
<br />47GG.9
<br />50
<br />9604.7
<br />553t.7
<br />109
<br />8032.7
<br />4137.1
<br />114
<br />8822.9
<br />4790.4
<br />11,9.
<br />9727.0
<br />5559.4
<br />19
<br />S057.4
<br />4157.3
<br />10
<br />6851.0
<br />4814.1
<br />ID
<br />9759.4
<br />5587.4
<br />20
<br />8082.3
<br />4177.5
<br />20
<br />SS79.3
<br />4S37.8
<br />20
<br />9792.0
<br />5615.5
<br />30
<br />5107.3
<br />4197.9
<br />30
<br />8907.7
<br />4S6 I 7
<br />3D
<br />9824.8
<br />5643.8
<br />40-
<br />5132.3
<br />421.5.4
<br />40
<br />5936.3
<br />4585.7
<br />40
<br />9857.7
<br />5G72.3
<br />50
<br />8157.5
<br />4239:0
<br />50 _
<br />5965.0
<br />4909.9
<br />50
<br />9890.5
<br />5700.9
<br />110
<br />8182.8
<br />4259.7
<br />115
<br />899:3.8
<br />4934.1
<br />120
<br />9924.0
<br />5729.7
<br />10
<br />820S.2
<br />'4280.5
<br />10
<br />9022.7
<br />4958,6
<br />10
<br />9957.5
<br />Wag.G
<br />20
<br />8233-7
<br />4301.4
<br />20
<br />0054.7.
<br />4983.1
<br />20
<br />9991.0
<br />57S7,7
<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 />8310.3
<br />4364.5
<br />50
<br />9139.8
<br />5057.6
<br />510
<br />10093.0 -
<br />5876.1
<br />Corrections to be Added (T=Tangent. E =External.)
<br />lnt.
<br />Angle
<br />Curare 5'
<br />10° 15°
<br />20'
<br />25°
<br />30° 35° 40°
<br />45°
<br />50° 55° - 60° 65°
<br />70°
<br />1D0°
<br />T=.43
<br />.86 1.30
<br />1.74
<br />2.18
<br />".G2 3.06 3.50
<br />3.05
<br />4.40 4.88 5.37 5.85
<br />0.34
<br />E=.200
<br />:401 .601
<br />.809
<br />1.01
<br />1,22 1,43 1.64
<br />1.35`
<br />2,00 239 ?,50 2.73
<br />2.96
<br />105°
<br />T=.40
<br />.94 1.42
<br />140
<br />2.38
<br />2.87 jj ''.34 3.84
<br />4.3:14.84
<br />5.35 5.87 6.40U13
<br />E-.230
<br />AM .700
<br />Q381
<br />1.1'
<br />1.12 1.55 L9U
<br />2.14
<br />2.39 2.61 2,90 3.101
<br />3.41
<br />110
<br />T=•50
<br />1.03 11.55
<br />2.03
<br />2.00
<br />3.14 3.56 4.21
<br />4.76
<br />5.31 5:86 $.13 7.O1
<br />7,53
<br />1;=.260
<br />:i35L .808
<br />1.08
<br />1.36
<br />1.63 1.91 2 I9
<br />2A0
<br />2.61 3.05 3.3a 3.65
<br />3,95
<br />11."
<br />T-.54
<br />1.13 1.70
<br />2.21)
<br />2.86
<br />3.45 4.63 4.53
<br />5,23
<br />5.53 6.14 7.111 7.70
<br />8.33
<br />31 =.307
<br />•.6246 .4391.26
<br />1..57
<br />1.E9 2.21 284
<br />2.57
<br />3.20 3.53 3.83 4.23
<br />4,53
<br />120"
<br />T=,62
<br />1 S=,339
<br />1.25 11,3'3
<br />1.03
<br />2.52
<br />1.45
<br />3.16
<br />1,82
<br />3.81 4.44 511
<br />'2 20 2.1-61
<br />375
<br />6.44. 7.11 7,80 3.51
<br />4.10 4.•1-0 4.91
<br />9,21
<br />5,32
<br />.720
<br />2.93
<br />3.33
<br />3.721
<br />
|