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VI TABLE'.I. Tangents and Externals to a V Curve.- <br />Chord- 100- ft. <br />Int <br />Angle <br />Tangent <br />External <br />Int. <br />Angle <br />Tangent <br />External <br />Int. <br />Angle <br />Tangent <br />External <br />SW - <br />5250.3 <br />2041.7 <br />92° <br />5933.2 <br />2518:5 <br />99° <br />65708.6 <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 />6763.1 <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 />86: <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 />0073.1 <br />.2619.7 <br />20, <br />6368.8 <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 />6103.6 <br />2645.5 <br />40 <br />6909.6 <br />3246.5 <br />'50 <br />6421.4 <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 />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 />5169.0 <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 />7033:8 <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 />88'"': <br />5533:1 <br />2235:5 <br />95 <br />6252.8 <br />2751.3 <br />102` ' <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 />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 />632G.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 />6646.9 <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 <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 />6476.2 <br />2917.3 <br />104. <br />7333.6 <br />3576.8 <br />10 <br />5746.3 <br />2355.1 <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 />7 <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 />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 />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`, Curve 5° <br />10° <br />IS- 20° 25° 30° 35° 40° '45° <br />50° 55° <br />60° <br />65° 70° <br />850 T=.33 <br />.66 <br />1.00 1.33 1.68 2.02 2.36 2.70 3.05 <br />3.40 3.77 <br />4.14 <br />4.55 4.89 <br />E =.128 <br />.259 <br />.391 .524 .6571 .790 .92611.06 1.20 <br />1.34 1.47 <br />1.62 <br />1.76 1.91 <br />goo T=.36 <br />.72 <br />1.09 1.45 1.83 2.20 2.57 2.94 13.32 <br />3.70 4.10 <br />4.50 <br />4.91 5.32 <br />E=.149 <br />.299 <br />.450 .603 ..756 .910 1.07 1.22 1.38 <br />1.54 1.70 <br />1.87 <br />2.03 2.20 <br />95° <br />8388.9 <br />1 <br />1.706 2.985 <br />20 <br />9229.0 <br />5133.3 <br />."PE = 174 <br />.350 <br />522 1.06 1.28 1.43 1.62 <br />1.80 1.99 <br />2.18 <br />2.58 <br />100o J T= .43 <br />.86 <br />1.30 1.74 2.18 2.62 3.00 3.50 3.95 <br />4.40 4.88 <br />5.37, <br />_2.38 <br />5.85 6.34 <br />f E =.200 <br />401 <br />.604 .80911:01 1.22 1.43 1.64 1.85 <br />.06. 2.28 <br />2.06.12.2'0 <br />2.50 <br />2.73 2.96 <br />105° i. T=.46 . <br />.94 <br />1.42 1.90 2.38 2.87 3.34 3.84 435 <br />4.84 .5.35 <br />5.87. <br />6.40 6.93 <br />E =230' <br />.470 <br />.700 .938 1.17 1.42 1.65 1.90 2.14 <br />2.39 "2.64 <br />2.90 <br />3.16 3:41 <br />-A <br />TABLE I. - Tangents and Externals to a 1° Curve. - VTI <br />Chord= 100 ft.- <br />Snt. •." <br />'Angle <br />Tangent <br />External <br />'Int.Int. <br />• Angle <br />Tangent <br />External <br />'- Angle' <br />Tangent <br />External <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 />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 />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 />7760:8 <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 />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 />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 />0824.8 <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 />8965.0 <br />4909.9 <br />50' <br />9390.8 <br />5700.9 <br />110 <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 />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 />4822.4 <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 />5S76:1 <br />Int. <br />Corrections to be Added (T <br />=Tangent. <br />E =External.) <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° 70° <br />100° <br />T=.43 <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° 70° <br />100° <br />T=.43 <br />.88 <br />1.30 <br />1:74 <br />2.18 <br />2.02. <br />3.06 <br />3.50 <br />'3.95 <br />4.40 <br />4.88 <br />5.37 <br />5.85 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 2.96 <br />105° <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 />5.36 <br />5.87 <br />6.40 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 3.41 <br />1100 <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 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 3.95 <br />115' <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 8.35 <br />11;=.307 <br />..624 <br />.939 <br />1.26 <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 4.58 <br />1206L. <br />T=.61 <br />1.25 <br />1.89 <br />2.52 <br />3:18 <br />3.81 <br />4.44 <br />5.11 <br />5.78 <br />6.44 <br />7.11 <br />7.80 <br />8.51, 9.21 <br />E='.339 <br />.720 <br />1.08 <br />1.45 <br />1 132 <br />12.20 <br />2.56 <br />2.95 <br />3.33 <br />3.72 <br />4.10 <br />4.550 <br />4.91 5.312 <br />MIM <br />MOM <br />