. 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 . T. Therefore Ty = T r (^). Substituting in (1) theralue of Ty in (2), we have a T— ax ■. 7 r + 2:r, or a a: + Tor -|-Tx = aT; a-\-T-\-T Txand, since from {2),y = -y- , a-\-T-\-T The intersection points D and G and the common tangent pomt Care now easily obtained on the ground, and the radii may
. 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 . T. Therefore Ty = T r (^). Substituting in (1) theralue of Ty in (2), we have a T— ax ■. 7 r + 2:r, or a a: + Tor -|-Tx = aT; a-\-T-\-T Txand, since from {2),y = -y- , a-\-T-\-T The intersection points D and G and the common tangent pomt Care now easily obtained on the ground, and the radii may be found bythe usual methods. Or, if the angles TAB = A and A BI -^ B 30 CIRCULAR CURVES. have been measured or calculated, we have (§ 5) R =^ x cot. ^ A, andR = y cot. ^ B. Substituting the values of x and y found above, wa have R = q^y^r ^^^ ^ = M=^M= T<250 -r 1040 = , and ^ = 500 X 290 -r- 1040 = 48. Probleaea. Given the tangents Al = T, Bl =T, and tfuangle of intersection /, to unite the tangent points A and B (Jig. 13) hy acompound curve, on condition that the tivo branches shall have their anglesof intersection IDG and I GD equal. Fig 13. ^ututiirn. feince IDG = lGD = hl^yf& have ID = 1 G. Rep■escnt the line Ih ~ 1 Ghy x. Then if the perpendicular IHhe let ♦ The radii of an oval of given length and breadth, or of a three-centre arch of givenepan and rise, may also be found from these formulae In these cases A-^ B = 90-, and the values of R and R may be reduced to R =—;—^^, 7;;^ and R = aTi a+ T— Ticalculated a+T — T. These values admit of an easy construction, or they may be readily TURNOUTS AND CROSSINGS. 31 fall fiom /, we !iave (Tab. X. U) D H = ID cos. IDG = x cos. ^ i,sxiUDG^lx COS. ^ /. But DG = DC^CG = AD-\-BG==7 ~ 2 + T — X = r + Ti — 2x. Therefore 2 a: cos. \l =r + T — 2 .r, or 2 T + 2 .r cos. i / =- T -\- T; whence jt = j^:^^^;j^,or() I^ 2r = ^{T+rO CO s.^i/ The tangents AD = T— x and B G =- T — x are now readi
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Keywords: ., bookcentury1800, bookdecade1870, booksubjectrailroadengineering
