. 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 . e necessa-ry, in order that the rails may be properly curved (§ 28), to knowhow the radius of curvature may be found. It will, in general, benecessary to find the radius of curvature at a few points only. Inshort curves it may be found at the two tangent points and at the mid-dle station, and in
. 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 . e necessa-ry, in order that the rails may be properly curved (§ 28), to knowhow the radius of curvature may be found. It will, in general, benecessary to find the radius of curvature at a few points only. Inshort curves it may be found at the two tangent points and at the mid-dle station, and in^onger curves at two or more intermediate pointsbesides. The rails curved according to the radius at any point shouldbe sufficient in number to reach, on each side of that point, half-way tothe next point. 93. Problem. To find the radius of curvature at certain stations on a parabola. Solution. Let AEB (fig. 41) be any parabola, and let it be re-quired to find the radii of curvature at a certain number of stations 72 PARABOLIC CURVES. fron. A to E. Tliese stations must be selected at regular interralfrom those determined by any of the preceding methods. Let n denote the number of parts into which ^ £ is divided, and divide CLinto the same number of equal parts. Draw lines from A to the points. of division. Thus, if n — 4, as in the figure, divide CD into fourequal parts, and draw A F, A E, and A G. Let A D = c^ A F = CiA E = C2, A G — C3, and A C = T. Denote, moreover, C D hy dand the area of the triangle A CB hy A. Then the respective radiifor the points .£,1,2, 3, and A will be R = 2, /?, = A II V2 A A*3 A Ra = A The area A may be found by form. 18, Tab. X.; c and T are known;and Ci, Co, c^ may be found approximately by measurement on a figurecarefully constructed, or exactly by these general formulae : — &c. 7^2 _c2 {n~\)d^ n f2 — c2 n ji — C2 n fi — c2 n [n -3) d^ n2 [n -5) f/2 n2 [n_ -7) «2 d^ &c. It will be seen, that each of these values is formed from th
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Keywords: ., bookcentury1800, bookdecade1870, booksubjectrailroadengineering
