|
VI TA LD I. - Tangents.and Externals to -a V. Curve:
<br />Chord=100 ft.
<br />• Angle
<br />Tangent
<br />External
<br />'Angle
<br />Tangent
<br />External
<br />t Int.
<br />n tie"'
<br />Tangent
<br />External
<br />85°:;
<br />:5250:3
<br />2041
<br />92°
<br />'5933.2
<br />2515.5
<br />99°
<br />6708.6'
<br />3092.7
<br />10'
<br />`'5265.6
<br />2052..7 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 />X20
<br />5967.9
<br />2543.5
<br />20
<br />6748.23122.9
<br />.657
<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 />6803.2
<br />3168.7
<br />;86'
<br />5343:0
<br />2104:7
<br />`93'
<br />'6037
<br />2594.0
<br />100 _ "
<br />'6828.3
<br />3184:1
<br />10
<br />`5358.6
<br />2115.3
<br />10:
<br />4
<br />2606.8
<br />10
<br />6848:5
<br />3199.6
<br />1.;,,.20
<br />5374:2:
<br />2126.0
<br />20-
<br />.6055..8
<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 />�610S.6
<br />2645.5
<br />' 40
<br />6909.6,
<br />3246.5
<br />50
<br />5421.4:
<br />2158.4
<br />50
<br />612614
<br />2658.5
<br />50
<br />6930.1
<br />3262.3
<br />'87 "
<br />'5437.2
<br />2160.2
<br />94: ;
<br />'6144:S
<br />2671.6.
<br />101 '
<br />`6950:6
<br />3278.1
<br />10
<br />545311,
<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 />2697.9
<br />20
<br />`6992.0
<br />3310.1
<br />-30
<br />'5184:9'
<br />15500.9
<br />2202.2
<br />'30;
<br />16198.3
<br />2711.2
<br />• 30
<br />7012,7
<br />3326,1
<br />j ,40
<br />1.17-
<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 />BS."�
<br />5533:1
<br />2235:5
<br />95
<br />2751=:3
<br />102
<br />7075:'b
<br />3374.9
<br />- 30
<br />.554912;
<br />2246.7
<br />10
<br />,6252.8
<br />6271:1
<br />2764.8
<br />10
<br />'7096.6
<br />3391.2
<br />C 20
<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 />80
<br />'6307.9
<br />2792.0
<br />30
<br />7139.0
<br />3424.3
<br />40
<br />5597.8
<br />2280.6 i
<br />'- • 40
<br />G326.3
<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 />7181'.7"
<br />3457.6
<br />'49.'
<br />5630.51
<br />2303.5
<br />X96
<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 />8491.3
<br />20
<br />15663.4.
<br />2326.6
<br />'
<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 />'7268:0
<br />3525.2
<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 />i
<br />50
<br />7311,7
<br />3559.6
<br />90 r
<br />-5729.72373.3:
<br />.87'
<br />6476.2
<br />2917.3 `:
<br />104 '-:
<br />7333.6
<br />3576.8
<br />10
<br />X5746:3
<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 4
<br />`-•'-20
<br />'7377.8
<br />3611.7
<br />30
<br />5779.9
<br />2408.0
<br />30
<br />:6533.4
<br />2960.3
<br />• 30
<br />-7399.9
<br />'3629.2
<br />;40 .'5796.7
<br />2420.9 .
<br />40
<br />'
<br />6552.6'
<br />2974.7 ;
<br />40
<br />7422:2
<br />8646.8
<br />••50 .
<br />'5813.6
<br />2432.9 4
<br />50
<br />6571.9
<br />2989.2
<br />'•50
<br />:7444:6
<br />3664:5
<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 />5847.5
<br />2457.1`
<br />'•,'10
<br />6610.6
<br />3018.4
<br />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 .'"7512.2
<br />'3718.2
<br />30
<br />: 5881.7-2481.5
<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 />13754.4
<br />50
<br />5916.0
<br />2506.1
<br />50
<br />6688.8
<br />3077.7"
<br />; 50
<br />`7580.5
<br />8772.6
<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°i
<br />45°;
<br />50°i
<br />, 55°
<br />60°
<br />65°
<br />70°
<br />85°
<br />T=.33
<br />.66
<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 />8.77
<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 />.92611.06.
<br />'3846.5
<br />'3865.2
<br />1.20
<br />1:34
<br />1.47
<br />1:62
<br />1.76
<br />.1.91
<br />906
<br />T =.36
<br />•.72
<br />1.09
<br />1.45
<br />1.83.
<br />2.20
<br />2.57.
<br />2.94'
<br />3.32.-3.70,
<br />7743,2
<br />4.10
<br />4.50.
<br />4.91
<br />5.32
<br />117:
<br />E=.149,
<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 />i 95°
<br />T ='.39
<br />..79
<br />1.19
<br />1.55,
<br />2.00 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 />5315.0,.
<br />E =.174'
<br />'.350
<br />.522
<br />..706
<br />.985
<br />1.06
<br />1.25
<br />1.43
<br />1.62
<br />1.80
<br />.1.99
<br />2.18
<br />2.38
<br />12.58
<br />110, f'
<br />T=.43
<br />'.85
<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 />i105°
<br />T=.46
<br />.94
<br />1.42
<br />1.90
<br />2.38
<br />2.8T
<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 />4743.6
<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 />1 2.39
<br />2.64
<br />2.90
<br />3.16
<br />3.41
<br />TABLE I. --Tangents and Externals to a 1° Curve. VII'
<br />1 t n,nrd=100 ft..
<br />-Int..:
<br />Angle,
<br />Tangent
<br />Eitemal
<br />Irit. _
<br />Angle' .Tangent
<br />30° 35°
<br />External
<br />Int.
<br />Angle _
<br />Tangent 'External
<br />60°
<br />106° '"'
<br />'3791.0
<br />111°
<br />8336.7
<br />4386.1
<br />116°i
<br />9169.4•5082:7.
<br />-7603.5
<br />7626.6
<br />'3809.4..'
<br />: 10^
<br />8362.7..,
<br />4107.6
<br />10'
<br />9199.1
<br />.5107.9
<br />.10'
<br />20'
<br />7649.7
<br />3827:9
<br />:; 20
<br />8388.9'
<br />4429.2
<br />20
<br />30•.9259.0
<br />9229.0
<br />5133.3
<br />30-
<br />7672.9
<br />'3846.5
<br />'3865.2
<br />30.
<br />40
<br />8415,.1,,:4450.9
<br />8441.5
<br />.4472.7
<br />: ..
<br />40.
<br />.5158.8
<br />9289,.2.,;
<br />5184.5
<br />40'
<br />50
<br />:,7696.3
<br />7710.7r
<br />3884.0.
<br />50
<br />8468.0..
<br />444,4.6
<br />50
<br />9319.5
<br />5210.3
<br />107
<br />7743,2
<br />3902:9
<br />11.2
<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,.4538:8
<br />3.35
<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 />941L 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 />39'38:7
<br />`50
<br />8629.3':
<br />4628.6
<br />50'
<br />'9504.4
<br />5368.2
<br />108 -
<br />7886:2,4018:2
<br />113.
<br />8656.6'
<br />4651.3'
<br />118'`
<br />9535;7-
<br />5395.1
<br />" 10
<br />7910.4'•4037:8108684.0
<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-'.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:P
<br />5476.5
<br />40`
<br />7983:5'
<br />4097A
<br />40
<br />8767.0,
<br />4743.6
<br />X40
<br />9662.6
<br />5504.0
<br />5008.0
<br />4117.0 •
<br />°- - , 50
<br />- 5794.9
<br />476G.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 />;16,
<br />4157,.3-
<br />_ :108851.0
<br />4814.1
<br />10..
<br />9759,.4
<br />5587.4
<br />t20•
<br />.8057.4
<br />8052.3:
<br />'4177.!5
<br />20'•
<br />8879.3
<br />4837.8
<br />20'
<br />9792.0
<br />5615.5
<br />30'.'8107.3.
<br />4197.9
<br />.30
<br />8907:.7
<br />4861:7
<br />30
<br />9824.8
<br />5643.8
<br />0'.•40.'
<br />'8132:3'
<br />4218.4.
<br />t .'40
<br />X8936:3
<br />4885:7
<br />40
<br />9857.7
<br />5672.3
<br />'.50:
<br />.8157.5
<br />4239.0
<br />50 .
<br />,'8965:Q
<br />4909,.9'.
<br />50,
<br />9390.8'
<br />5700.9
<br />1101 %
<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 />- ,. 110 `'9957.5
<br />5758.6
<br />`-20
<br />20
<br />•9051.7'
<br />4983.1
<br />20
<br />9991.0
<br />5787.7
<br />':�30'
<br />;8233:7
<br />8259.3
<br />.4301.4
<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':G
<br />40
<br />0110.3
<br />5032.6
<br />`•-40
<br />" '10093:0.
<br />10059:0
<br />.5846.5.
<br />587G. -I
<br />:50
<br />:8310:8
<br />4364'.8'
<br />50
<br />9139.8'
<br />5057,6
<br />50
<br />Corrections to be Added (T =Tangent.' E = External:)
<br />Int.Angle Curve 5°
<br />10°'
<br />15° 20°
<br />25°
<br />30° 35°
<br />40°
<br />'45°' 50°
<br />55°
<br />60°
<br />65° 70°
<br />1 1
<br />100° E =.200
<br />.401
<br />604 809
<br />1.01
<br />1.22 1.43
<br />1.64
<br />1.85 2.06
<br />2.28
<br />2 50
<br />2.73 2.96
<br />T=.46
<br />1.42 1.90
<br />2.38
<br />2.87, 3.34
<br />3.84
<br />4.35 4.84
<br />5.35
<br />5.87
<br />8.40 8 �3
<br />105°' E =.230.
<br />.94
<br />.470
<br />.700 '.938
<br />1.17
<br />1.42 1.65
<br />1.90
<br />2.14 2.39
<br />2.64
<br />2.90
<br />3.16 3.41
<br />T=.50
<br />1.03
<br />1.55 2.08
<br />12.60
<br />3.14 3.66
<br />.4.21
<br />4.76 5.31
<br />5.86
<br />6.43
<br />7.01 7.59
<br />110° E=.260
<br />':535
<br />.808 1.08
<br />1.36
<br />1.63 1.91
<br />2.19
<br />2.49 2.61
<br />3:05
<br />3.35
<br />3:65 3.95
<br />T=.54 .1.13
<br />1.70 2.29
<br />2.86
<br />3.45 4.03
<br />4.63
<br />,5.23, 5.83
<br />6.44
<br />7.07
<br />7.70 8.35
<br />115° E =.307
<br />.624
<br />.939 1.26
<br />1.57
<br />1.89. 2.21
<br />2.54
<br />2.87 3.20
<br />3.53
<br />3.88
<br />4.23 4.58
<br />T=.61
<br />1.25
<br />1.89 2.52,
<br />3.16
<br />3.81 4.44
<br />5.11
<br />5.78 6.44
<br />7.11
<br />7.80
<br />8.51 9.21
<br />120°.. ,E =,339
<br />..720
<br />1.08 1:45
<br />1.82
<br />2.20 2.66
<br />2.05
<br />3.33 3.72
<br />4:10
<br />4.50
<br />4.91 5:32
<br />m ru
<br />
|