. 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 . o the curve at G, and dra^7 C 0 to the cen-tre 0. Denote DFbyc. Then in the right triangle CDF we have(Tab. X. U) DF= CD cos. CDF, or c = a cos. Denote the distance A D from D to the tangent point by x. Then, byGeometry, x^ = D E X D G. But D G = D F-\- FG = DF +EF=2DF—DE = 2c — b. Therefore, x^
. 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 . o the curve at G, and dra^7 C 0 to the cen-tre 0. Denote DFbyc. Then in the right triangle CDF we have(Tab. X. U) DF= CD cos. CDF, or c = a cos. Denote the distance A D from D to the tangent point by x. Then, byGeometry, x^ = D E X D G. But D G = D F-\- FG = DF +EF=2DF—DE = 2c — b. Therefore, x^ = b{2c — b), and 5^ x = ^b{2c — b). Having thus found A Z), we have the tangent AC = AD -{• DC= X -\- a. Hence, R ox D may be found (^ 5 or § 11). If the point E is given by £^^and Ci/perpendicular to each other,a and b may be found from these lines. For a = C H -\- DH ^ (75+JE;77cot. iZ(Tab. X. 9). and6 =^DE = ^^i- MISCELLANEOUS PROBLEMS. 5i Example. Given I = 20° 16, a = 600, and 6 = 80, to find x andH. Here c = 600 cos. 10° 8 = 59064, 2 c - 6 = , and x =ySO X 110^28 = Then T = 600 + = , andR = cot. 10° 8 = 73. Problem. Given the tangent A C {Jig. 25), and the choraA By uniting the tangent points A and B, to Jind the radius A 0 -- Fig. 25 Solution. Measure or calculate the perpendicular CD. Then if CZ)be produced to the centre 0, the right triangles AD C and CA 0,having th3 jungle at G common, are similar, and give CD : A D =AC: A 0, or ^^A^XACCD If it is inconvenient to measure the chord A B, a line E F, parallelto it, may be obtained by laying off from C equal distances CE andCF. Then measuring E G and G C, we have, from the similar tri- GEXAC%ng\esE GCand CAO, CG:GE =AC:AO,orR=—^G—* Example. Given ^ C = 246 and AD = 240, to find R. Here 240 X 246VD = 54, and R = - ^^= 52 CIRCULAR CURVES. 74. Problem. Given the radius AO = R [foj 25), to find :httangent A C = J- of a curve to unite two straight lin
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Keywords: ., bookcentury1800, bookdecade1870, booksubjectrailroadengineering
