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General Equations and Useful Data <br />Table I. -Minutes in Decimals of a Degree. <br />1' .0167 11' .1833 21' ,3500 31' .5167 41' .6833 5 <br />Symbol <br />on Equation <br />Numerical <br />Value <br />Area of circle ................... <br />2 <br />.0260 <br />.0313 <br />4 <br />.0521 <br />Area of Sector of Circle (Length of <br />l' <br />.8500 <br />are = 1) ...................... <br />1/21r <br />12 <br />Area of Segment of Parabola (app.) <br />92 <br />.3667 <br />(c = chord; m = mid. Ord.) .... <br />2/3 cm <br />49 <br />Area of Segment of Circle ........ <br />2/3 cm <br />.8667 <br />Cubic Feet in 1 Cubic Meter..... <br />.0500 <br />35.3145 <br />Cubic Inches in 1 Imperial Gallon. <br />23 <br />277.274 <br />Cubic Inches in 1 U.S. Gallon.... <br />.5500 <br />231 <br />Feet in 1 Meter, I ........... <br />53 <br />3.2808 <br />Feet in 1 Mile. I .I ... I ...... <br />.0667 <br />5280 <br />Gallons (Imperial) in 1 Cubic Foot. <br />24 <br />6.2321 <br />Gallons (U.S.) in 1 Cubic Foot.... <br />.5867 <br />7.48 <br />Miles in 1 Kilometer.., .......... <br />54 <br />0.6213 <br />Pounds (Av.) in 1 Kilogram...... <br />.0833 <br />2.2046 <br />Ratio of Circumference to Diameter <br />7 <br />3.14159 <br />Reciprocal of r. I ..... I ......... <br />.5833 <br />0.31831 <br />Square Feet in 1 Acre............ <br />56 <br />43,560 <br />Volume of Sphere................ <br />4/3 7rr' <br />16 <br />Table I. -Minutes in Decimals of a Degree. <br />1' .0167 11' .1833 21' ,3500 31' .5167 41' .6833 5 <br />Table II.-rnches in Decimals of a Foot. <br />.0052 <br />.0078 <br />.0104 <br />.0156 <br />.0208 <br />.0260 <br />.0313 <br />.0417 <br />.0521 <br />.0625 <br />l' <br />.8500 <br />2 <br />.0333 <br />12 <br />.2000 <br />92 <br />.3667 <br />39 <br />.5333 <br />49 <br />.7060 <br />52 <br />.8667 <br />3 <br />.0500 <br />13 <br />2167 <br />23 <br />.3833 <br />33 <br />.5500 <br />43 <br />.145 <br />53 <br />.8833 <br />4 <br />.0667 <br />14 <br />.2333 <br />24 <br />.4000 <br />34 <br />.5867 <br />44 <br />.7167 <br />.7333 <br />54 <br />.9000 <br />5 <br />.0833 <br />16 <br />.2500 <br />25 <br />.4167 <br />36 <br />.5833 <br />45 <br />.7500 <br />56 <br />.9167 <br />6 <br />.1000 <br />16 <br />.2667 <br />26 <br />.4333 <br />36 <br />.6000 <br />46 <br />.7667 <br />56 <br />.9333 <br />7 <br />.1167 <br />17 <br />.2833 <br />97 <br />.4500 <br />37 <br />.8187 <br />47 <br />.7833 <br />57 <br />.9500 <br />8 <br />.1333 <br />18 <br />.3000 <br />28 <br />.4667 <br />38 <br />.6333 <br />48 <br />.8000 <br />5 <br />.9667 <br />9 <br />.1500 <br />19 <br />.3167 <br />99 <br />.4833 <br />39 <br />.6500 <br />49 <br />.8167 <br />699 <br />.9833 <br />10 <br />.1667 <br />20 <br />.3333 <br />30 <br />.5000 <br />40 <br />.8887 <br />60 <br />.8333 <br />60 <br />1.0000 <br />Table II.-rnches in Decimals of a Foot. <br />.0052 <br />.0078 <br />.0104 <br />.0156 <br />.0208 <br />.0260 <br />.0313 <br />.0417 <br />.0521 <br />.0625 <br />0729 <br />Radius <br />Mid. <br />Tan <br />for <br />Deg. <br />Radius <br />Mid. <br />Tan <br />for <br />3010' <br />30 58' <br />.0833 I <br />.1667 I <br />.2500 I <br />.3333 I <br />.4167 I <br />.50600 <br />.58733 I <br />.68667 I <br />.79500 <br />.8333 I <br />918] <br />.145 <br />0.05' <br />7° <br />101.66 <br />380 <br />153.58 <br />20 20' <br />819.02 <br />1.528 <br />6.105 <br />2.10' <br />Table III. -Radii, Ordinates and Deflections <br />Table IV. -Defl <br />Def. <br />12.6 Ft. <br />15 Ft <br />20 Ft. <br />26 Ft, <br />Def. <br />Deg. <br />Radius <br />Mid. <br />Tan <br />for <br />Deg. <br />Radius <br />Mid. <br />Tan <br />for <br />3010' <br />30 58' <br />Ord. <br />Offset <br />I Foot <br />20 0V <br />20 33' <br />Ord. <br />Offset <br />I Foot <br />0° 10' <br />34377.5 <br />.036 <br />.145 <br />0.05' <br />7° <br />101.66 <br />380 <br />153.58 <br />20 20' <br />819.02 <br />1.528 <br />6.105 <br />2.10' <br />20 <br />17188.8 <br />.073 <br />.291 <br />0.10 <br />20 <br />781.84 <br />1.600 <br />6.395 <br />2.20 <br />30 <br />11459.2 <br />.109 <br />.436 <br />0.15 <br />30 <br />764.49 <br />1.637 <br />6.540 <br />2.26 <br />40 <br />8594.42 <br />.145 <br />.582 <br />0.20 <br />40 <br />747.89 <br />1.673 <br />6.685 <br />2.30 <br />50 <br />6875.65 <br />.182 <br />.727 <br />0.25 <br />500 <br />118.31 <br />30021 <br />30 38' <br />40511 <br />1 <br />6729.66 <br />520 <br />114.06 <br />0.30 <br />8 <br />20 <br />716.78 <br />1.746 <br />6.976 <br />2.40 <br />2.50 <br />10 <br />4911.16 <br />.218 <br />.255 <br />,873 <br />1.018 <br />0.35 <br />30 <br />688.16 <br />674.69 <br />1.819 <br />1.855 <br />7.266' <br />7.411 <br />2.55 <br />20 <br />4297.28 <br />.291 <br />1,164 <br />0.40 <br />40 <br />661.74 <br />1.392 <br />7.656 <br />2.60 <br />30 <br />3819.83 <br />.327 <br />1.309 <br />0.45 <br />7011' 1 <br />104.72 <br />40 <br />3437.87 <br />.364 <br />1.454 <br />0.50 <br />9 <br />637.28 <br />1.965 <br />7.846 <br />2.70 <br />50 <br />3125.36 <br />.400 <br />1.600 <br />0.55 <br />20 <br />614.56 <br />2.037 <br />8.136 <br />2.80 <br />2 <br />30 <br />603.80 <br />2.074 <br />8.281 <br />.86 <br />240 <br />2864.93 <br />.436 <br />1.745 <br />0.60 <br />593.42 <br />2.110 <br />8.426 <br />2.90 <br />10 <br />2644.58 <br />.473 <br />2.891 <br />0.65 <br />20 <br />2. <br />.509 <br />2.038 <br />0.70 <br />30 <br />573.89 <br />2.183 <br />8.716 <br />3.00 <br />30 <br />2292292.0101 <br />.646 <br />2.181 <br />0.76 <br />30 <br />546.99 <br />2.292 <br />9.150 <br />3.15 <br />90 <br />2148.79 <br />.582 <br />2.327 <br />0.80 <br />11 <br />521.67 <br />2.402 <br />3.30 <br />60 <br />2022.41 <br />.618 <br />2.472 <br />0.85 <br />30 <br />499.06 <br />2.511 <br />.685 <br />100.02 <br />3.45 <br />3 <br />12 <br />978.39 <br />2.620 <br />10.46 <br />3.60 <br />1910.08 <br />.655 <br />2.618 <br />0.90 <br />30 <br />459.28 <br />2.730 <br />10.89 <br />3.75 <br />10 <br />1809.57 <br />.691 <br />2.763 <br />0.95 <br />13 <br />491.68 <br />2.839 <br />11.32 <br />3.90 <br />20 <br />1719.12 <br />.727 <br />2.908 <br />1.05 . <br />30 <br />426.40 <br />2.949 <br />11.76 <br />4.05 <br />30 <br />2637.28 <br />.764 <br />3.054 <br />1.06 <br />14 <br />410.28 <br />3.058 <br />12.18 <br />4.20 <br />40 <br />1562.88 <br />.800 <br />3.199 <br />1.10 <br />30 <br />396.20 <br />3.168 <br />12.82 <br />9.35 <br />50 <br />1994.95 <br />.836 <br />3.395 <br />1.16 <br />16 <br />383.07 <br />3.277 <br />13.06 <br />4 <br />1432.69 <br />.873 <br />3.990 <br />1.20 <br />30 <br />370.78 <br />3.387 <br />13.99 <br />.50 <br />4 4.65 <br />1375.40 <br />.909 <br />3.635 <br />1 .2530 <br />16 <br />359348..27 <br />3.496 <br />13.92 <br />4.80 <br />20 <br />2 <br />1322.53 <br />.996 <br />3.718 <br />.0 <br />1:3205 <br />30 <br />96 <br />3.808 <br />14.35 <br />4.95 <br />30 <br />1273.67 <br />.982 <br />3.928 <br />1.35 <br />17 <br />338.27 <br />3.716 <br />14.78 <br />5.10 <br />40 <br />1228.11 <br />1.018 <br />4.071 <br />1.40 <br />18 <br />319.62 <br />3.935 <br />15.64 <br />5.40 <br />50 <br />1186.78 <br />1.055 <br />4.217 <br />1.45 <br />19 <br />302.94 <br />4.155 <br />16.61 <br />5.70 <br />6 <br />1146.28 <br />1.091 <br />4.362 <br />1.50 <br />20 <br />287.94 <br />4.374 <br />17.37 <br />6.00 <br />10 <br />1109.33 <br />1.127 <br />4.507 <br />1.55 <br />21 <br />274.37 <br />4.594 <br />18.22 <br />6.30 <br />20 <br />1074.68 <br />1.164 <br />4.653 <br />1.60 <br />92 <br />262.04 <br />4.814 <br />19.08 <br />6.60 <br />30 <br />1042.14 <br />1.200 <br />4.798 <br />1.65 <br />23 <br />250.79 <br />5.035 <br />19.94 <br />6.90 <br />40 <br />1011.51 <br />1.237 <br />4.943 <br />1.70 <br />94 <br />240.49 <br />5.255 <br />20.79 <br />7.20 <br />50 <br />982.64 <br />1.273 <br />5.088 <br />1.75 <br />S5 <br />231.01 <br />0.476 <br />21.64 <br />7.50 <br />6 <br />966.37 <br />1.309 <br />5.234 <br />1.80 <br />26 <br />222.27 <br />5.697 <br />22.50 <br />7.80 <br />10 <br />929.57 <br />1.346 <br />5.379 <br />1.85 <br />27 <br />214.18 <br />5.918 <br />23.35 <br />8.10 <br />20 <br />905.13 <br />1.382 <br />5.524 <br />1.90 <br />28 <br />206.68 <br />6.139 <br />24.19 <br />8.40 <br />30 <br />881.95 <br />1.418 <br />6!669 <br />1.95 <br />99 <br />199.70 <br />8.360 <br />26.04 <br />8.70 <br />40 <br />859.92 <br />1.455 <br />5.814 <br />2.00 <br />30 <br />193.18 <br />6.683 <br />25.88 <br />9.00 <br />Nora. Chord Deflection=2 times tangent deflection. <br />ections for Sub Chords <br />for Short Radius Curves <br />egrDee Radius Bab ChmdaeofsVarious Lengths Length of <br />Of Are for <br />(.rove <br />100 Ft. Chord <br />12.6 Ft. <br />15 Ft <br />20 Ft. <br />26 Ft, <br />$0° <br />193.18 <br />1° 51 <br />2° 17' <br />20 58' <br />30 43' <br />101.15 <br />320 <br />- 181.39 <br />10 59' <br />20251 <br />3010' <br />30 58' <br />101.33 <br />340 <br />171.01 <br />20 0V <br />20 33' <br />30 21' <br />4012' <br />101.48 <br />360 <br />161.80 <br />2013' <br />20 41' <br />30331 <br />40 20' <br />101.66 <br />380 <br />153.58 <br />20 20' <br />20490 <br />30441 <br />4040' <br />101.85 <br />400 <br />146.19 <br />20 27' <br />20 57' <br />30651 <br />40 54' <br />102.06 <br />420 <br />139.52 <br />2034' <br />3006' <br />4007' <br />50 OB' <br />102.29 <br />440 <br />133.47 <br />2°41' <br />3013' <br />4018' <br />5022' <br />102.53 <br />460 <br />127.97 <br />20 48' <br />30 21' <br />40291 <br />50 3fi' <br />102.76 <br />480 <br />122.92 <br />2°65' <br />3029' <br />4040' <br />5050' <br />103.00 <br />500 <br />118.31 <br />30021 <br />30 38' <br />40511 <br />60 04' <br />10324 <br />520 <br />114.06 <br />30091 <br />30 46' <br />50021 <br />6017' <br />103.64 <br />540 <br />110.11 <br />30161 <br />30 54' <br />5013' <br />60 31' <br />103.84 <br />560 <br />106.50 <br />30221 <br />40 02' <br />50 23' <br />60441 <br />104.14 <br />560 <br />103.14 <br />30 29' <br />4010' <br />S0 34' <br />60 57' <br />104.43 <br />600 1 <br />100.00 1 <br />30351 <br />P 4018' <br />1 50441 1 <br />7011' 1 <br />104.72 <br />