. 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 . tney have different radii, and form a compound curve. Thus A B Cfiff. .5) is a reversed cirve, and .1 B D % comoound curve. 16 CIRCULAR CURVES. 31, ProbleiJl. To lay out a reversed or a compound cun>e, radii or dejiection anyles and the tangent points are known. Solution. I/ay out
. 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 . tney have different radii, and form a compound curve. Thus A B Cfiff. .5) is a reversed cirve, and .1 B D % comoound curve. 16 CIRCULAR CURVES. 31, ProbleiJl. To lay out a reversed or a compound cun>e, radii or dejiection anyles and the tangent points are known. Solution. I/ay out the first portion of the curve from A to B Cfig. 5),by one of the usual methods. Find B F, the tangent to A B at thepoint B (§ 16 or ^ 21). Then B F will be tlie tangent also of the sec-ond portion B C oi a reversed, or Zi D of a compound curve, and fromthis tangent cither of these portions may be laid ofl in the usual manner A. Reversed Curves. 32 ISieOJCRi. Tlie reversing point of a reversed curve letwcesparallel tangents is in the line joining the tangent points. Fig. t\ Demonstration. Let A CB (fig. 6) be a reversed curve, uniting tinparallel tangents HA and B K, having its radii equal or unequal, andreversing at C. If now the chords A Cam] CB are drawn, we haveto prove that these chords are in the same straight line. The radiiE C and C F, being perpendicular to the common tangent at C (§ 2,1.),are in the same straight line, and the radii A E and B F, being per-pendicular to the parallel tangents HA and B K, are parallel. There-fore, the angle AE C= CFB, and, consequently, E CA, the halfsupplement of A E C, is equal to F C B, the half supplement of CFB;but these angles cannot be equal, unless A Cand C B are in the samestraight line. 33. Proljlem. Given the perpendicular distance between two par-alM tangents B D =^ b {Jig 6), and the distance between the two tangenivoints A B = a, to determine the reversing point C and the common radntiE C ^ C F = R of a reversed curve
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Keywords: ., bookcentury1800, bookdecade1870, booksubjectrailroadengineering
