. Field-book for railroad engineers. Containing formulas for laying out curves, determining frog angles, levelling, calculating earth-work, etc., etc., together with tables of radii, ordinates deflections, long chords, magnetic variation, logarithms, logarithmic and natural sines, tangents, etc., etc . om each other. These points are usually sufficientfor grading a road ; but when the track is laid, it is desirable to haveintermediate points on the curve accurately determined. For this pur-pose the chord of 100 feet is divided into a certain number of equalparts, and the perpendicular distance
. Field-book for railroad engineers. Containing formulas for laying out curves, determining frog angles, levelling, calculating earth-work, etc., etc., together with tables of radii, ordinates deflections, long chords, magnetic variation, logarithms, logarithmic and natural sines, tangents, etc., etc . om each other. These points are usually sufficientfor grading a road ; but when the track is laid, it is desirable to haveintermediate points on the curve accurately determined. For this pur-pose the chord of 100 feet is divided into a certain number of equalparts, and the perpendicular distances from the points of division tothe curve are calculated. These distances are called ordinates. If thechord is divided into eight equal parts, we shall have points on thecurve at every feet, and this will be often enough, if the rails,which are seldom shorter than 15 feet, have been properly curved(§ 28). 25. Problem. Given the dpflection angle D or the radius R of acame, to Jind the ordinates for any chord. Solution. I. To find the middle ordinate. Let AEB (fig. 4) beft portion of a curve, subtended by a chord A B, which may be de- i^ CIRCULAR CURVES. noted by c. Draw the middle ordinate ED, and denote it by m. Pro-duce ED to the centre F, and join AF and AE. Then (Tab. X. 3« I Xu ED Id. = tan. E A D, or E D But, since the angle EAD is measured by half the arc BE, or by half the equal arc AE^we have EAD=hAFE. Tlierefore E D = AD tan. ^ AFE, ox ^ m^ hciVin-^AFE. When c = 100, A FE = /) (§ ), and m = 50 tan. 5 /), whence 7/)may be obtained from the tabic of natural tangents, by <liA-iding tan4 Z) by 2, and removing the decimal point two places to the right. The value of m may be obtained in another form thus. In thetriangle ADFwe have DF= ^A F^ — A if- = ^72^ _ ^^2. Thenm = EF— DF= R — DF, or 7)1 = R — s/R- 4 ^ • II. To find any other ordinate, as i?iV, at a distance DN =h fromihe centre of the chord. Produce RN until it meets the diameter parallel to ^ ^ in
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Keywords: ., bookcentury1800, bookdecade1870, booksubjectrailroadengineering
