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Externals to a 1° Curve.` <br />1 n0 'ft-" <br />;ent <br />External <br />Int. Angle <br />Tangent <br />External <br />3.2 <br />2518.5 <br />99° <br />6708.6 <br />3092.7 <br />D.5 <br />2531.0 <br />10' <br />6728.4 <br />3107.7 <br />7.9 <br />2543.5 <br />. 20 <br />6748.2 <br />3122.9 <br />5.3 <br />2556.0 <br />30 <br />6768.1 <br />3138.1 <br />2:7 <br />2568.6 <br />40 <br />6788:1 <br />3153.3 <br />D:2 <br />2581.3 <br />50 <br />6808.2 <br />3168.7 <br />7.8 <br />2594.0 <br />100 .. <br />6828.3 <br />3184.1 <br />5.4 <br />2606.8 <br />10 <br />6848.5 <br />3199.6 <br />3.1 <br />2619.7 <br />20 <br />6868.8 <br />3215.1 <br />D.8 <br />2632.6 <br />30 <br />6889.2 <br />3230.8 <br />3.6 <br />2645.5 <br />40 <br />6909.6 <br />3246.5 <br />5.4 <br />2658.5 <br />50 <br />6930.1 <br />3262.3 <br />4.3 <br />2671'.6 <br />101 <br />6950.6 <br />3278.1 <br />2.6 <br />2684.7 <br />10 <br />6971.3 <br />3294.1 <br />0.2 <br />2697.9 <br />20 <br />6992.0 <br />3310.1 <br />8.3 <br />2711.2 <br />30 <br />7012.7 <br />3326.1 <br />6.4 <br />2724.5 <br />40 <br />7033.6 <br />3342.3 <br />4.6 <br />2737.9 <br />50 <br />7054.5 <br />3358.5 <br />2.8 <br />2751.3 <br />102 <br />7075.5 <br />3374.9 <br />1.1 <br />2764.8 <br />10 <br />7096.6 <br />3391.2 <br />9.4 <br />2778.3 <br />20 <br />7117.8 <br />3407.7 <br />X7.9 <br />2792.0 <br />30' <br />7139.0 <br />3424.3 <br />3.3 <br />2805.6 <br />40 <br />7160.3 <br />3440.9 <br />4.8 <br />2819.4 <br />50 <br />7181.7 <br />3457.6 <br />2.4 <br />2833.2 <br />103 <br />7203.2 <br />3474.4 <br />12.1 <br />2847.0 <br />10 <br />7224.7 <br />3491.3 <br />10.8 <br />2861.0 <br />20 <br />7246.3 <br />3508.2 <br />9.5 <br />2875.0 <br />30 <br />•7268.0 <br />3525.2 <br />18.4 <br />2889.0 <br />40 <br />7289.8 <br />3542.4 <br />i7.3 <br />2903.1 <br />50 <br />7311.7 <br />3559.6 <br />16.2 <br />2917.3 <br />104 <br />7333.6 <br />3576.8 <br />)5.2 <br />2931.6 <br />10 <br />7355.6 <br />3594.2 <br />L4.3 <br />2945.9 <br />20 <br />7377.8 <br />3611.7 <br />33.4 <br />2960.3 <br />30 <br />7399.9 <br />3629.2 <br />52.6 <br />2974.7 <br />40 <br />7422.2 <br />3646.8 <br />71:9 <br />2989.2 <br />50 <br />7444.6 <br />3664.5 <br />31.2 <br />3003.8 <br />105 <br />7467.0 <br />3682.3 <br />10.6 <br />3018.4 <br />-10; <br />7489.6 <br />3700.2 <br />30.1 <br />3033.1 <br />20 <br />7512.2 <br />3718.2 <br />49.6 <br />3047.9 <br />30 <br />7534.9 <br />3736.2 <br />69.2 <br />3062.8 <br />40 <br />7557.7' <br />3754.4 <br />88.8 <br />3077.7 <br />50• <br />7580.5 <br />3772.6 <br />- l <br />' = Tangent. E. = External.) <br />ngle Curve 5° 10° 15° 20° 25° 30° 350 <br />40° 45° 50°, 55° 60° 65° <br />70° <br />$50 •T'=.33= .66 1.00 1.33 1.68 2.02 2.36 <br />2.70 3.05 3.40 3.77 4.14 4.55 <br />1.47 1.62 1.76 <br />4.89 <br />1.91 <br />E=.128 .259 .391 .524 .657 .790 .926 <br />1.06 1.20 1.34 <br />4.50 4.91 <br />5.32 <br />900 T=.36 .72 1.09 1.45 1.83 2.20 2.57 <br />E =.149 .603 .756 .910 1.07 <br />2.94 3.32 3.70 4.10 <br />1.22 1.38' 1.54 .1.70 1.87 2.03 <br />2.20 <br />.299 .450 <br />T=.39 79 1.19 1.65 2.00 2.40 2.80 <br />3.20 3.61 4.02 4.49 4.98. '5.38 <br />2.18 2.38 <br />5.83 <br />2•`3 <br />950 E=.174 .350 .522 .706 .985 1.06 1.25 <br />1.43 1.62 1.80 1.99 <br />4.83 5.37 5.86 6.34 <br />1.30 1.74 809 1.Oi 1.22 <br />100° ' E=2 00 <br />1.85 2.06 2282.50 273 <br />210� <br />�13.06 <br />.401 .604 <br />T=.46 .94 1.42 1.90 2.38 2.87 <br />�13- <br />4.35 4.84 5.35 5.87- 6.40 <br />2.14' 2.39 2.64 2.90- 3.16 <br />6.93 <br />3.41 <br />Fi=.230 .470.700 .938 1.17 1.42 <br />9169.4 <br />5082:7 <br />,,,.TABLE I. -,Tangents and Externals to a V Curve., � <br />Chard =100 ft_ . <br />Int. <br />Angle <br />Tangent <br />External <br />_ <br />Int.- <br />Angle <br />Tan entEtrnlInt <br />Angie <br />Tangent <br />External <br />_ <br />45° <br />50° <br />55° 60° 65° 70° <br />100° T=.43 .88 1.30 1.74 2.15 <br />2.62 <br />3.06 3.50 <br />3.95 <br />4.40 <br />4.83 5.37 5.86 6.34 <br />106'. <br />7603.5 <br />3791.0 <br />111° <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 />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 <br />5158.8 <br />140. <br />7696.3 <br />3865.2 <br />.. 40 <br />8441.5 <br />4472.7 <br />40 <br />9289.2 <br />5184.5 <br />50..'7719.7. <br />6.44 <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 />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 />7934.6 <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 />50 <br />8008.0 <br />4117.0 <br />50 <br />8794.9 <br />4766.9 <br />50 <br />9694.7 <br />.5504.0 <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 />6559.4 <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 />60 <br />;8965.0 <br />4909.9 <br />50 <br />9890.8 <br />5760.9 <br />110 <br />8182.8 <br />4259:7 <br />115 <br />8993.8 <br />4934.1 <br />120 <br />0924.0 <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 />40 ' <br />8285.0 <br />4343.6 <br />40 <br />9110.3 <br />5032.6- <br />4010059.0 <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 Curve 5° 10° 15° 20° 25° <br />30° <br />35° 40° <br />45° <br />50° <br />55° 60° 65° 70° <br />100° T=.43 .88 1.30 1.74 2.15 <br />2.62 <br />3.06 3.50 <br />3.95 <br />4.40 <br />4.83 5.37 5.86 6.34 <br />E =.200 .401 .604 .809 1.01 <br />1.22 <br />1.43 1.64 <br />1.85 <br />2.06 <br />2.28 2.50 2.73 2.96 <br />105° -T=.46 .94 1.42 1.90 2.38 <br />2.87 <br />3.34 3.84 <br />4.35 <br />4.84 <br />5.35 5.87 6.40 6.93 <br />E=.230 .470 .700 .938 1.17 <br />1.42 <br />1.65 1.90 <br />2.14 <br />2.39 <br />2.64 2.90 3.16 3.41 <br />1100 T=.50 1.03 1.55 2.08 2.60 <br />3.14 <br />3.66 4.21 <br />4.76 <br />5.31 <br />5.86' 6.43 7.01 7.59 <br />E=.260 .535 .808 1.08 1.36 <br />1.63 <br />1.91 2.19 <br />2.49 <br />2.61 <br />3.05 3.35 3.65 3.95 <br />1150 ..T=.54 1.13 1.70 2.29 2.86 <br />3.45 <br />4.03 4.63 <br />5.23 <br />5.83 <br />6.44 7.07 7.70 8.35 <br />E=.307 .624 .939 1.26 1.57 <br />1.89 <br />2.21 2.54 <br />2.87 <br />3.20 <br />3.53 3.88 4.23 4.58 <br />120° . T=.61 1.25 1.89 2.52 3.16 <br />3.81 <br />4.44 5.11 <br />5.78 <br />6.44 <br />7.11 7.80 8.51 9.21 <br />E=.339 .720 1.08 1.45 1.82 <br />J <br />2.20 <br />2.561 2.95 <br />3.33 <br />3.72 <br />4.10 4.50 4.91 5.32 <br />