Horseshoe curve

A horseshoe curve is a class of climbing curve in a roadbed which reverses turn direction (inflection) twice on either side of a single tight curve that varies through an angle of about 180 degrees or more.

For other uses, see Horseshoe Curve (disambiguation).
See also: Hairpin turn
A road switchbacks into a canyon in Utah's Canyonlands National Park.
Aerial shot of the Horseshoe Curve that helps trains cross the Allegheny Mountains west of Altoona, Pennsylvania.

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.

Theory

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.

Examples

Germany

Norway
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

Slovakia

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.

United States

Pennsylvania

Alaska

  • 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. Track relocation in 1951 removed the original horseshoe, the spiral and all the trestles but added a new horseshoe at milepost 48.[2]

California

Colorado

Horseshoe curves were used extensively on the many narrow gauge railroads in the Colorado Rocky Mountains, now mostly abandoned,[4] for example:

  • On the Cumbres and Toltec Scenic Railroad (formerly D&RGW); 3 ft (914 mm) gauge:
    • Coxo Curve; Cumbres, Colorado
    • Tanglefoot Curve; Cumbres, Colorado
    • Los Pinos Curve; Los Pinos, Colorado
    • Phantom Curve; Sublette, New Mexico
    • Whiplash Curve; Big Horn, Colorado
    • Lava Loop; Lava, Colorado
  • Ophir Loop; Ophir, Colorado; Rio Grande Southern Railroad – 3 ft (914 mm) gauge (abandoned)
  • Altura Curve; Altura, Colorado; Rio Grande, Pagosa and Northern; 3 ft (914 mm) gauge (abandoned)
  • On the Uintah Railway; 3 ft (914 mm) gauge (abandoned):[5]
    • 66° curve; Moro Castle, Colorado;
    • Balloon Loop; Columbine, Colorado
    • Hairpin Curve and Muleshoe Curve; McAndrews, Colorado

Idaho

Maryland

Montana

Nevada

  • Arnold Loop; on the eastern approach to Silver Zone Pass in the Toano Range in eastern Nevada; Union Pacific (formerly Western Pacific).

New York

  • Swain, New York; Pittsburg, Shawmut, & Northern Railroad (abandoned)
  • Richburg, New York; Pittsburg, Shawmut, & Northern Railroad (abandoned)

Oregon

Utah

Washington

Canada

British Columbia

  • Notch Hill, on CP's Shuswap Sub near Salmon Arm, British Columbia.

China

Jiangsu

Shaanxi

  • Baoji-Chengdu Railway
    • Guanyin hill Curve, on Baoji-Chengdu Railway in China, a double horseshoe and a buttrtfly curve, south of Weibin District, at 34°16′00″N 107°00′35″E
    • Majia Dam Curve.[6]

Sichuan

  • Chengdu–Kunming Railway
    • Naituo Curve, aishiyan Station.
    • Lewu Curve.
    • Handulu-lianghekou Curve.
    • Liudu River Curve.
    • Liugou Curve.

Xinjiang

Yunnan

Gansu

Qinghai

  • Guanjiao Curve Group, Qinghai–Tibet Railway
    • Erlang Curve.
    • Erlang North Curve.
    • Nanshan Curve.
    • Luobei Curve.
    • Luobei South Curve.

Iran

Japan

Australia

New Zealand
  • The Raurimu Spiral in New Zealand has a horseshoe curve as the first part of the climb.
  • The U-bend south of Maddingly, Victoria takes a large detour to descend 100m.
  • Turangarere, New Zealand North Island Main Trunk line near Hīhītahi.

References
  1. Avslutningsrapport for Dovrebanen: avgit til Den kgl. norske regjerings departement for de offentlige arbeider. Oslo: Baneforlaget. 1926 (original), 2000 (reprint). ISBN 8291448353.
  2. Prince, B.D. The Alaska Railroad in Pictures 1914-1964, Ken Wray's Print Shop, Anchorage, 1964
  3. Crump, Spencer (1998). Redwoods, Iron Horses, and the Pacific (Fifth ed.). Fort Bragg, California: California Western Railroad. p. 60. ISBN 0-918376-12-2.
  4. Ormes, R.M. Tracking Ghost Railroads in Colorado, Century One Press 1975 (Contains extensive local maps identifying railroad names and dates of service).
  5. Bender, Henry E, Jr. (1970). Uintah Railway: The Gilsonite Route. Berkeley, California: Howell-North Books. p. 42. ISBN 0-8310-7080-3.{{cite book}}: CS1 maint: multiple names: authors list (link)
  6. "404,您访问的页面已经不存在!". www.sohu.com. Retrieved 2021-07-21. {{cite web}}: Cite uses generic title (help)
  7. John Brian Hollingsworth (1982). Atlas of the world's railways. Bison.
  8. Hugh Hughes (1981). Middle East railways. Continental Railway Circle.
  • Clark, Ken (2016). Pittsburg, Shawmut, & Northern Railroad. Arcadia Publishing. pp. 20, 37. ISBN 978-1-4671-1726-5.
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