Track transition curve

A transition curve (also, spiral easement or, simply, spiral) is a spiral-shaped length of highway or railroad track that is used between sections having different profiles and radii, such as between straightaways (tangents) and curves, or between two different curves. In the horizontal plane, the radius of a transition curve varies continually over its length between the disparate radii of the sections that it joins—for example, from infinite radius at a tangent to the nominal radius of a smooth curve. The resulting spiral provides a gradual, eased transition, preventing undesirable sudden, abrupt changes in lateral (centripetal) acceleration that would otherwise occur without a transition curve. Similarly, on highways, transition curves allow drivers to change steering gradually when entering or exiting curves. Transition curves also serve as a transition in the vertical plane, whereby the elevation of the inside or outside of the curve is lowered or raised to reach the nominal amount of bank for the curve. On early railroads, because of the low speeds and wide-radius curves employed, the surveyors were able to ignore any form of easement, but during the 19th century, as speeds increased, the need for a track curve with gradually increasing curvature became apparent. Rankine's 1862 "Civil Engineering" cites several such curves, including an 1828 or 1829 proposal based on the "curve of sines" by William Gravatt, and the curve of adjustment by William Froude around 1842 approximating the elastic curve. The actual equation given in Rankine is that of a cubic curve, which is a polynomial curve of degree 3, at the time also known as a cubic parabola. In the UK, only from 1845, when legislation and land costs began to constrain the laying out of rail routes and tighter curves were necessary, were the principles beginning to be applied in practice. The 'true spiral', whose curvature is exactly linear in arclength, requires more sophisticated mathematics (in particular, the ability to integrate its intrinsic equation) to compute than the proposals that were cited by Rankine.

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PHYS-101(de): General physics : mechanics (German)

Die Studenten erwerben die Grundkenntnisse zum Verständnis von physikalischen Phänomenen der Mechanik. Sie entwickeln die Fähigkeit, die Auswirkungen dieser Phänomene mit den entsprechenden theoretisc

Degree of curvature

Degree of curve or degree of curvature is a measure of curvature of a circular arc used in civil engineering for its easy use in layout surveying. The degree of curvature is defined as the central angle to the ends of an agreed length of either an arc or a chord; various lengths are commonly used in different areas of practice. This angle is also the change in forward direction as that portion of the curve is traveled. In an n-degree curve, the forward bearing changes by n degrees over the standard length of arc or chord.

Minimum railway curve radius

The minimum railway curve radius is the shortest allowable design radius for the centerline of railway tracks under a particular set of conditions. It has an important bearing on construction costs and operating costs and, in combination with superelevation (difference in elevation of the two rails) in the case of train tracks, determines the maximum safe speed of a curve. The minimum radius of a curve is one parameter in the design of railway vehicles as well as trams; monorails and automated guideways are also subject to a minimum radius.

Cant (road/rail)

The cant of a railway track or camber of a road (also referred to as superelevation, cross slope or cross fall) is the rate of change in elevation (height) between the two rails or edges of the road. This is normally greater where the railway or road is curved; raising the outer rail or the outer edge of the road creates a banked turn, thus allowing vehicles to travel round the curve at faster speeds which would otherwise not be possible if the surface is flat or level.

Renewal of a fixed railway track using UHPFRC - first use worldwide of UHPFRC in rail track construction, part 1

Antonina Hochuli

This two-part article reports on the renewal and adaptation of the fixed railway track in the heavily frequented underground train station at Zurich Airport. The fixed track built in 1980 had reached the service duration predicted by the system provider an ...

ERNST & SOHN2021

Application of vertex and mass constraints in track-based alignment

Olivier Schneider, Christophe Salzmann, Matthew Needham, Maurizio Martinelli, Frédéric Guillaume Dupertuis, Vincent Fave, Géraldine Conti, Louis Nicolas, Gerhard Raven

The software alignment of planar tracking detectors using samples of charged particle trajectories may lead to global detector distortions that affect vertex and momentum resolution. We present an alignment procedure that constrains such distortions by mak ...

Elsevier Science Bv2013

Comportement du ballast sous l'action du bourrage et du trafic ferroviaire

Chiara Paderno

The geometry of the railway track is degraded under traffic load, and must be maintained periodically. This degradation is due to the arrangement of ballast particles under loads and vibrations, which results into irreversible plastic settlements. Tamping ...

EPFL2010