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M <br />VI TAnLr 1. - Tangents and Externals to .a V Curve. <br />Chnrrl=1(in ft <br />Int. <br />Angle <br />Tangent <br />External <br />Int. <br />An Le <br />Tangent <br />External <br />Int. <br />Angle <br />Tangen <br />I g tj <br />External <br />85° <br />5250.3 <br />2041.7 <br />920 <br />5933.2 <br />2:113.:1 <br />99° <br />l <br />6108.6 <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 />5251.0 <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 />2356.0 <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 />6303.2 <br />316S.7 <br />68 <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 />2506.5 <br />10 <br />GS43.5 <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 />6839.2 <br />3230.8 <br />40 <br />5405.6 <br />2147.5 <br />40 <br />6103.6 <br />26.15.5 <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 />67 <br />5437.2 <br />2169.2 <br />94 <br />6144:3 <br />2671.6 <br />101 <br />6950.G <br />3273.1 <br />10 <br />5453.1 <br />2180.2 <br />.10. <br />6162.6 <br />2684.7 <br />10 <br />6,971.3 <br />329-4.1 <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 />5454.9 <br />2202.2 <br />30 <br />6198.3 <br />2711.2 <br />30 <br />7012.7 <br />332G.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 />-60 <br />5517.0 <br />2224.3 <br />50 <br />6234.6 <br />2737.9 <br />50 <br />7054.5 <br />3358.5 <br />109 <br />5032.7 <br />4137.1 <br />114 <br />8522.0 <br />4790:4 <br />119 <br />9727.0 <br />5559.4 <br />88 <br />5533.1 <br />2235.5 <br />95 <br />61252.8 <br />2751.3 <br />102 <br />"7075.53374.9 <br />5557.4 <br />10 <br />5549.2 <br />2246.7 <br />10 <br />6271.1 <br />2764.8 <br />10 <br />7006.6, <br />3301.2 <br />20 <br />5565.4 <br />2253.0 <br />20 <br />6259.4 <br />2778.3 <br />20 <br />7117.8 <br />3407.7 <br />30 <br />5551.6 <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 />2250.6 <br />40 <br />6326.3 <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 />2519.4 <br />50 <br />7151.7 <br />3457. Ci <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 />28.17.0 <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 />3505.2 <br />30 <br />5679.9 <br />2333.2 <br />30 <br />6419.5. <br />2375.0 <br />30 <br />7265.0 <br />3525.2 <br />40 <br />5696.4 <br />2349.S . <br />40 <br />6438.4 <br />2SS9.0 <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 />S. <br />90 <br />5729.7 <br />2373.3 <br />97 <br />6476.2 <br />2917.3 <br />101 <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 />2403.9 <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.S <br />50 <br />5S13.6 <br />2432.9 <br />50 <br />6571.9 <br />2989.2 <br />50 <br />7444.6 <br />3GG4.5 <br />91 <br />5530.5 <br />2444.0 <br />98 <br />61591.2 <br />3003.8 <br />105 1 <br />7467.0 <br />3632.3 <br />10 <br />5347.5 <br />2457.1 <br />10 <br />61610.6 <br />3018.4 <br />10 <br />7489.6 <br />3700.2 <br />20 <br />5S64.6 <br />2469.3 <br />20 <br />6630.1 <br />3033.1 <br />20 <br />7512.2 <br />371.8.2 <br />30 <br />5381.7 <br />2481.5 <br />30 <br />6649.6 <br />3017.9 <br />30 <br />7534.9 <br />3736.2 <br />40 <br />5S93.S <br />2-193.8 <br />40 <br />6669.2 <br />3062.5 <br />X40 <br />7557.7 <br />3754.4 <br />50 <br />5916.0 <br />2506.1 <br />50 <br />6685.3 <br />3077.7 <br />50 <br />7550.5 <br />3772.6 <br />11 <br />I <br />i <br />! <br />. Angle <br />Corrections to be Added (T =Tangent. E. =External.) <br />! 11'11 <br />� <br />I <br />Int <br />Anxie <br />Carve 5° <br />10' IS° 20' 25° 30° 35° 40' 1 45° 1 50° 1 55° 1 <br />60'1 65° 70° <br />111° <br />5336.7 <br />ba° <br />T=.33 <br />.66 100 1.33 1.68 `2 03 2.36 2.70 3.05 3.40 3.77 <br />11.20 <br />4.14A .55 4.89 <br />10' <br />762G.6 <br />3SO9.4 <br />E =.128 <br />.259 .391 .524 .657 .790 .928 1.06 1.34 1.47 <br />1.82 L'r,0 1.91 <br />10' <br />9199.1 <br />9D° <br />T=.36 <br />.72 1.09 1.45 1.83 2.20 2.57 2.9413.3213.70 4.10 <br />4..5D 4.91 5.32 <br />20 <br />8388.9 <br />4429.2 <br />E =.149 <br />.299 .450 .803 .756 .910 1.07 1.22 1.38 1.54' LiOl <br />1.87 2.03 2.20 <br />j' <br />7672.9 <br />95° <br />T=.39 <br />.70 1.19 1.55 2.00 2.40 12.80 3.20 4.02 4.49 <br />4.95 5.38 5.83 <br />! <br />9259.0 <br />5153.8 <br />E =.174 <br />13.61 <br />.350 .522 .706 .985 1.06 1.25 1.43 1.62 1.80 1.99 <br />2.18 2.38 2.58 <br />1` <br />8441.5 <br />100° <br />T=•43 <br />.36 1.30 1.74 2.13 2.62 3.08 3.50 3.15 4.40 4.83 <br />5.37 5.85 6.34 <br />50 <br />7719.7 <br />3884.0 <br />E=.200 <br />.401 .604 .809 1.01 1.22 1.43 1.64 1.8:1 2.06 2.28 <br />2.50 2.73 2.96 <br />50 <br />105° <br />T =.46 <br />D41.42 1.00 2.33 2.87 3.34 3.84 4.35 4.84 5.35 <br />5.87 6.40 6.93 <br />' I <br />112 <br />E=.230 <br />.4701 .7001 .93811.17 1.42 1.65 11.D0 2.14 2.3D 3.84 <br />2.90 3.1E 3.41 <br />9349.9 <br />5236.2 <br />10 <br />7766.3 <br />3921.9 <br />TABLE I. - Tangents and Externals to a V Curve. <br />Chord= 100 ft. <br />VII <br />Int.Int. <br />Angle <br />TangentlExternal <br />a�° 40'1 <br />. Angle <br />Tangent <br />External <br />Int. <br />Angle <br />Tangent <br />External <br />106° <br />7603.5 <br />3791.0 <br />111° <br />5336.7 <br />4356.1 <br />.116° <br />9169.4 <br />5OS2.7 <br />10' <br />762G.6 <br />3SO9.4 <br />10' <br />5362.7 <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 />•1450.9 <br />30 <br />9259.0 <br />5153.8 <br />40 <br />7696.3 <br />3365.2 <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 />8463.0 <br />4494.6 <br />50 <br />9319.5 <br />5210.3 <br />107 <br />7743.2 <br />3902.9 <br />112 <br />5494.6 <br />4516.6 <br />117 <br />9349.9 <br />5236.2 <br />10 <br />7766.3 <br />3921.9 <br />10 <br />8521.3 <br />4535.8 <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 />5233.6 <br />30 <br />7814.3 <br />3960.1 <br />30 <br />5575.0 <br />4533.4 <br />3U <br />9442.2 <br />5315.0 <br />40 <br />7835.1 <br />3979.4 <br />40 <br />8602.1 <br />4606.0 <br />40 <br />9473.2 <br />5341.5 <br />5o <br />7562.1 <br />3998.7 <br />50 <br />8629.3 <br />4628.G <br />50 <br />9504.4 <br />5363.2 <br />109 <br />7886.2 <br />4018.2 <br />113 <br />8656.6 <br />4651.3 <br />118 . <br />953:;.7 <br />5395.1 <br />10 <br />7910.4 <br />4037.3, <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 />0630.7 <br />5476.5 <br />40 <br />7983.5 <br />4097.1 <br />40 <br />87117.0 <br />4743.6 <br />40 <br />06612.6 <br />5504.0 <br />50 <br />SOOS.0 <br />4117.0 <br />50 <br />8794.9 <br />4766.9 <br />50 <br />OG94.7 <br />5531.7 <br />109 <br />5032.7 <br />4137.1 <br />114 <br />8522.0 <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 />5557.4 <br />20 <br />SOS2.3 <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 />4197.0 <br />30 <br />8907.7 <br />4361.7 <br />30 <br />9524.8 <br />5643.8 <br />4U <br />8132.3 <br />4218.4 <br />40 <br />8936.3 <br />4835.7 <br />40 <br />9557.7 <br />5672.3 <br />50 <br />8157.5 <br />4239.0 <br />50 <br />5065.0 <br />4909.9 <br />50 <br />9890.8 <br />5700.9 <br />110 <br />8182.8 <br />4259.7' <br />115 <br />5993.3 <br />4934.1 <br />120 <br />9924.0 <br />5720.7 <br />10 <br />620S.2 <br />4250.5 <br />10 <br />9022.7 <br />4955.6 <br />10 <br />9957.5 <br />5758.6 <br />20 <br />5233.7 <br />4301.4 <br />20 <br />9051.7 <br />4953.1 <br />20 <br />9991.0 <br />5787.7 . <br />30 <br />8259:3 <br />4322.4 <br />30 <br />OOSO.9 <br />5007.8 <br />30 <br />10025.0 <br />5817.0 <br />40 <br />3285.0 <br />4343.6 <br />40 <br />9110.3 <br />5032.6 <br />40 <br />10059.0 <br />5546.5 <br />50 <br />S310.S <br />43G4.8 <br />50 <br />9139.8 <br />5057.6 <br />50 <br />10093.0 <br />5376.1 <br />Corrections to be Added (T =Tangent. E =External.) <br />Int <br />C.,, 5° 110- 15° 20' <br />25'1 30° <br />a�° 40'1 <br />45° 50° <br />55° 60'1 <br />65'1 <br />70° <br />Angle <br />3.06 <br />T=.43 .86 1.30 1.74 <br />2.1S <br />1 3.501 <br />'i.431 <br />3.05 4.40 <br />4.83 5.31 <br />5.85 <br />6.34 <br />106' 1 P =.200 .401 .601 .809 <br />12.62 <br />1.01 1.2_ <br />1.64 <br />1.85 06 <br />2.23 2.50 <br />73 <br />96 <br />T=.46 1.42 1.90 <br />2.33 2.81 <br />3.34:1 3.84 <br />4.35 4.84 <br />5.35 5.87 <br />6.40 <br />6.93 <br />.94 <br />105° E,=.230 '1 .470 .00 .933 <br />1.17 1.42 <br />1.651 Moo <br />2.14 2.39 <br />2.6-1 2.90 <br />3.16 <br />3.41 <br />T=.50 1.03 1.55 2.08 <br />2.60 3.14 <br />3.66 4.21 <br />4.76 5.31 <br />5.86 6.43 <br />7.01 <br />7.59 <br />110° <br />E=.260 .5351 .SOS 1.05 <br />1.36 I.G3 <br />UJl 2.19. <br />2.49 MI. <br />3.09 3.35 <br />3.63 <br />3.95 <br />T=.54 11.13 2.29 <br />2.S8 3.45 <br />4.G3 4.63 <br />5.23 5.83 <br />6.44 7.07 <br />7.70 <br />3.35 <br />11.70 <br />115° <br />19=.307 .624. !039 1.26 <br />1..17 1 1.891 <br />1.21 2.54 <br />2.87 3.20 <br />3.53 1 3.SS <br />4.23 <br />4.55' <br />120° T=.61 1.25 1.89 2.52 <br />! <br />3.16 3.81 <br />1 <br />4.44 5.11 <br />5.73 6.44 <br />7.11 '.SO <br />4.501 <br />8.51 <br />4.911 <br />9.21 <br />5.32 <br />1 E=.339 1 .i 2011.03 1.45 <br />1.82 2.20 <br />2.56 3.95 <br />3.33 3.711 <br />4.11 <br />