Laserfiche WebLink
y TABLn II - Radii, Ordinates and Deflections. Chord 100 ft. <br />]Deg. <br />diu <br />Radius <br />Ord. <br />Tan. <br />Diet. <br />. Def. <br />D,st. <br />Def. <br />lfor <br />Deg. <br />Radius <br />Mid <br />' OidFt.. <br />Tan <br />Dist. " <br />'Def. <br />Dist. <br />Def. <br />f r <br />1°51' <br />t. - <br />`ft: <br />ft. <br />ft. -,I <br />.. <br />_3°.43' <br />ft., <br />ft. <br />ft: <br />ft:".. <br />1° <br />0° 10' <br />34377. ' <br />- .036 <br />.145 <br />.291 <br />.05 <br />7° <br />819.0 <br />1.528 <br />6:105 <br />12.21 <br />2:10 <br />20 <br />17189. <br />.073 <br />.291' <br />.582 <br />0.10 <br />20' <br />781.8 <br />1.600 <br />6.395 <br />12.79 <br />2.20 <br />30 <br />11459. <br />.109 <br />.436 <br />.873 <br />0.15 <br />30 <br />764.5 <br />1.637 <br />6.540 <br />13.08 <br />2.25 <br />40: <br />8594.4 <br />.145 <br />. .582 <br />1.164 <br />0.20 <br />40 <br />747.9 <br />1.673. <br />6.685 <br />13.37 <br />2.30 <br />50 <br />6875.5 <br />'.182 <br />.727 <br />1:454 <br />0.25 <br />8 <br />716.8 <br />1.746 <br />6.976 <br />13.95 <br />2.40 <br />II <br />5729.6 <br />.218 <br />.873 <br />,1.745 <br />0.30 <br />.20 <br />688.2 <br />1.819 <br />7.266..14:53 <br />18' <br />2.50 <br />10 <br />4911.2 <br />.255 <br />1.018 <br />2.036 <br />0.35 <br />30 <br />674.7 <br />1.855 <br />7.411 <br />14.82 <br />2.55 <br />20 <br />4297.3 <br />.291 <br />1.164 <br />2.327 <br />0.40 <br />40 <br />661.7 <br />1.892 <br />7.556 <br />15.11 <br />2.60 <br />"30 <br />3819.8 <br />'.327 <br />1:309 <br />2.618 <br />0.45 <br />9 • <br />637.3 <br />1.965. <br />7.846 <br />15.69 <br />2.70 <br />40 <br />3437.9 <br />.364 <br />1:454 <br />2.909 <br />0.50 <br />20 <br />614.6 <br />2.037 <br />8.136 <br />16.27 <br />2.80 <br />50 <br />3125:4 <br />.400 <br />1.600 <br />3.200 <br />0.55 <br />30 <br />603.8 <br />2.074 <br />8.281 <br />16.56 <br />2.85 <br />22' <br />2864.9 <br />.436 <br />1.745 <br />3.490 <br />0.60 <br />40 <br />593.4 <br />2.110 <br />8:426 <br />16.85 <br />2.90 <br />10 <br />2644.6 <br />.473 <br />1.891 <br />3.7810.65 <br />10 <br />573.7 <br />2.183 <br />8.716 <br />17.43 <br />3.00 <br />20 <br />2455.7 <br />.509 <br />2.036 <br />4.072 <br />0.70 <br />30 <br />546.4 <br />2.292 <br />9.150 <br />18.30 <br />3.15 <br />30 <br />2292.0 <br />.545 <br />2.181 <br />4.363 <br />0.75 <br />11 <br />521.7 <br />2.402 <br />9.585 <br />19.16 <br />3.30 <br />40 <br />2148.8 <br />..582 <br />2.327 <br />4.654 <br />0.80 <br />30 <br />499.1 <br />2.511 <br />10.02 <br />20'.04 <br />3.45 <br />50 <br />2022.4 <br />,.618 <br />2.472 <br />4.945 <br />0.85 <br />12 <br />478.3 <br />2.620 <br />10;45, <br />20.91 <br />3.60 <br />$' <br />• <br />1910.1 <br />.652.618' <br />5 <br />5.235 <br />0.90 <br />30 <br />469.3 <br />2.730 <br />10.89 <br />21:77 <br />3.75 <br />10 <br />1809.6 <br />.691.2.763 <br />5.526 <br />0.95 <br />.13 <br />441.7 <br />2.839 <br />11.32. <br />22'.64 <br />3.90 <br />20 <br />1719.1 <br />.727 <br />2.908 <br />5.817 <br />1.00 <br />30 <br />425.4 <br />2.949 <br />11.75 <br />23.51 <br />4.05 <br />30. <br />1637.3 <br />.764 <br />3.054. <br />6.108 <br />1.05 <br />14 <br />410.3 <br />3.058 <br />12.18. <br />24.37 <br />4.20 <br />40' <br />1562.9 <br />.800 <br />3.199' <br />6.398 <br />1.10 <br />30 <br />396.2 <br />3.168 <br />12.62 <br />25.24 <br />4.35 <br />50 <br />1495.0 <br />.836 <br />3.345 <br />6.689 <br />1.15 <br />15 <br />383.1 <br />3.277 <br />13.05 <br />26.11 <br />4.50 <br />6: <br />1432:7 <br />.873 <br />3.490 <br />6.980 <br />1.20 <br />30 <br />370:8 <br />3.387 <br />13.49 <br />26:97 <br />4.65 <br />10 <br />1375.4 <br />.909 <br />3.635 <br />7.271 <br />1.25' <br />16 <br />359.3 <br />3.496 <br />13.92 <br />27.84 <br />4.80 <br />20 <br />.1322.5 <br />.945 <br />3.718 <br />7.561 <br />1.30 <br />'30 <br />348.5 <br />3.606 <br />14.35 <br />28.70 <br />4.95 <br />30 <br />1273:6 <br />.982 <br />3.926 <br />7.852 <br />1.35• <br />-17 <br />338.3 <br />3.716 <br />14.78, <br />29.56 <br />5.10 <br />40. <br />1228:1 <br />1.018 <br />4.071 <br />8.143 <br />1.40 <br />18. <br />319.6 <br />3.935 <br />15.64" <br />31.29 <br />5.40 <br />50" <br />1185.8 <br />1.055 <br />4.217 <br />8.433 <br />1.45 <br />19 <br />302.9 <br />4.155 <br />16.51 <br />33.01 <br />5.70 <br />6 <br />1146.3 <br />1.091 <br />4.362 <br />8.724 <br />1.50 <br />20 <br />287.9 <br />4.374 <br />17.37 <br />34.73 <br />6.00 <br />10 <br />.1109.3 <br />1.127 <br />4.507 <br />9.014 <br />1.55 <br />21' <br />274.4 <br />4.594 <br />18.22 <br />36.44 <br />6.30 <br />20. <br />1074:7 <br />1.164 <br />4.653 <br />9.305 <br />1.60 <br />22 <br />262.0 <br />4.814 <br />19.08 <br />38.16 <br />6.60 <br />30 <br />1042.1 <br />1.200 <br />4.798 <br />9.596 <br />1.65 <br />23 <br />250.8 <br />5.035 <br />19.94" <br />39.87 <br />6.90 <br />40 <br />1011.5 <br />1.237 <br />4.943 <br />9.886 <br />1.70. <br />24 <br />240.5 <br />5.255 <br />20.79 <br />41.58 <br />7.20 <br />50 <br />982.6 <br />1.275.088 <br />3 <br />10:18 <br />1.75 <br />25 <br />231.0 <br />5:476 <br />21.64 <br />43.28 <br />7.50 <br />8' <br />955.4 <br />1:309 <br />5.234 <br />10.47 <br />1.80 <br />26 <br />222.3 <br />5:697'22.50 <br />44:99 <br />7.80 <br />10 <br />929:6 <br />1:346 <br />5.379 <br />10.76 <br />1.85 <br />27 <br />214.2 <br />5.918 <br />23.35" <br />46.69 <br />8.10 <br />20 <br />905.1 <br />1.382 <br />5.524 <br />11.05 <br />1.90 <br />28 <br />206.7 <br />6.139 <br />24.19 <br />48.38 <br />8.40 <br />30 <br />881.9 <br />1.418 <br />5.669 <br />11.34 <br />1.95 <br />29 <br />199.7 <br />6.360 <br />25.04 <br />50.07 <br />8.70 <br />40 <br />859.9 <br />1.455 <br />5.814 <br />11.63 <br />2.00 <br />30 <br />193.2 <br />6.583 <br />25.88 <br />51.76 <br />9.00 <br />-The middle ordinate in inches for any cord of length (C) is equal to .0012 C' <br />piultiplied by the middle 'ordinate taken from the above table. Thus, if it <br />desired to bend a 30 ft. rail to fit a 10 degree curve, its middle ordinate should <br />tie .0012X900X2.183 or 2.36 inches. <br />TABLE III 'Deflections for Sub Chords for Short Radius Curves. <br />0egrea <br />of <br />[,urve <br />Radius <br />b <br />suchord = sin of I def. angle <br />R <br />mgt' <br />of arc <br />for 100 ft. <br />sin. $ def, ang. <br />12.5 Ft. <br />15 Ft. <br />20 Ft. <br />25 Ft. <br />30° <br />193.18 <br />1°51' <br />.0333 <br />2° <br />17' <br />2°58' <br />.. <br />_3°.43' <br />.5333 <br />101.15 <br />32° <br />181.39 <br />1° <br />59' <br />2° <br />25' <br />3° <br />10' <br />3° <br />58' <br />101.33 <br />34° <br />171.01 <br />20 <br />o6' <br />2° <br />33' <br />3° <br />21' <br />4° <br />12' <br />I0I.48 <br />.5667 <br />161.8o <br />2°.13' <br />. <br />2° <br />41' <br />3° <br />33' .. <br />4° <br />26' _ <br />- ro1.66 <br />36° <br />80 <br />153.58 <br />20 <br />20' <br />20 <br />491 <br />30.441 <br />.1000 <br />-4 0.40` <br />.2667 <br />101.85 <br />40 <br />146.19 <br />2 <br />27' <br />2 <br />57 <br />3 <br />55 <br />4 <br />54 <br />102.o6 <br />42° <br />139.52 <br />2° <br />34' <br />3° <br />05' <br />4° <br />07' <br />5° <br />08' <br />101.29 <br />44°- <br />133.47 <br />2° <br />41' <br />3° <br />13' <br />40 <br />18' <br />50 <br />22' <br />-102.53 <br />460 <br />127.97 <br />20 <br />48! <br />3°.21' <br />.6500 <br />4° <br />29' <br />5°.36' <br />.9833 <br />102.76 <br />48° <br />122.92 <br />2°55' <br />3°29'- <br />40 <br />4°40' <br />50 <br />5°50' <br />60' <br />103.00 <br />50° <br />118.31 <br />3° <br />02' <br />3o381 <br />4° <br />51' <br />6° <br />04' <br />103.24 <br />5z°. <br />114.o6 <br />3°09' <br />30461 <br />5°O2' <br />6°17, <br />103.54 <br />S4° <br />II0.11 <br />3°-16' <br />3° <br />54' <br />5° <br />13' <br />6° <br />31' <br />103•.84 <br />56° <br />1o6.5o <br />3° <br />22' <br />4° <br />02' <br />5023 <br />6° <br />44' <br />104.14 <br />58- <br />103.14 <br />30 <br />291 <br />40 <br />10�. <br />50 <br />34� <br />60.57' <br />104.43 <br />60 <br />100.00 <br />3 <br />35 <br />4 <br />i8 • <br />5 <br />44 ' <br />7 <br />11 <br />104.72 <br />CURVE FORMULAS - <br />T 50. an J I R= T cot. z I Chord def. = chords <br />T 60 R <br />Sin. J D R = <br />Sin. J D = 50 Sin. 1;, D No. chords = I' <br />R E= R ex. sec 8 <br />tan I <br />_ Sin. � D T E = T an I I Tan. def. _ chord def. <br />The square of any distance, divided by twice the radius, will equal <br />the distance from tangent to curve, very nearly. <br />To find "angle for a given distance and deflection'. <br />Rule I. Multiply the given distance by .01745 (def: for a° for I ft. <br />"see 'Table II.), -and divide given deflection by the product. <br />Rule 2. Multiply'given deflection by 57.3, and divide the product by <br />the' given distance. <br />To find deflection for a given angle and distance. Multiply the angle <br />by .01745, and"the product by the distance. <br />GENERAL DATA <br />RIGHT'ANGLE TRIANGLES. Square the altitude, divide by twice the <br />base. Add quotient to base for hypotenuse. <br />Given Base loo, Alt.,io.102+200=.5. 1oo+.5=1oo.5 hyp. <br />Given Hyp. Error <br />Alt. 25.252+200=3.125. 100-3.125=96.875=Base. <br />Error in" first. example, .002; in last, .045• <br />To find Tons" of Rail in one mile of track: multiply weight per yard <br />by'iI, and divide by 7. <br />LEVELING. The correction for curvature and refraction, in feet <br />and decimals of feet is equal to 0.574de;where,d-is the distance in miles. <br />The correction for curvature alone is closely, Ids. The combined cor- <br />rection is negative- <br />PRosnBLE ERROR. If dl, d„ da, etc. are the discrepancies of various <br />results from the mean; and if 7 -ds =the sum of the squares. of these dilior- <br />ences and n=the number of observations, then the probable error of the. <br />mean= J= 0.6745 7d= <br />n (n-1) <br />SOLAR EPHEMERIS. Attention is called to the Solar Ephemeks for <br />the. current year, published by Keuffel &Esser Co., and furnished free of <br />charge upon request, which is 34x5) in., with about 90 pages of data very <br />useful to the Surveyor; such as the adjustments of transits, levels and <br />solar attachments; directions and tables for determining the meridian <br />and the latitude from observations `on the sun and Polaris; stadia meas-. <br />urements; magnetic declination; arithmetic constants; English and Metric <br />conversions; trigonometric f ormulas; Natural andLogarithmic Functions; <br />and Logarithms of Numbers. • • <br />TABLn IV. - Minutes in Decimals of a Degree. <br />1' <br />.0167 <br />ll' <br />1833 <br />21' <br />.3500 <br />31'5167 <br />41' <br />.6833 <br />51' <br />.8500 <br />2 <br />.0333 <br />12 <br />.2000 <br />22 <br />.3667 <br />32 <br />.5333 <br />42.7000 <br />7 <br />.52 <br />.8667 <br />8 <br />.0500 <br />13 <br />.2167 <br />23 <br />.3833 <br />33 <br />.5500 <br />43 <br />.7167 <br />53 <br />.8833 <br />4 <br />.0667 <br />14 <br />.2333 <br />24 <br />.4000 <br />34 <br />.5667 <br />44 <br />.7333 <br />54 <br />.9000 <br />5 <br />.0833 <br />15 <br />.2500 <br />25 <br />.4167 <br />35 <br />.5833 <br />45 <br />.75005� <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 />27 <br />.4500 <br />37 <br />.6167 <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 />58 <br />..9667 <br />9 <br />.1500 <br />19 <br />.3167 <br />29 <br />.4833 <br />39 <br />.6500 <br />49 <br />.8167 <br />59 <br />.9833 <br />10 <br />1 .1667 <br />20 <br />.3333 1130 <br />.5000 <br />40 <br />.6667 <br />50 <br />j -.83331, <br />60' <br />1.0000 <br />TABLE V. - Inches in Decimals of a -Foot. <br />1-16 3-32 <br />3-16 <br />5-16 <br />08 <br />74 <br />.0052 0078 <br />.0104.0156 <br />.02 02 0 <br />313 <br />.0417 21 <br />.06Y425 .0729 <br />1 2 <br />3 <br />4 <br />5 6 <br />7 <br />8 9 <br />10 11 <br />.11833 .1667 <br />.2500 <br />.333$ <br />.4167 .5000 <br />.5833 <br />.6667 .7500 <br />.8333 .9167 <br />