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VI TAs1.m.I. = Tangents and'Externals to a V Curve. TABLE I. - Tangents and Externals to a V Curve. = VII <br />Chord =100 ft. Chord =100 ft. <br />'Angle <br />Tangent <br />External <br />'Angle <br />Tangent <br />External <br />Angle <br />'Tangent <br />External <br />85° ' <br />5250.3 <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 />ld <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 />,6985.3 <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 />U. <br />6327.4 <br />2094.1 <br />50 <br />6020.2 <br />, 2581.3 <br />50- <br />6808.2 <br />3168.7 <br />89-'- <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 />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 />6108.6 <br />2645.5 <br />'40 <br />6909.6 <br />3246.5 <br />50 <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 />101` ' <br />6950.6 <br />3278:1 <br />10 <br />5453.1 <br />2180.2 <br />10 . <br />6162.6 <br />2684.7 <br />110 <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 />80 <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 />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 />5535.4 <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 />344.0.9 <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 r " <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 J <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 />0 <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 />.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 />1 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 />3664.8 <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 <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 />Int. <br />Angle <br />Curve 5' <br />10°, `15° 20° 25° 30° 35° 40° 45° '50° 55° <br />60°1. 65°. 70° <br />85o' <br />'T=.33 <br />.66 1.00 1.33 1.68 2.02 2.36 2.70 3.05 3.40 3.77 <br />4.14 4.55 4.89 <br />External <br />E =.128 <br />.259 .391 .524 '.657 .790 .:928 1.06 1.20 1.34 1.47 <br />1.62 -1.76 1.91 <br />90°- <br />'T=.36 <br />.72. 1.09 11.45 1.83, 2.20-12.57 2.94 3.32 3.70, 4.10 <br />4.50 4.91 5.32 <br />9169.4 <br />E=.149 <br />'.299 .450 .603 .756 .910 1.07 1.22 1.38 1.54 1.70 <br />11.87 2.03 2.20 <br />95o <br />T=.39' <br />79 1.19 1.55 2.00 2.40 2.80 3.20 3.61 4.02 14.4914.98 <br />5.38 5.83 <br />10' <br />E =.174 <br />.350 .522 -.706 .985 1.06 1.25 1.43 1.62 1.80 1.99 <br />2.18 2.38 2128 <br />1W <br />T=.43 <br />.86 1.30 1.74 2.18 2.62 3.06 3.50 3.95 4.40 4.88 <br />5.37 5185 6.34 <br />4429.2 <br />E=.200 <br />.401 .604 .809 1.01 1.22 1.43 1.64 1.85 2.06 2.28 <br />2.50 2.73 2.96 <br />105o <br />T=.46 , <br />.94 1.42 11.90 12.38 2.87. 3.34 3.84 4.35 .4.84 5.35 <br />5.87 8.40 6.93 <br />8415.1 <br />E=.230 <br />.470 .700 .08 1.17 1.42 1.65 1.90 2.14 2.39 2.64 <br />2.90 3.16 3.41 <br />Ang0 _..Tangent <br />Curve 5° <br />External <br />Augje <br />Tangent <br />External <br />Angie <br />Tangent <br />External <br />i06° <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 />5183.3 <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 />39M.'O <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 />5262.8 <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 />r30. <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 />5616.5 <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 />50 <br />8965.0 <br />4909.9 <br />50 <br />9890.8 <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 •'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° IP 20° 25° 30° 35° 40° 45° 50° <br />55° 60° 65° 70° <br />leo <br />T=.43 <br />.88 1.30 1.74 2.18 2.62 3.08 3.50 3.95 4.40 <br />4.88 . <br />5.3715.8516T4- <br />E =.200 <br />-.401 .604 .809 1.01 1.'22 1.43 1.64 1.85 2.06 <br />2.28 2.50 2.73 2.90 <br />leo , <br />„T=.46 <br />.94 1.42 1.90 2.38 2.87 3 34 3.84 4.35 4.84 <br />5.35 5.87 6.40 6.93 <br />E =.230 <br />.470 .700 .93 1.17 1.42 1.85 1.90 2.14 2.39 <br />2.61 2.90 3.18 3.41 <br />110° <br />T=.50 <br />1.03 1.55 2.08, 2.60 3.14 3.66 4.21 4.76 5.31 <br />5.86 6.43 7.01 7.59 <br />E=.260 <br />.535 .808 1.08 1.38 1.63 1.91 2.19 2.49 2.61 <br />3.05 3.35 3.65 3:95 <br />1150 <br />T-.54 <br />1.13 1.70 2.29 2.86 3.45 4.03 4.63 5.23 5.83 <br />6.44 7.07 7.70 8.35 <br />E =.307 <br />:624 .939 1.26 1.57 1.89 2.21 2.54 2.87 3.20 <br />3.53 .3.88 4.23 4.58 <br />1290'.. <br />T=.61 <br />1.25 1.89 12.52 13.16 3.81 4.44 5.11 5.78 6.44 <br />7.11 7.80 8.51 9.21 <br />E=.339 <br />.72011.08 1.45 1.82 2.20, 2.56 2.95 3.33 3.72 <br />4.10 4.50 4.91 5.82. <br />1 <br />