Horseshoe curve

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Switchback in Utah.jpg
Horse shoe shaped switch backs going down into a canyon at Canyonlands National Park in Utah..
Usgs photo horseshoe bend pennsylvania.jpg
Aerial shot of the Horseshoe Curve (Pennsylvania) sitting above and framing the upper impoundment of the Kittanning Reservoir, the second larger part of the reservoir is visible to the far right in the picture.

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.

Contents

Such curves are more commonly found in a railway line of travel but are also used in roads. The characteristic U shape, or even slight balloon shape, of such a curve resembles a horseshoe, hence the name. On roadways such curves, if the hard curve is tight enough, 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 would be 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

Europe

Map of Storegjeltunnelen and Dalbergtunnelen in Mabodalen gorge, a complex system of horseshoe curves and tunnels on Norwegian National Road 7. Storegjeltunnelen OSM.JPG
Map of Storegjeltunnelen and Dalbergtunnelen in Måbødalen gorge, a complex system of horseshoe curves and tunnels on Norwegian National Road 7.
The Flam Line, 1926 shortly after construction
Credit: Anders Beer Wilse Vatnahalsen-Reinunga Wilse 1939.jpg
The Flåm Line, 1926 shortly after construction
Credit: Anders Beer Wilse

North America

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.

Asia

Australasia

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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.
  6. John Brian Hollingsworth (1982). Atlas of the world's railways. Bison.
  7. Hugh Hughes (1981). Middle East railways. Continental Railway Circle.