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…
Prologue One of the giants on whose shoulders stood proudly Isaac Newton, is the French mathematician Renatus Cartesius. He was the first to label the unknowns in equations by the letters X and Y and also he defined the annotation of powers as superscripted labels X2 . Believe it or not, that was a giant…
If we consider a circular curve of radius R2, tangent to a straight and mark the offsets O1, O2 and O3, measured perpendicular from the circle to the straight and placed at regular C/2 interval we will get something like this: The offsets O1 and O3 are the bases of a trapezoid and O2+V2 is…
I have discussed here the principle of Virtual Transition, used in the UK and in other countries with British inspired track design principles, to evaluate the changes of the cant parameters at the points where the curvature changes suddenly, without the use of an actual, real transition curve. This method of calculation is not however…
… or – How to convert a curve into an angle? In the track design handbook we have a too complex formula that refers to “degree of curvature”. Before discussing about the equivalent gradient, let’s see first what this is – what is the degree of curvature? This measure is used in United States in…
As demonstrated in a previous post here: https://pwayblog.com/2015/10/29/11-82_cant-deficiency-un-compensated-acceleration-pway/ , the cant deficiency is the conventional representation of the uncompensated lateral acceleration. And since cant deficiency is an acceleration, we can easily represent it as a percentage of g, the gravitational acceleration. The formula that relates the cant deficiency D to un-compensated lateral acceleration is: The…
(Quickly but nostalgically written, remembering the good old days when Taylor was not yet known as the name of a beautiful singer but as the laborious math trick used to solve rather painful Mathematical Analysis problems …) The deflection angle (θ) of the Bloss transition is: The rectangular equations (x and y) of the curve are…
Motto: Tolle lege. Most of the railway track design standards around the world are presenting the particular issue of the reverse transition. All these standards are insisting on keeping a constant rate of change of curvature – a constant A. By doing this in fact the design will include a single continuous transition between the two opposite circular…
A railway track blog 