. 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 . DC X R- Second Solution. By this method the second radius may bt founuby calculation alone. The figure being drawn as above, we have, inthe triangle A BD, AB = a, AD = 2R sin. ^ (A — B), and theincluded angle DAB = HA li ~ HAD = A — h (A — B) ^^ {A -\- B). Find in this triangle (Tab. X. 14 and \
. 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 . DC X R- Second Solution. By this method the second radius may bt founuby calculation alone. The figure being drawn as above, we have, inthe triangle A BD, AB = a, AD = 2R sin. ^ (A — B), and theincluded angle DAB = HA li ~ HAD = A — h (A — B) ^^ {A -\- B). Find in this triangle (Tab. X. 14 and \2) BD and theangle ABD. Find also the angle DBL^B-\-ABD. Then the chord CB = 2 R sin. hBFC =2R sin. DB L, and the chord D GCB = BD —DBL, = 2R sin. ^DE C = 2R sin. DBL (§ 69). ButD C; whence 2 R sin. D B L = B D — 2 R sm .R> BD 2 sin. DBL — R. When the point D falls on the other side of A, that is, when theangle B is greater than jl, the solution is the same, except that themgle DAB is then 180° — ^(A -\- B), and the angle DBL= B —ABD. REVERSED CURVES. 21 39. Probloiia. Given the length of the common tangent D G — a^and the angles of intersection I and I (Jig. 10), to determine the commonradms C E = C F = li of a reversed curve to urate the tangents IIArtnn B L. Fig. T- Solution. By § 4 wc have DC = R tan. | /, and CG= Rtan. | /.whence R (tan. ^ / + tan. hi) = D C -{- C G = a, or R = tan. ^ / + ti^n- k ^This formula may be adapted to calculation by logarithms; for we have (Tab. X. 35) tan. ^7+ tm.^P = ^T.^^jcot fj- Substitutingthis value, we get rw R - «gos. ^7cos. ^7^ (^+/0 The tangent points A and B are obtained by measuring from D aiistance J. Z) = 72 tan |- 7, and from G a distance B G — R tan. \ I, Example. Given a = 600, 1 = 12°, and F = 8° to find R. Here a = 600 i7=6° cos. f 7 = 4° cos. R = 22 CIRCULAR CURVES 40. Problem. Given the line AB = a {fig- 10), which jchis
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Keywords: ., bookcentury1800, bookdecade1870, booksubjectrailroadengineering
