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VI TABLM' I.•= Tangents and Externals to a-1' Curve. <br />Chord =100 ft. <br />Int" <br />Angle <br />Tangent <br />External <br />Int. <br />Angle <br />Tangent <br />External <br />fit' <br />Angle <br />Tangent <br />External <br />80 <br />6250.$ <br />2041.7 <br />92' <br />5933.2 <br />2518.5 <br />990- <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 />1,30 <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 />6808.2 <br />3168.7 <br />8.6 <br />5343.,0 <br />'2104.7 <br />93 <br />6037.8 <br />2594:6 <br />100 <br />6828.3 <br />3184.1 <br />16 <br />5358.6 <br />.2115.3:10 <br />10 <br />•6055.42606.8 <br />14538.8 <br />10' <br />6848.5 <br />3199.6 <br />•'-20• <br />.7790.5 <br />2126.0 <br />•20 <br />6073.1 <br />'2619.7 <br />20 <br />6868.8 <br />3215.1 <br />30 <br />,5374.2 <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 />6108.6 <br />2845.5 <br />40; <br />6909.6 <br />3246.5 <br />'S0 <br />5421.4 <br />,2158.4 <br />50 <br />'6126.4 <br />2658.5 <br />50 <br />6930.1, <br />3262.3 <br />87. . <br />5437.2 <br />2169.2 <br />94 <br />6144.3 <br />2671.6 <br />161 -' <br />6950:6 <br />3278.1 <br />30- <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 />2697.9 <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 />b0• <br />7054.5 <br />3358.6 <br />88; . <br />'b533:1 <br />2235.5 <br />-95 <br />6252.8 <br />2751.3 <br />102 '' <br />7075.5 <br />-7096.0 <br />3374.9 <br />10 <br />.5549.2 <br />.2246.7 <br />30 <br />6271.1 <br />2764.8 <br />- 10• <br />9759.4 <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 />'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 />6323.3_ <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 />89 <br />5630.5 <br />2303.5 <br />'96 • <br />6363.4 <br />2833.2 <br />103 <br />7203.2 <br />3474.4 <br />10 <br />'5646.9 <br />_2315.0 <br />10 <br />.6382.1 <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 />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 />40'7289.8 <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 />00 - <br />5729.7 <br />2373.3 <br />97 <br />6476.2 <br />2917.3 <br />104 <br />7333.6 <br />'3576.8 <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 />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 />6571.9 <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 />10 <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'.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 />Angle <br />Curve 5° <br />10° <br />0° <br />15° 20° 25° 30° 35° '40° 45° 50° 55° 60° 65° 70- <br />Tangent <br />External <br />Int. - <br />Angle <br />12.02 <br />85° <br />T= <br />T=.33 <br />.66 <br />1.00 1.33 1.68 2.36 2.70 3.05 3.40 3.77 4.14, 4.55' 4.89 <br />111° <br />E=l <br />.259 <br />.391 '..524 .657 .790 .926 1.08 1.20 1.34 1.47 1.82 1.78 1.91 <br />9169.4: <br />T=.36 <br />...'..101 <br />1.09 1.45 1.83 2.20 2.57 2.94 3.32 3.70 4.10 4.50 4.91 5.32 ' <br />90° <br />E=.149 <br />.72 <br />.299 <br />.450 .603 '.756 .910' 1.07 1.22 1.38 1.54 1.70 11.87 2.03 2.20 <br />95°. <br />T =.39 <br />.79 <br />1.19 1.55 2.00 2.40 2.80 3.20 3.61 4.02 4.49 4.98 5.38 5.83 <br />7649.7 <br />E=.174 <br />'.350 <br />.522 .706 .985 1.06 1.25 1.43 1.62 1.80 1.99 2.18 .2.38 2.68 <br />160.T=.43 <br />20• <br />.86 <br />1.30 1.74 2.18 2.62 3.06 3.50' 3.95 4.40 4.88 5.37 '5.85 6.34 <br />30. <br />E=.200 <br />.401 <br />.604 .809 1.01 1.22 1.43 1.64 1.85 2.06 2.28 2.50 2.73, 2.96 <br />8415.1 <br />T=.48 <br />30-' <br />1.42 1.90 12.38 2.87. 3.34 3.84 4.35 4.84 5.35 15.87 16.40 6.93 <br />105° <br />E=.230 <br />.94 <br />.470 <br />.700 .9381.17 1.42 1.85 1.90 2.14 2.39 2.64 12.90 1.MG 3.41 <br />TABLE I. - Tangents and Externals to a V Curve. <br />-. Chord=100'ft.-'- ' ` -- <br />-Iat. - <br />Angle <br />Tangent <br />Externa] <br />Int. <br />Angle <br />Tangent <br />External <br />Int. - <br />Angle <br />Tang -t <br />.External <br />106° <br />7603.5 <br />3791.0 <br />111° <br />8336.7 <br />4386.1 <br />.116°1' . <br />9169.4: <br />5082.7 <br />...'..101 <br />7626.6 <br />3809.4 <br />10'_ <br />8362.7 <br />4407.6' <br />101, <br />4.40 <br />,5107.9 <br />,20 <br />7649.7 <br />3827-.9. <br />20 <br />8388:9., <br />4429.2 <br />20• <br />,9199.1 <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 />o 40 <br />-;7696.3. <br />' <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 />.3884.6 <br />50' <br />84680 <br />4494.6 <br />50, <br />9319.5 <br />5210.3 <br />107.' <br />7743.2 <br />3902.9 <br />1128494.6 <br />1.90 <br />4516.`8: <br />117 <br />'9349.9' <br />5236.2 <br />'10 <br />7766.8 <br />3921.9 <br />10 <br />8521:3 <br />14538.8 <br />10 - <br />9380.5 <br />5262.3 <br />20 <br />.7790.5 <br />13940.9 <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 />18684.0 <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 />9830.7. <br />5478.8 <br />40 <br />'7983.5 <br />'4097.1 <br />-..40' <br />8767:0 <br />4743.8 <br />40 '.0662.6 <br />4.10 <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 />6559.4 <br />10 <br />8057.41 <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.`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 />50 <br />r8965.0- <br />4909.9 <br />50 <br />9890.8 <br />5700.9 <br />110 <br />8182.8. <br />4259.7, <br />lib <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 />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 />- 40 <br />10059.0 <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 <br />Curve 5° <br />10° <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 />.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 />E=.200 <br />.401 <br />.601 <br />.809 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 />.94 <br />1.42 <br />1.90 <br />2.38 <br />2.87 <br />3.34 <br />3.844.84 <br />5.35. <br />5.87 <br />6.40 <br />6.93 <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 />115° <br />T=•54 <br />1.13 <br />1.70 <br />2.29 <br />2.86 <br />3.45T4.13 <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 />1.624 <br />.939 <br />1.26 <br />1.57 <br />182.21 <br />2.54 <br />2.87 <br />3.20 <br />3.53 <br />3.88 <br />4.23 <br />4.58 <br />120° <br />T=•G1 <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 />6.44 <br />7.11 <br />7.80 <br />8.51 <br />9.21 <br />- <br />E=.339 <br />. <br />.7201-1.08 <br />1.45 <br />1.82 <br />2.20 <br />2.56 <br />2.95 <br />3.33 <br />3.72 <br />4.10 <br />4.50 <br />4.91 <br />5.32 <br />