A horseshoe curve is a class of climbing curve in a roadbed that reverses turn direction (inflection) twice on either side of a single tight curve that varies through an angle of about 180 degrees or more.
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Such curves are more commonly found in a railway line but are also used in roads. The characteristic U shape, or even slight balloon shape, of such a curve resembles a horseshoe. On roadways, particularly tight versions of such curves are typically called hairpin turns.
A horseshoe curve is a means to lengthen an ascending or descending grade and thereby reduce the maximum gradient. Grade or gradient is defined as the rise divided by the run (length) or distance, so in principle such curves add to length for the same altitude gain, just as would a climbing spiral around one or more peaks, or a climbing traverse (cutting) wrapping around an end of a ridge.
If the straight route between two points is too steep to climb, a more circuitous route will increase the distance traveled, allowing the difference in altitude to be averaged over a longer track (or road) length. Unlike a spiral, a horseshoe curve does not involve the track crossing over itself, and the full horseshoe involves both relatively straight sections, curve deflections in both directions and tightly curved segment; while a spiral generally has a more uniform curvature. Obviously, a horseshoe also gives rise to a severe change in direction requiring another corrective curve to regain displacement in the overall direction of travel, while a spiral generally does not.
A horseshoe curve is sometimes used where the route bridges a deep gully. Deviating from a straight-line route along the edge of the gully may allow it to be crossed at a better location.
Horseshoe curves are common on railway lines in steeply graded or hilly country, where means must be found to achieve acceptable grades and minimize construction costs. As with spirals, the main limitation in laying out a horseshoe is keeping its radius as large as possible, as sharp curves limit train speed, and through increased friction, are harder on rails, requiring more frequent replacement of outer tracks.
Map of Storegjeltunnelen and Dalbergtunnelen in Måbødalen gorge, a complex system of horseshoe curves, tunnels and loops on Norwegian National Road 7.The Flåm Line, 1926 shortly after construction Credit: Anders Beer Wilse
The Dovre Line, the main line of the Norwegian railway network, has a horseshoe within Grønbogen tunnel from Dombås at the steep hills to the Dovre plateau, standard gauge, single track.[1]
The Flåm Line, Norway, has a double horseshoe, one inside a tunnel, one in the open, few kilometres below top station, standard gauge, single track.
The Rauma Line, Norway, has a double horseshoe through the steep and narrow valley at Verma, one inside a tunnel and one that includes the Kylling Bridge, standard gauge, single track.
Poland
Grybów, Poland has a horseshoe curve 2,5km west of the town.
Kalisz, Poland has a double horseshoe curve leading the tracks from a flat plateau down to the valley of the Prosna river.
In Slovakia there is a significant number of horseshoe curves on the Banská Bystrica to Turčianske Teplice railway track and on the railway from Zvolen to Turčianske Teplice. More than 20 tunnels and couple of horseshoe curves were built to overcome rough terrain and elevation differences.
United Kingdom
Newcastle Quayside branch, a goods-only railway from the main line to the river quayside, through a steeply descending horseshoe tunnel.
The horseshoe curve on the West Highland Line in Scotland between Upper Tyndrum and Bridge of Orchy was built because the engineers of the railway couldn't afford to build a viaduct crossing the remote valley.
Mance Curve, between Meyersdale and Hyndman, Pennsylvania, along Sand Patch Grade. Long operated by the Baltimore & Ohio Railroad, it is today part of CSX Transportation's Keystone Subdivision) used by freight trains and Amtrak's Capitol Limited (Chicago-Washington, D.C.) passenger train
In the Loop District of the Alaska Railroad between mileposts 48 and 51 northeast of Seward, Alaska, there was a horseshoe and a spiral, both on an extensive range of timber trestles up to 106 feet high. In 1951, a new route removed the original horseshoe, the spiral and all the trestles but added a new horseshoe at milepost 48.[2]
Also on the Trans-Iranian in the Zagros Mountains, a pair of tightly linked horseshoes forms a "figure of 8" in which one loop almost completely contains the small city of Sepiddasht, Lorestan. The other loop is almost entirely within a tunnel, with both its portals nearly side-by-side but several meters different in elevation. Both loops rotate about 250 degrees each.
The Cougal Spiral is a feature of the North Coast Railway in Australia that connects New South Wales with Queensland through Richmond Gap. The railway line climbs at a steady ruling gradient from Kyogle to the summit at a tunnel at the border between the two states.
Avslutningsrapport for Dovrebanen: avgit til Den kgl. norske regjerings departement for de offentlige arbeider. Oslo: Baneforlaget. 1926 (original), 2000 (reprint). ISBN82-91448-35-3.
Crump, Spencer (1998). Redwoods, Iron Horses, and the Pacific (Fifthed.). Fort Bragg, California: California Western Railroad. p.60. ISBN0-918376-12-2.
Ormes, R.M. Tracking Ghost Railroads in Colorado, Century One Press 1975 (Contains extensive local maps identifying railroad names and dates of service).
"铁影 – 宏伟壮丽的展线群——成昆铁路运转记其四"[Iron Shadow – The magnificent railway line group - the fourth chapter of the operation of Chengdu-Kunming Railway] (in Chinese). 2017-07-17. Retrieved 2024-08-08.
