Where the author eloquently discusses the versine formula and the accuracy loss implied by ignoring a historically insignificant term of its equation, demonstrates an easily replicable CAD check of this inaccuracy, and reveals the EXACT versine formula.
I mentioned in a previous article, The Cubic Parabola – a complicated simplification, that the curvature diagram of the Cubic Parabola increases linearly up to a peak point and then drops down. Only that first section of the parabolic curve can be used as an alignment transition. The curvature diagram of the Clothoid is however…
For the track realignment methods (Hallade or similar) the existing alignment is surveyed by measuring the outer rail offsets (versines) to overlapping chords. One such setup is drawn below: A’, B’, C’ are points on the outer rail of the track and for point B’ the versine B’D’ = vB ex is measured to the chord A’C’. We…
A field measurement of any kind is never exact and intrinsically contains errors (NJDoT Survey Manual – 2014). For track topographical measurements some of these errors are known and eliminated by applying appropriate corrections and compensations. Even after all known errors are eliminated however, a site measurement will still be in error by some unknown value. To minimise the…
A railway track blog 