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V1 TAB1g L - Tangents and Externals to a V Curve, <br />Chord =100 ft. <br />Angle <br />Tangent <br />External <br />Int. <br />Angle <br />Tangent <br />External <br />_Int. <br />Angle <br />Tangent <br />External <br />$5° ' <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 />5265.6 <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 />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 />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 />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 />'60 <br />5421.4 <br />2158.4 <br />60 <br />6126.4 <br />2658.5 <br />.50 <br />6930.1 <br />3262.3 <br />i87 <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 />.• 101 <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 />x.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 />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 />80- <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 />2315.3 <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 />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 />01 <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 />140 <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° 10° 15° 20° 25° <br />30° 35° 40° <br />45° <br />50° 55°I 60° 651 701 <br />85° T=.33 .66 1.00 1.33' 1.68 <br />2.02 2.36 2.70 <br />3.05 <br />3.40 3.77 4.14 4.55 4.89 <br />E=.128 .259 .391 .524 .657 <br />.790 .926 1.06 <br />1:20 <br />1.34 1.47 1.62 1.76 1.91 <br />90° T=.36 .72 1.09 1.45 1.83 <br />2.20 2.57 2.94 <br />3.32 <br />3.70 4.10 4.50 4.91 5.32 <br />R=149 .299 .450 .603 .756 <br />.910 1.07 1.22 <br />1.38 <br />1.54. 1.70 1.87 2.03 2.20 <br />9Bo T=.39 .79 1.19 1.55 2.00 <br />2.40 2.80 3.20 <br />3.61 <br />4.02 4.49 14.98 5.38 5.83 <br />E=.174 .350 .522 .706 .985 <br />1.06 1.25 1.43 <br />1.62 <br />1.80 1.99 2.18 2.38 2.58 <br />100° T=.43.. :86 1.30 1.74 2.18 <br />2.62 3.06 3:50 <br />3.95 <br />4.40 4.88 5.37 5.85 6.34 <br />E=.200 401 :604 .809 1.01 <br />1.22 1.43 1.64 <br />1.85 <br />2.06 2.28 2.50 2.73 2.96 <br />105° T=.46 .94 1.42 1.90.2.38 <br />2.87 3.34 3.84 <br />4.35 <br />4.84 5.35 5.87 6.40 6.93 <br />E=.230 .470 .700 .938 1.17 <br />1.42 1.65 1.90 <br />2.14 <br />2.39 2.64 2.90 3.1 6 3.41 <br />TABLE I. - Tangents and Externals to a 1° Curve. VH <br />Chord =100 f t. <br />Ange_ <br />Tangent <br />External <br />Angle <br />Tangent <br />ExternalAngle <br />Int <br />Tangent <br />External <br />10G° <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 />101 <br />8362.7 <br />4407.6. <br />10' <br />9199.1 <br />5107.9 <br />20 <br />7649.7 <br />3527.9. <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 />'40 <br />8415:1 <br />4450.9 <br />30 <br />9259.0 <br />5158.8 <br />40 <br />7696.3 <br />3865.2 <br />3.05 3.35 .3.65 3.95 <br />8441.5 <br />4472.7 <br />40 <br />9289.2 <br />4184.5 <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 />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-.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 />150 <br />7862.1 <br />3998.7 <br />50, <br />`8629:3 <br />4628.6 <br />50 <br />9504.4 .;5368.2 <br />108 <br />7586.2 <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 />4561.7 <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 />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 />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. Curve 5 10 15° <br />Angle ° ° <br />o <br />20 25° 30.]35° <br />40° <br />45° <br />50° <br />55° 60° 65° 70° <br />100° T=.43 .86 1.30 <br />1.74 2.18 2.02 <br />.3.06 <br />3.50 <br />3.95 <br />4.40 <br />4,88 5.37 5.85 '6.34 <br />. E.200 .401 .604 <br />.809 1.01 1.22 <br />1.43- <br />1.64 <br />1.85 <br />2.06 <br />2,28 2.50 2.73 2.96 <br />105°` T=.46 .94 11.42 <br />1.90 2.38 2.87 <br />3.34 <br />3.84 <br />4.35 <br />4.84 <br />5.35 5.87 6.40 6.93 <br />E =.230 .470 .700 <br />.938 1.17 1.42 <br />1.65 <br />1.90 <br />2.14 <br />2.39 <br />2.64 2.90 3.16 3.41 <br />110° T=.50 1.03 1.55 <br />2.08 2.60 3.14 <br />3.66 <br />4.21 <br />4.76 <br />5.31 <br />5.86 6.43 7.01 7.59 <br />.. <br />E=.260 .535 .808 <br />1.08. 1.36 1.63 <br />1.91 <br />2.19 <br />2.49 <br />2.61 <br />3.05 3.35 .3.65 3.95 <br />115°.T=.54 1.13 1.70' <br />2.29 2.86 3.45 <br />"4.03 <br />4.63 <br />5.23 <br />5.83 <br />6.44 7.07 7.70 8.35 <br />E =.307 .624 .939 <br />1.26 1.57 1.80 <br />2.21 <br />2.54 <br />2.87 <br />3.20 <br />3.53 3.88 4.23 4.58,= <br />120o T=.61 1.25 1.89 <br />2,52. 3.16 3.81 <br />4.44 <br />5.11 <br />5.78 <br />6.44 <br />7.11 7.80 8.51 9.21 <br />E=.339 .720 1.08 <br />1.45 1.82 2.20 <br />2.56 <br />2.95 <br />3.33 <br />3:72 <br />4,10 4.50 .4.91 b $l. <br />