Laserfiche WebLink
7M <br />TABLE IL- - Radii, Ordinates and Deflections Chord=100 ft. <br />Deg <br />Radius <br />-rt-- <br />Mid <br />Ord.. <br />Tan. <br />Dist. <br />Def. <br />Dist.1for <br />Def. <br />Deg. <br />Radius <br />Mid. <br />'Ord. <br />Ts..Def..-Def. <br />Dist. <br />Dist. <br />1 r <br />51' <br />- <br />ft. ' <br />-. ft. <br />ft <br />/ <br />43 <br />ft. <br />- ft. <br />ft: <br />'ft. <br />i <br />0'10' <br />34377. <br />.036 <br />.145 <br />' :291 <br />0.05 <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 />1' , <br />5729.6 <br />.218 <br />.873 <br />.1.745 <br />0.30 <br />- 20 <br />688.2 <br />1.819 <br />7.266 <br />14.53 <br />2.50 <br />10 <br />4911.2 <br />.255 <br />1.018 <br />2.036 <br />0.35 <br />80 <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 />3819.5 <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 />'2.009 <br />0.50' <br />' 20.614.6 <br />17' <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 />8 <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'.781,0.65 <br />104.43 <br />10 <br />573.7 <br />2.183, <br />8.716 <br />17.48 <br />3 <br />.00 <br />'•20 <br />-2455.7 <br />.500 <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 />80 <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 />8 <br />1910.1 <br />.655 <br />2.618 <br />5.235 <br />0.90 <br />30 <br />459.3 <br />2.73010.89 <br />21.77, <br />3.75 <br />10 <br />1809.6 <br />.691 <br />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 />80 <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 />36 <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 />Il:.' <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 />3.496'13.92 <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 />B <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 />4.594.18.22 <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 :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 />1.273 <br />5.088 <br />10.18 <br />1.75 <br />25 <br />231.0 <br />5.476 <br />21.64 <br />'43.28 <br />7.50 <br />6 <br />955:4 <br />1.309 <br />5.234 <br />10.47 <br />1.80 <br />26 <br />222.3 <br />5.697 <br />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 />1 859.9 <br />1.455 <br />5.814 <br />11.63 <br />2.00 <br />1 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 02 <br />(i multiplied 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 />be .0012X900X2.183 or 2.36 inches. <br />TABLE IIL Deflections for Sub Chords for Short Radius Curves. <br />Degree <br />of <br />Curve <br />Radius <br />34 sub chord = sin of } def, angle <br />R <br />Length50 <br />of arc <br />for 100 ft. <br />sin. Is def. ang. <br />12.5 Ft. <br />15 Ft. <br />20 Ft. <br />25 Ft. <br />300 <br />193.18 <br />1° <br />51' <br />2° <br />17' <br />2° <br />58' <br />3° <br />43 <br />IOI ,15 <br />gs° <br />181.39 <br />1°59' <br />42 <br />2°25, <br />52 <br />3°10 <br />. <br />3058' <br />13 <br />101.33 <br />34° <br />171.0I <br />2° <br />06' <br />2° <br />33' <br />3° <br />21' <br />4° <br />12' <br />101.48 <br />360 <br />16i.8o <br />2° <br />13' <br />2°41' <br />44 <br />3°33' <br />54 <br />4°26'. <br />6 <br />Io1.66 <br />380 <br />.2500 <br />2020, <br />.4167 <br />2° <br />49' -- <br />3° <br />44' <br />4° <br />40' _ <br />101.85 <br />- 406 <br />_153.58 <br />146 "z9 <br />2° <br />27' <br />2° <br />57' <br />3° <br />55' <br />40,54' <br />56 <br />J62.06 <br />42°139.52 <br />.1167. <br />2° <br />34' . <br />3° <br />05' <br />4° <br />07' <br />5° <br />o8' <br />102.29 <br />44° <br />i33-47,--- <br />20 <br />41' : <br />30 <br />13' <br />40 <br />18' <br />5° <br />22' <br />102.53 <br />46° <br />127.97 <br />2°48' <br />.1500 <br />3°21' <br />.3167 <br />4°29' <br />.4833 <br />5036 <br />.6500 <br />102.76 <br />480 <br />122.92' <br />2°55' <br />10 <br />3'29'. <br />20 <br />4°40'' <br />30 <br />5°50' <br />40 <br />103.00 <br />50° <br />118.31 <br />3°02' <br />. <br />3°38' <br />4°51' <br />6°04' <br />103.24 <br />52° <br />114.06' <br />3° <br />09, <br />3° <br />46 <br />5° <br />02' <br />60 <br />17' <br />203.54 <br />540 <br />110.11 ' <br />` <br />3° <br />16 <br />3054 <br />5° <br />13 <br />6031 6° <br />31' <br />103.84 <br />56° <br />106.50 <br />3022 <br />400 <br />S° <br />23' <br />6° <br />44. <br />104:14 <br />580 <br />103-14' <br />3° <br />29' <br />4° <br />Io' <br />5° <br />34 <br />6057 <br />104.43 <br />60° <br />100.00 <br />30 <br />35' <br />4° <br />18' <br />5° <br />44' <br />7°. <br />II' <br />IO4.. 72 <br />�lk <br />l� <br />CURVE" FORMULAS <br />g <br />T 8 _ ,Sot n R' <br />, I R = T cot. I Chord def. =chord <br />50 <br />T Sin. J ll R = 4 <br />Sin. J D = 50 Sin. j No. chords = I <br />R E = R ex. sec ,.I D <br />Sin. D = 50 tagn $ I E = T tan } 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 I° for I ft: <br />�f see Table H.), 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 .di745, and the product by the distance. <br />GENERAL DATA <br />RIGHT ANGLE TRIANGLES. Square the altitude, divide by twice the <br />Vase. Add quotient to base for hypotenuse. <br />Given Base zoo, Alt. 10.102- 200,=.5. 100-}-.5=1o0.5 hyp. <br />Given Hyp. zoo, 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'1I, and divide by 7. <br />LEVELING. The correction for curvature and refraction, in feet <br />and decimals of feet is equal to 0.574ds, where d is the distance in miles. <br />The correction for curvature alone is closely,.jd2. The combined cor- <br />rection is negative. <br />PROBABLE ERROR. If d, , de, da, etc. are the discrepancies of various <br />results from the mean, and if ids=the sum of the squares of these differ- <br />ences and n=the number of observations; then the probable error of the, <br />mean f 0.6745 n n 1) <br />SOLAR EPHEMERIS.. Attention is called to the Solar Ephemeks f0i" <br />the current year, published by Keuffel & Esser Co.; and furnished free of <br />charge upon request, which is 31$58 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 />TABLE IV. - Minutes <br />- <br />in Decimals of a Degree. <br />1' <br />.0167 <br />11' <br />.1833 <br />21' <br />.3500 <br />31' <br />.5167 <br />41' <br />.6833 <br />51' <br />.8506 <br />2 <br />.0333 <br />12 <br />.2000 <br />22.3667 <br />1 <br />32 <br />.5333 <br />42 <br />.7000 <br />52 <br />.8667 <br />g <br />.0500 <br />13 <br />.2167 <br />23 <br />.3833 <br />33 <br />.5500 <br />43 <br />.7167 <br />53 <br />.8833 <br />6 <br />.0667 <br />14 <br />.2333 <br />24 <br />.4000 <br />34 <br />.5667 <br />44 <br />.7333 <br />54 <br />.9000 <br />6 <br />.0833 <br />15 <br />.2500 <br />25 <br />.4167 <br />35 <br />.5833 <br />45 <br />.7500 <br />55 <br />.9167 <br />61000 <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 />58 <br />.9833 <br />10 <br />.1667 <br />20 <br />.3333 <br />30 <br />.5000 <br />40 <br />.6667 <br />50 <br />.8333 <br />60 '1.0 <br />000 <br />- <br />- <br />TABLE V. - Inches in Decimals of a Foot. <br />1.16 <br />3-32 <br />jy 3-16 <br />Y <br />'_16 <br />Y. <br />% <br />r <br />.0052 <br />.0078 <br />.0104 .0158 <br />.0208 <br />.0260 <br />.0313 <br />.0417 .0521 <br />.0625 :07� <br />1 <br />23 <br />4: <br />5 <br />6 <br />7 <br />8 9 <br />10 11 <br />.0833.-.1667 <br />..2500 .3333 <br />.4167 <br />.5000 <br />.5833 <br />.6667 .7500 <br />.8333 .9167 <br />