Curve resistance

In railroad engineering, curve resistance is a part of train resistance, namely the additional rolling resistance a train must overcome when travelling on a curved section of track. Curve resistance is typically measured in per mille, with the correct physical unit being Newton per kilo-Newton or N/kN. Older texts still use the wrong unit of kilogram-force per tonne or kgf/t, which mixes an (outdated) unit of force and a unit of mass. Sometimes also kg/t was used, which confused the resisting force with a mass.

Curve resistance depends on various factors, the most important being the radius and the superelevation of a curve. Since curves are usually banked by superelevation, there will exist some speed at which there will be no sideways force on the train and where therefore curve resistance is minimum. At higher or lower speeds, curve resistance may be a few (or several) times greater.

Formulas typically used in railway engineering in general compute the resistance as inversely proportional to the radius of curvature (thus, they neglect the fact that the resistance is dependent on both speed and superelevation). For example, in the USSR, the standard formula is Wr (curve resistance in parts per thousand or kgf/tonne) = 700/R where R is the radius of the curve in meters. Other countries often use the same formula, but with a different numerator-constant. For example, the US used 446/R, Italy 800/R, England 600/R, China 573/R, etc. In Germany, Austria, Switzerland, Czechoslovakia, Hungary, and Romania the term R - b is used in the denominator (instead of just R), where b is some constant. Typically, the expressions used are "Röckl's formula", which uses 650/(R - 55) for R above 300 meters, and 500/(R - 30) for smaller radii. The fact that, at 300 meters, the two values of Röckl's formula differ by more than 30% shows that these formulas are rough estimates at best.

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