. 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 ; for ithas already been proved, that A a cuts F G on the curve. NowDa:MG^BD:B G = b:^,or M G =lDaK But Da= \ C , MG = h CE. Again, F G : CD =^ A G : A D = I ■:>.Therefore, FG = \CD = lCE. We have then FM = F G —MG = f CE — ii CE = is CE. As this is the proper deflectionfrom the
. 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 ; for ithas already been proved, that A a cuts F G on the curve. NowDa:MG^BD:B G = b:^,or M G =lDaK But Da= \ C , MG = h CE. Again, F G : CD =^ A G : A D = I ■:>.Therefore, FG = \CD = lCE. We have then FM = F G —MG = f CE — ii CE = is CE. As this is the proper deflectionfrom the tangent at F to the cm-ve (§ 85), the intersection of B a withF G is on the curve. This furnishes another method of laying out aparabola by intersections. 91. The following example is given in illustration of several of thepreceding methods. Example. Given AC = B C ^ 832 (fig. 40), and -1 B = 1536 tolay out a parabola A EB. We here find CD = 320. To begin withthe method by tangent deflections (§ 85), divide the tangent A C into C E ^(\0 eight equal parts. Then a = —^ = -wr = Lay off from the divisions on the tangent Fl = , G2 =4 X 25 = 10, ^3 =9X25 = , and /v 4 = 16 X = 40. Suppose now that it isinconvenient to continue this method beyond K. In this case we may Fig. 40. find a new tangent at E, by bisecting A Cand B C {^ 89), and draw-ing KL through the points of bisection. Divide the new tangentKE =^ ^ AD ^ 384 into four equal parts, and lay oflT from KE the RADIUS OF CURVATURE. 71 same tangent deflections as were laid off from .fi iiT, namely, 3 A^6 = 10, and 07 = To lay off the second half of thecurve by middle ordinates (§86), measure EB= BisectEB in P, and lay off the middle ordinate P R = ^D E ^ ER^ , and BR = , and lay off the middle or-dinates S T and V IF, each equal to ^ P /2 = 10. By measuring thechords ET, TR, R TF, and WB, and laying off an ordinate froneach, equal to 2 5. four additional points
Size: 2098px × 1191px
Photo credit: © Reading Room 2020 / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1800, bookdecade1870, booksubjectrailroadengineering
