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.
The first proper railway was the Liverpool and Manchester Railway, which opened in 1830. Like the tram roads that had preceded it over a hundred years, the L&M had gentle curves and gradients. Reasons for these gentle curves include the lack of strength of the track, which might have overturned if the curves were too sharp causing derailments. The gentler the curves, the greater the visibility, thus boosting safety via increased situational awareness. The earliest were made in short lengths of wrought iron, which does not bend like later steel rails introduced in the 1850s.
Minimum curve radii for railways are governed by the speed operated and by the mechanical ability of the rolling stock to adjust to the curvature. In North America, equipment for unlimited interchange between railway companies is built to accommodate for a radius, but normally a radius is used as a minimum, as some freight carriages (freight cars) are handled by special agreement between railways that cannot take the sharper curvature. For the handling of long freight trains, a minimum radius is preferred.
The sharpest curves tend to be on the narrowest of narrow gauge railways, where almost all the equipment is proportionately smaller. But standard gauge can also have tight curves, if rolling stocks are built for it, which however removes the standardisation benefit of standard gauge. Tramways can have below curve radius.
As the need for more powerful steam locomotives grew, the need for more driving wheels on a longer, fixed wheelbase grew too.
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Gauge conversion is the changing of one railway track gauge (the distance between the running rails) to another. If tracks are converted to a narrower gauge, the existing sleepers (ties) may be used. However, replacement is required if the conversion is to a wider gauge. Some sleepers may be long enough to accommodate the fittings of both existing and alternative gauges. Wooden sleepers are suitable for conversion because they can be drilled for the repositioned rail spikes.
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.
In differential geometry, the radius of curvature (Rc), R, is the reciprocal of the curvature. For a curve, it equals the radius of the circular arc which best approximates the curve at that point. For surfaces, the radius of curvature is the radius of a circle that best fits a normal section or combinations thereof. In the case of a space curve, the radius of curvature is the length of the curvature vector. In the case of a plane curve, then R is the absolute value of where s is the arc length from a fixed point on the curve, φ is the tangential angle and κ is the curvature.
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