When can a rail be called long?

Thermal expansion When exposed to temperature variations, the rail tends to vary its length. If this tendency is freely allowed, for a temperature variance Δt°, the rail length L will vary by ΔL. This length variance can be computed as: ΔL = αLΔt° In this formula, α is the steel expansion coefficient = 11.5·10−6 mm/mm°C. If…

Relative position of adjacent tracks

General considerations The relative position of  railway double or multiple adjacent lines is of critical importance for level crossings. On canted tracks, the road traffic is affected if the level crossing does not provide a good riding plane, especially for long vehicles or the (sometimes expensive) low profile ones. This is why the design of…

The orphan rule of cant design over a reverse transition

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…

The Clothoid

INTRODUCTION In transportation infrastructure design the route is defined based on its axis (centreline) – the alignment model. This simplified abstract model is designed in such a way to clearly define the principle course of the infrastructure project. For most of the transportation means the infrastructure alignment design is split into two main two-dimensional complex…

Circle or “egg”?

After the post about the limits of vertical acceleration, and even before, I was asked what was the original curve used to connect vertical gradients. What was first, the circle or the “egg”- the parabolic curve? The expected answer was “the circular curve” because, presumably, a circle can be drawn easier than a parabola… “How…

The versine formulae

An anecdote: Track geometry exam, somewhere at a Civil Engineering University. One of the exam subjects is realignment methods and types of versines. This important subject was covered during the track course hours but also in four seminars and in a realignment project homework – so it was supposed to be an easy one … After checking the…

The limits of vertical acceleration

The theory of vertical movement. The parabolic projectile motion An object thrown in the air, near the earth’s surface, moves along a parabolic path under the action of gravity only. The only force of significance that acts on the object is gravity, which acts downward to cause a downward acceleration. Because of the object’s inertia, no external horizontal force is needed…