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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 ...
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.
Track gauge or rail gauge (also known as track gage in North America [8]) is the distance between the inner sides (gauge sides) of the heads of the two load bearing rails that make up a single railway line. Each country uses different gauges for different types of trains.
The general standard in Germany and Switzerland had been to build new tracks with a centre-to-centre spacing of 3.8 m (12 ft) and a spacing of 4.5 m (15 ft) in railway stations. Depending on the usage of the tracks it was still possible to build new double track lines with track centres of just 3.5 m (11 ft).
For the United States, with a standard maximum unbalanced superelevation of 75 mm (3 in), the formula is this: v m a x = E a + 3 0.00066 d {\displaystyle v_{max}={\sqrt {\frac {E_{a}+3}{0.00066d}}}} where E a {\displaystyle E_{a}} is the superelevation in inches, d {\displaystyle d} is the curvature of the track in degrees per 100 feet, and v m ...
1520 mm gauge: rails 1 and 3; 1435 mm gauge: rails 2 and 4. [g] 1524 / 1435 mm (5 ft 0 / 4 ft 8 1 / 2 in). A line comprising European standard gauge and "Russian" gauge, a legacy of the former satellite states of the Soviet Union. The 89 mm difference between the two gauges is too small to allow a three-rail configuration. [h]
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Where degree of curvature is based on 100 units of arc length, the conversion between degree of curvature and radius is Dr = 18000/π ≈ 5729.57795, where D is degree and r is radius. Since rail routes have very large radii, they are laid out in chords, as the difference to the arc is inconsequential; this made work easier before electronic ...