. 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 . branch of a compound curve he produced^HJilil the tangent at its extremity is parallel to the tangent at the extremityof the second branchy the common tangent point of the tico arcs is in thestraight line produced, which passes through the tangent points of these par-allel tangents. Demonstratio
. 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 . branch of a compound curve he produced^HJilil the tangent at its extremity is parallel to the tangent at the extremityof the second branchy the common tangent point of the tico arcs is in thestraight line produced, which passes through the tangent points of these par-allel tangents. Demonstration. Let A CB (fig. 11) be a compound curve, unitingthe tangents HA and B K. The radii CF and CF, being perpen-dicular to the common tangent at C (§ 2,1.), are in the same straightline. Continue the curve A C to Z>, where its tangent OD becomesparallel to B K, and consequently the radius DE parallel to B if the chords CD and CB be drawn, we have the angle CED= CFB; whence E CD, the half-supplement of CE D, is equal toFCB, the half-supplement of CFB. But E CD cannot be equal toF CB, unless CD coincides Avith CB. Therefore the line B D pro-inced passes through the common tangent point C 24 42. Problem. compound curve. CIRCULAR CURVES. To find a limit in one direction of each radius of ol. !S)lution. Let AI and Bl (fig. 11) be the tangents of the the intersection point 7, draw IM bisecting the angle A A L and B M perpendicular respectively to A I and B /, niect-ing 1M in L and M. Then the radius of the branch commencing onthe shorter tangent A /must be less than AL^ and the radius of thebranch commencing on the longer tangent B I must be greater thanBM. For suppose the shorter radius to be made equal to A L^ andmake IN = A I, and join L N. Then the equal triangles A IL andNIL give A L = L N; so that the curve, if continued, will passthrough iV, where its tangent will coincide with IN. Then (§ 41) thecommon tangent point would be the intersection of
Size: 1643px × 1521px
Photo credit: © Reading Room 2020 / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1800, bookdecade1870, booksubjectrailroadengineering
