|
VI TAsr rl L - Tangents and Externals to a V Curve.
<br />Chord =100 ft.'
<br />gle
<br />Tangent
<br />External
<br />Angle
<br />Tangent
<br />External
<br />Angle
<br />Tangent
<br />External
<br />850
<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 />•'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 />60
<br />5327.4'
<br />2094.1
<br />'50
<br />6020.2
<br />'2581.3
<br />- 50
<br />6808.2
<br />3168.7
<br />86r:.,.
<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 />X40
<br />'5405.6
<br />2147.5
<br />40 :
<br />;6108.6
<br />2645.5
<br />40:
<br />6909.6
<br />3248.5
<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 />2.38
<br />5437.2
<br />'2169:2
<br />-94 .'`
<br />;6144.3
<br />,2671.6
<br />101
<br />6950.6
<br />3278.1
<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 />:2191.1
<br />20
<br />6180.2
<br />;2697.920
<br />1.43
<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 />12213.2
<br />40
<br />6216.4
<br />4.35
<br />40,
<br />7033.6
<br />3342.3
<br />cb0
<br />5517.0
<br />(2224.3
<br />60 -
<br />6234. 6.
<br />,2724.5
<br />2737.9
<br />', '''b0
<br />7054.5
<br />3358.5
<br />88,
<br />5533.1
<br />2235.5
<br />95
<br />6252.8
<br />2751.3
<br />162
<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 />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 />80.
<br />,5581.6
<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 />6323.3
<br />2805.6
<br />40`
<br />7160:3
<br />3440.9
<br />50
<br />,5614.2
<br />2292.0
<br />- 59
<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 />t10.
<br />.2315.)
<br />10
<br />6382.1
<br />2847.0
<br />10
<br />.7224.7
<br />3491.3
<br />•20
<br />.5646.9
<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 />:9080:9
<br />9110.3
<br />2875.0
<br />30
<br />7268:0
<br />3525.2
<br />40
<br />5696.4•
<br />2349.8
<br />40
<br />.6419.5
<br />6438.4'
<br />2889.0
<br />40
<br />;7289.8
<br />3542.4
<br />•'=b0
<br />5713.0
<br />2361.5
<br />50
<br />-6457.3
<br />'2903.1
<br />50
<br />7311.7
<br />3559.6
<br />60- -
<br />5729.7
<br />'2373.3
<br />,97 '
<br />6476.2
<br />'2917.3
<br />104- -
<br />.7333.63576.8
<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 />,
<br />20'
<br />6514:3
<br />2945.9
<br />20
<br />7377.8
<br />.3611.7
<br />30.
<br />2408.9
<br />30
<br />6533.4
<br />2960.3
<br />30
<br />7399.9
<br />3629.2
<br />`.40.
<br />,5779.9
<br />:5796.7
<br />.2420.9
<br />--40-
<br />6552.6
<br />'2974.7
<br />40
<br />17422.2
<br />3646.8
<br />- 50
<br />5813.6
<br />2432.9
<br />60
<br />6571.9
<br />2989.2
<br />50
<br />7444.6
<br />3664.8
<br />91`
<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 />10
<br />-6610.6
<br />'3018.4
<br />1.10
<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 />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 />b0'
<br />;5916.0
<br />• 2506.1
<br />50
<br />6688:8
<br />'3077.7
<br />50
<br />'7580.5''3772.6
<br />:Corrections to be Added (T = Tangent. E. =External.)
<br />Angle,
<br />Curve 5°
<br />-106
<br />15°
<br />20°
<br />25°
<br />30°
<br />35°'
<br />40°
<br />45°
<br />'50°;
<br />;55°
<br />60°
<br />65°
<br />'70°
<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 />55°
<br />20...7649.7
<br />65°
<br />3827..9.
<br />20
<br />T=.33
<br />4429.2
<br />1.00
<br />1.33
<br />1.68
<br />2.02
<br />2.36
<br />2.70
<br />3.05
<br />3.40,
<br />3.77
<br />4.14
<br />4.55
<br />4.89
<br />85°-1
<br />E=.128
<br />.66
<br />.259
<br />.391
<br />.524
<br />.657
<br />.790..926
<br />9289.2
<br />1.06
<br />1.20
<br />1.34
<br />1.47
<br />1.62
<br />1.76.
<br />1.91
<br />60
<br />T=.36•..,
<br />5210.3
<br />1.09
<br />1.45
<br />1.83.
<br />2.20
<br />12.57
<br />2.94: 3.32'
<br />3.70
<br />4.10
<br />4.50
<br />4.91
<br />5.32 '
<br />90°
<br />E=:149
<br />.72
<br />.:299
<br />.:450
<br />.603
<br />.756
<br />.910
<br />1.07
<br />1.22
<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 />3.20
<br />3.61
<br />4.02 ,
<br />4.49
<br />4.98
<br />5.38
<br />5.83
<br />,4606:0
<br />E=.174'
<br />.350
<br />:522
<br />.706
<br />.985
<br />1.08
<br />1.25.
<br />1.43
<br />1.62
<br />'1.80
<br />-1.99
<br />2.18
<br />2.38
<br />2.58
<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 />5422.1
<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 />.94'11.4211.90
<br />5476,5
<br />40
<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 />4117.0
<br />50
<br />.470
<br />.700 .938
<br />1.17
<br />1.42
<br />1.65
<br />1.90
<br />2.14
<br />2.39
<br />2.64 2.90
<br />3.15
<br />3.41
<br />TABLE I. Tangents and Externals to a P Curve. _ VII.
<br />" •' - --= Chord =100 ft- -
<br />t.
<br />Anngle,l
<br />:Tangent
<br />Extemal
<br />..Angie
<br />..Tangent
<br />External
<br />..Angle'.
<br />Tangent
<br />External
<br />106°
<br />7603.5.
<br />3791.0
<br />711°
<br />8336.7
<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 />55°
<br />20...7649.7
<br />65°
<br />3827..9.
<br />20
<br />8388_.9
<br />4429.2
<br />20
<br />9229.0
<br />.5107.9
<br />5133,3
<br />30'•
<br />7672.9
<br />3846.5
<br />30.
<br />8415.1
<br />4450.9
<br />30
<br />9259.0'
<br />5158.8
<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 />- 60
<br />8468.0
<br />.4494.6
<br />60
<br />9319.5
<br />5210.3
<br />107
<br />7743.2
<br />3902.9
<br />712
<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 />.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 />9473.2
<br />5341.5'
<br />50
<br />.7862:1,
<br />3998.7
<br />50
<br />-8629.3
<br />'4628.6
<br />,40
<br />"-50.
<br />9504:4
<br />5368.2
<br />108 ." ..7886'.2
<br />3.65
<br />4018.2
<br />'4037:8
<br />113
<br />8656.6
<br />4651.3
<br />113-'--
<br />9535.7:
<br />5395.1
<br />101
<br />7910:4'
<br />4.63
<br />16
<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 />9598.9
<br />6449.2
<br />.30•..7959:0
<br />3.20
<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'_
<br />5559.4
<br />10'
<br />8057.4
<br />4157_.3
<br />"4177.,5
<br />10
<br />8851:0"
<br />4814.1
<br />10
<br />9759.4
<br />5587,4
<br />20
<br />8082.3,
<br />20..
<br />8879.3
<br />4837.820,
<br />9792.0.
<br />5615.5
<br />30-"
<br />8107.3'
<br />4197:9
<br />30
<br />8907:7'
<br />4861.7
<br />36
<br />9824.8
<br />5643.8
<br />x40
<br />-8132:3
<br />-4218.4
<br />40
<br />8936.3
<br />4885.7
<br />40
<br />9857.7.1
<br />5672.3
<br />-50
<br />;8157.5
<br />•4239.0,
<br />50
<br />8965:0'
<br />4909.9
<br />60'
<br />9890.8.
<br />5700.9
<br />110'''-
<br />8182.8
<br />'8208.2
<br />4259.7
<br />115 ;
<br />8993:8
<br />4934.1
<br />120
<br />9924:0
<br />5729.7
<br />:10
<br />4280:5.
<br />10
<br />9022.7
<br />4958.6
<br />10
<br />9957.5
<br />5758.6
<br />20
<br />30
<br />8233:7.'
<br />8259.3:
<br />4301:4.,
<br />'4322.4.
<br />- 20
<br />9051.7•.4983.1
<br />'20•
<br />9991.0
<br />5787.7
<br />40.
<br />8285.0
<br />4343.6
<br />30
<br />40
<br />:9080:9
<br />9110.3
<br />5007.8
<br />.5032.6
<br />30
<br />40
<br />10025:0
<br />10059.0
<br />5817.0
<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 />Angle
<br />Curve 5°
<br />W.
<br />'15°
<br />20°
<br />25°
<br />30°
<br />35°
<br />40°
<br />45°
<br />50°
<br />55°
<br />60°
<br />65°
<br />. 70°
<br />100°
<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 />8.34
<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 />2.90
<br />lOSo,
<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 />8.93
<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 />1150 '
<br />, T=.54
<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 />'.8241.28
<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 />4.58
<br />�0a
<br />T=.61
<br />1.25
<br />1.89
<br />2.52
<br />3.16
<br />3.81
<br />4.44
<br />5.11
<br />5.78
<br />8.44
<br />7.11
<br />7.80
<br />8.51
<br />9.21
<br />E=.339
<br />:7201.08
<br />1.45
<br />1.82
<br />2.20
<br />2.58
<br />2.95
<br />3.33
<br />3.72
<br />4.10
<br />4:50
<br />4.91
<br />532
<br />
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