. 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 . F =F -\- K — S, and sin. ^(F+A^—6^) II. When the turnout is from the outside of the curve, the precedingsolution requires a few modifications. In the present case, the angleEFK = F (fig. 19) and EB L = S. To find K, we have in thetriangle B FK, K F -\- B K : KF — B K = tan. ^ (FB K +BFK) : tan.
. 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 . F =F -\- K — S, and sin. ^(F+A^—6^) II. When the turnout is from the outside of the curve, the precedingsolution requires a few modifications. In the present case, the angleEFK = F (fig. 19) and EB L = S. To find K, we have in thetriangle B FK, K F -\- B K : KF — B K = tan. ^ (FB K +BFK) : tan. i (FCA — i5FA^. But KF= R-{-lg, and BK= R — i g + d. Therefore, AF + B K =-- 2 R + d, and KF —BK = g — d. Moreover, FB A = 180° — FB L = 180° —(EBF—EBL) = 180°— (E BF — S), and BFK = 180° —BFK = 180^ — (BFE -\- EFK) = 180° — {EBF + F).Therefore, FBK—B FK = F + ^. Lastly, Fi3 K-\- B FK =180 —K Substituting these values in the preceding proportion, wehave 2R-\-d: q — d= tan. (90° — ^K) : tan. i (F + S), or ,an. (90° - i A^) =. (2A±^^i^±^ . But tan. (90° -1 /T) = tan. h K 2 g — d (2R -\-d) tan. ^ (F+ .S) 40 CIRCULAR CURVES. Next to find B F, we have, in the triangle B T -^ 3 F ^B Csin. B CF sin. BFC But BC = g ~ d, and B CF = 90^ En AA, or Fig. sin. BCF = COS. ^K. Moreover, BFC=^(F+ S); for BFK= KFC—BFC,and FB K= KC F-\-B F C = KF C + BF , FBK—B FK=2B F C. But, as shown above, FBK—BFK= F+ S. Therefore, 2 BFC = F-}-S,ovBFC=^ {F-\-S).Substituting these values in the expression for B F, we have, as before. BF= (ff — ^) cos. hK* },BF Sin. 1(^+5)Lastly, to find R, we have (§ GS) R -\- ^ fj =r E F = sin. i BEF Since ^ Z is generally very small, an approximate valu iof B F may be obtained By making cos. ^ K = 1. Tliis gives B F = — g-d -—, ; T-, r—c> 1 wbich is identicalsm. i (F+ 5) with the formula for BFm^ 50. Table V. will, therefore, give a close approxima- 4on to the value of .B F on curves also, for
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Keywords: ., bookcentury1800, bookdecade1870, booksubjectrailroadengineering
