|
VI
<br />TmiLE I. --Tangents and, Externals to a "I Cufve
<br />Chord=10G ft-
<br />Angle .
<br />Tangent
<br />External'
<br />' Angle
<br />Tangent
<br />External
<br />AnInt. -
<br />gle
<br />Tangent
<br />External
<br />86°
<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 />;5265:0
<br />2052.1
<br />101
<br />15950,5.
<br />2531.0
<br />10'
<br />0728.4:
<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 />'5290:41
<br />2073.0
<br />30
<br />5985.3
<br />2556,0
<br />30
<br />0768.V
<br />3138.1
<br />40
<br />_'5311:9'
<br />2083.5
<br />40
<br />6002.7
<br />2568,6
<br />40 ,'6788.1
<br />9259.2
<br />3153.3
<br />$0
<br />5327:4']
<br />2094.1
<br />50
<br />6020.2
<br />2581,3
<br />.50
<br />6808.2
<br />3168.7
<br />80. `
<br />:5343:0
<br />2104':7
<br />93 -
<br />60378
<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 1'
<br />2126.0.
<br />'20'
<br />G073.1
<br />2619.7
<br />20
<br />6368.8E
<br />3215.1
<br />30
<br />5389:9.
<br />2136.7
<br />' '',30;
<br />G090.8
<br />2632.6'
<br />30
<br />16889.2
<br />3230.8
<br />40
<br />5405:61
<br />2147.5
<br />40;'
<br />`61.08.6
<br />2645.5
<br />40 -
<br />6909.61
<br />3246.5
<br />50
<br />5421.4'
<br />2158.4
<br />" 60'
<br />6126.4
<br />2658.5
<br />50
<br />'6930,1;
<br />3262.3
<br />97
<br />5437.2
<br />2169.2
<br />94.
<br />6144.3'
<br />2671.6
<br />101.
<br />G950.6
<br />3275:1
<br />10
<br />'5453:1
<br />2130.2
<br />10'
<br />6162.6
<br />2654.7
<br />10 ,.6971.3
<br />9567.2'
<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 />:5454.9
<br />2202.2
<br />30
<br />6198.3
<br />2711.230
<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 />_ 1
<br />50
<br />7054.5'
<br />3358.5
<br />86
<br />'5533:1
<br />2235.5
<br />95
<br />6252.8'
<br />2751.3
<br />102
<br />. i
<br />7075,5
<br />3374.9
<br />10
<br />'5540.2
<br />2246.7
<br />30;
<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 />`G28914
<br />2775.3
<br />-20
<br />7117.8
<br />3407,7
<br />30
<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 />6326.3
<br />2865.0
<br />.40
<br />7160.3.
<br />3440.9
<br />130
<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 />fi3113.4
<br />2833.2
<br />103 -
<br />7203:2:
<br />3474.4
<br />10
<br />5646.9
<br />2315.0
<br />'16
<br />9382.1
<br />2847.0
<br />10:
<br />7224.7
<br />3491.3
<br />"'20
<br />5603.4
<br />2326.6
<br />20
<br />6400.8
<br />2861.0
<br />.'20
<br />7240.3
<br />3508.2
<br />,-30
<br />5679.9
<br />2338.230
<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 />50
<br />7311.7'
<br />3559.6
<br />.90
<br />5729.7
<br />2373.3
<br />97 •
<br />0476.2
<br />2917.3
<br />104
<br />7333.6'
<br />3570.8
<br />10
<br />5746.3
<br />2385.1-
<br />10-
<br />6495.2
<br />2931.6
<br />10
<br />7355.G'
<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 />579G.7
<br />2420.9
<br />40
<br />6552.6
<br />2974.7
<br />40 -
<br />7422.2
<br />3046.8
<br />50
<br />5813.6
<br />2432.9
<br />50
<br />6571.9
<br />21J89.2
<br />50
<br />7444,6
<br />3664.5
<br />B1
<br />58317,5
<br />2444.9
<br />98-
<br />6591.2
<br />3003.8
<br />105 -
<br />7467.0
<br />3652.3
<br />10
<br />5547.5
<br />2457,1
<br />10:
<br />6610.6
<br />3018:4
<br />10
<br />7489.6
<br />3700.2
<br />20
<br />5564.6
<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.G
<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 />7530.5
<br />8772.6
<br />,Corrections,t.o!Ve Added (T=Tangent.. , E. =External.)
<br />Angie Cu7e 5° ' 10° IS-
<br />20° 25°
<br />30°• 35° 40° 45° 50° 55°' 60°
<br />65° 70°
<br />SS` T=.33 G6 1.00
<br />1.33 1:68
<br />2.02 ' 2.3G 2.70 3.05 3.40 3.77 4,14
<br />4.55 4.89
<br />E =:128 _, .259 .391
<br />.524 .657
<br />.790 .926 1.06 120 1.34 X1.47 1.62
<br />1.76 1.91
<br />90° T=.36 .72 1.09
<br />1.45 11.83'
<br />2.20 2.57 2,94 3.32 3.70 4,10 4.50
<br />4.91 5.32
<br />E =.149 .299 .450'
<br />:603 .756
<br />.910 1.07 1.22 1.38 1.54 1.70 1.87
<br />2.03 2.20
<br />95° T=.30 .79 1.19
<br />1..55 2.00
<br />`2.40 2.80 3.20 3.61 4.02 4.49 4.98
<br />11.09
<br />5.33 5.83
<br />E =.174 350 .522
<br />.706 J85
<br />1.05 1.25 1.43 1.63 1.80 2,18
<br />2 38 2.53
<br />160° T=.43 .86 1.30
<br />1.74 12.18
<br />2.62 3.00 3.50 3.95 4.40 4.88 5.37
<br />12,06
<br />5.85 6.34
<br />E -.200 .401' .6D4
<br />.809 1.01
<br />7-22 1.43 1.64 1.95 2.28 2.50
<br />2.73 2.96
<br />105° T=.46 .94 1.42
<br />1.90 2.38
<br />2.67 3.34 3.84i 4.35 4.84 5:35 5.87
<br />6.40 6.93
<br />E=•230 .470 .700
<br />.9381.17
<br />1.42 1.65 1.9012.14 2.39 2.64 2,90
<br />3.16 3.41
<br />f
<br />LL
<br />�I
<br />TABLE I. Tangents and Externals to a 1° 'Curve.
<br />Mord =100 ft.
<br />VII•
<br />Int.
<br />Angle
<br />Tangent
<br />External
<br />Int.
<br />Angle !Tangent
<br />External
<br />lat.
<br />Angle
<br />Tangent
<br />External
<br />106°'
<br />.7603.5
<br />3791.0
<br />111°
<br />3336.7
<br />4356.1
<br />116°
<br />9169.4
<br />5082.7.
<br />10'
<br />7,626.6
<br />3809.4
<br />10'
<br />S362.7
<br />4407.6
<br />IV
<br />9199.1
<br />5107.9
<br />•'20
<br />7649,7.
<br />'3827,9
<br />20
<br />635S.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
<br />5158.8
<br />40:-
<br />7696.3
<br />3865.2
<br />40
<br />6441.5
<br />4472.7
<br />40
<br />9259.2
<br />5184.5
<br />.,50 .
<br />7719.7
<br />. 3884:0'
<br />50
<br />8463.0
<br />4494.6
<br />50'
<br />9319.5
<br />5210.3
<br />107 -
<br />7743.2
<br />3902.9
<br />112
<br />5494.6.
<br />4516.6
<br />117
<br />.9349.9
<br />5236.2
<br />•10
<br />.7766.8
<br />3921.9
<br />10
<br />5521.3
<br />453S.8
<br />10 .
<br />9380.5
<br />5262:3
<br />20::
<br />'7790.5
<br />3940.9
<br />20
<br />5548.1
<br />4561.1
<br />20
<br />9411,3
<br />5288.6
<br />30 .,
<br />7814.3
<br />3960.1
<br />30'
<br />5575.0
<br />4553.4
<br />30
<br />9442.2
<br />.5315.0
<br />40 •:7838.1
<br />2.36
<br />3979.4
<br />40
<br />5602.1
<br />460G.0
<br />40
<br />9473.2
<br />6341.5
<br />50
<br />7862:1.'
<br />3998.7
<br />50
<br />5629.3
<br />4628.6
<br />50
<br />9504.4
<br />5368.2
<br />108
<br />.7880.2
<br />•4018.2
<br />113
<br />8656.0
<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 />-7934.6
<br />4057:4
<br />120
<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:G
<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 />10
<br />8851.0
<br />4S14.1
<br />10
<br />9759.4
<br />,5587.4-
<br />20
<br />8082.3
<br />4177.5
<br />20
<br />8879.3
<br />.4537.3
<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 />9324.8
<br />5643.8
<br />40
<br />8132.3
<br />4218.4,
<br />40
<br />8936.3
<br />4885.7
<br />40 ,
<br />9657.7
<br />5672.3
<br />50;•
<br />8157.5
<br />4239.0
<br />50
<br />8065.0
<br />4909.9
<br />50
<br />.9390.8
<br />5700.9
<br />110
<br />5182.8
<br />14259:7
<br />115
<br />8993.8
<br />4934.1
<br />120
<br />9924.0
<br />5729.7
<br />10.
<br />.S208.2,
<br />'4280.5
<br />10
<br />9022.7
<br />4,958.6
<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 />S259.3
<br />4322.4
<br />•30
<br />9080.9,
<br />5007.8
<br />30
<br />10025.0
<br />5817.0
<br />40'
<br />S285.0
<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 />91.'.9.8
<br />5057-6
<br />50
<br />10093.0
<br />5870.1
<br />Corrections to be Added (T =Tangent. E=ExternaI.)
<br />lat.
<br />Angle Curve 5°
<br />10°
<br />15°
<br />20°
<br />25°
<br />30°
<br />38° 40°
<br />45°
<br />50°
<br />55°
<br />60°
<br />65° 70°
<br />100°T=13
<br />.85
<br />!1.3D
<br />1.74
<br />2.15
<br />2.62
<br />3.06 3.50
<br />3.95
<br />4.40
<br />4.88
<br />5-37
<br />5.85 0.84
<br />1 =.200
<br />.401
<br />.601
<br />809
<br />1.01
<br />1.x2
<br />1.49 1.64
<br />1.85
<br />2.06
<br />2,28
<br />2.30
<br />2.13 2.96
<br />1.70D
<br />1.933
<br />! 37
<br />M4
<br />4
<br />1051 E=.230
<br />.4#0
<br />1.17
<br />1.42
<br />1.65 1.2 80
<br />2.14 4
<br />- 2.39
<br />2.51
<br />2.90
<br />3.16 3.41
<br />110, T=.60
<br />1.03
<br />1.55
<br />2.08
<br />2.50
<br />3.A
<br />3.6G 421
<br />4.76
<br />5,31
<br />5.86
<br />G.43
<br />7.01 7.69
<br />E =.250 •
<br />.535
<br />.808
<br />1.08
<br />1.36
<br />1.63
<br />1.91 2.19
<br />2.49
<br />2.61
<br />3.C5
<br />3.35
<br />U5 3.05
<br />115° T=.54
<br />1.13
<br />11.70
<br />2.29
<br />2.36
<br />3.45
<br />4.03 4.63
<br />5.23
<br />1 5.83
<br />GA4
<br />7.07
<br />7.70 18.35
<br />E=.307
<br />.G2+
<br />.039
<br />1.26
<br />1.57
<br />1.89
<br />2.21 2.54
<br />2.i;7
<br />3.20
<br />3.53
<br />3.88
<br />4.23 14.58
<br />1.0' T =.61
<br />g - 339
<br />123
<br />1.89
<br />1.08
<br />3.52
<br />1.45
<br />3.16
<br />1.82
<br />3.81
<br />2.20
<br />4.44 5.11
<br />f 2.56 2.95
<br />5.78
<br />3.33
<br />ti.44
<br />3.72
<br />7.11
<br />14.10
<br />7.80
<br />4.50'
<br />8.51 9.21
<br />4.91 15.32
<br />I
<br />,720
<br />
|