. 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 . ide of the level is the same, the corrections will be equal, andwill destroy each other. 66 LEVELLING. Article III. — Vertical Curves. 106. Vertical curves are used to round off the angles fonaed b^the meeting; of two grades. Let A Cand CB (fig. 47) be two gradesmeeting at C. These grades are su
. 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 . ide of the level is the same, the corrections will be equal, andwill destroy each other. 66 LEVELLING. Article III. — Vertical Curves. 106. Vertical curves are used to round off the angles fonaed b^the meeting; of two grades. Let A Cand CB (fig. 47) be two gradesmeeting at C. These grades are supposed to be given by the rise per sta-tion in uoing in some particuU^r direction. Thus, starting from ^1. thegrades of A Cand (^B may be denoted respectively by^ and 9; thatis, (J denotes what is added to the height at every station on A C, andij denotes what is added to the height at every station on CB],huisince CB is a descending grade, the C[uantity added is a minus quan-tity, and (/ will therefore be negative. The parabola furnishes a verysimple method of putting in a vertical curve. 107. Problem. Given the grade g of A C [fig. 47), the grade aof C B, and the number of stations n on each side of C to the tangent pointsA and B, to unite these points by a parabolic vertical curve. Fig. 47. Solution. Let A E B he the required parabola. Through B and Cdraw the vertical lines FK and C H, and produce A C to meet FKin F. Through .1 draw the horizontal line A K, and join A B, cut-ting C H in D. Then, since the distance from C to A and B is meas-ured horizontally, we have A H =^ HK. and consequently AD =D B. The vertical line CD is, therefore, a diameter of the parabola(§ 84, L), and the distances of the curve in a vertical direction fromthe stations on the tangent A i^are to each other as the squares of thenumber of stations from A (^ 84, II.). Thus, if a represent this dis-tance at the first station from A, the distance at the second stationwould be 4 a, at the third station
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Keywords: ., bookcentury1800, bookdecade1870, booksubjectrailroadengineering
