# Horseshoe curve

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Horse shoe shaped switch backs going down into a canyon at Canyonlands National Park in Utah..
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

• 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.
• Grybów, Poland has a horseshoe curve 2,5 km 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.
• Between Jelenia Góra and Szklarska Poręba in Poland there is a five-times, elongated horseshoe curve (50°51′19"N, 15°34′17"E). Map
• Newcastle Quayside branch, a goods-only railway from the main line to the river quayside, through a steeply descending horseshoe tunnel.
• The Rhein-Ruhr S-Bahn in Germany has a horseshoe curve in Neviges, Velbert on the route between Essen and Wuppertal, known as the Prince William railway.
• 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.
• 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.

### North America

#### United States

Pennsylvania

• 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

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:
• Los Pinos Curve; Los Pinos, Colorado
• Phantom Curve; Sublette, New Mexico
• Whiplash Curve; Big Horn, 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;
• Hairpin Curve and Muleshoe Curve; McAndrews, Colorado

Idaho

Maryland

Montana

• 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

British Columbia

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

### Australasia

• 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.
• Picton railway station, New South Wales, turns back on itself at about 225 degrees.
• 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 Hihitahi.

## Related Research Articles

The Denver & Rio Grande Western Railroad, often shortened to Rio Grande, D&RG or D&RGW, formerly the Denver & Rio Grande Railroad, was an American Class I railroad company. The railroad started as a 3 ft narrow-gauge line running south from Denver, Colorado in 1870. It served mainly as a transcontinental bridge line between Denver, and Salt Lake City, Utah. The Rio Grande was also a major origin of coal and mineral traffic.

A mountain railway is a railway that operates in a mountainous region. It may operate through the mountains by following mountain valleys and tunneling beneath mountain passes, or it may climb a mountain to provide transport to and from the summit.

The Big Hill on the Canadian Pacific Railway main line in British Columbia, Canada, was the most difficult piece of railway track on the Canadian Pacific Railway's route. It was situated in the rugged Canadian Rockies west of the Continental Divide of the Americas and Kicking Horse Pass. Even though the Big Hill was replaced by the Spiral Tunnels in 1909, the area has long been a challenge to the operation of trains and remains so to this day.

A spiral is a technique employed by railways to ascend steep hills.

A double-track railway usually involves running one track in each direction, compared to a single-track railway where trains in both directions share the same track.

The Georgetown Loop Railroad is a 3 ft narrow gauge United States heritage railroad located in the Rocky Mountains in Clear Creek County, adjacent to Interstate 70 in Colorado.

The Pittsburg and Shawmut Railroad, also known as the Shawmut Line, was a short line railroad company operating passenger and freight service on standard gauge track in central and southwestern Pennsylvania. Since 2004, it has been operated as part of the Buffalo and Pittsburgh Railroad, which is owned by Genesee & Wyoming Inc.

The Pittsburg, Shawmut & Northern Railroad also known as the Shawmut Line, was a Class I railroad company operating passenger and freight service on standard gauge track in central Pennsylvania and western New York. The line was financially troubled for its entire life span and declared bankruptcy after just six years of operation. It would spend the remaining 42 year of its existence in receivership or trusteeship, one of the longest bankruptcy proceedings in American railroading history.

The Cumbres & Toltec Scenic Railroad, often abbreviated as the C&TSRR, is a 3 ft narrow-gauge heritage railroad running for 64 miles (103 km) of track between Antonito, Colorado and Chama, New Mexico, United States. The railroad gets its name from two geographical features along the route, the 10,015-foot (3,053 m)-high Cumbres Pass and the Toltec Gorge. Originally part of the Denver and Rio Grande Western Railroad's narrow-gauge network, the line has been jointly owned by the states of Colorado and New Mexico since 1970.

The Roaring Camp & Big Trees Narrow Gauge Railroad is a 3 ft narrow-gauge tourist railroad in California that starts from the Roaring Camp depot in Felton, California and runs up steep grades through redwood forests to the top of nearby Bear Mountain, a distance of 3.25 miles (5.23 km).

The Uintah Railway was a small 3 ft narrow gauge railroad company in Utah and Colorado in the United States. It was constructed to carry Gilsonite which provided most of its operating revenues; but it operated as a common carrier from 1904 to 1939, also carrying passengers, mail, express, and other cargoes including sheep and wool. When a public library was built in Dragon in 1910, the Uintah Railway agreed to deliver library books free of charge to and from any borrower along its route. Many area ranchers and miners took advantage of the opportunity.

The Sacramento Northern Railway was an 183-mile (295 km) electric interurban railway that connected Chico in northern California with Oakland via the California capital, Sacramento. In its operation it ran directly on the streets of Oakland, Sacramento, Yuba City, Chico, and Woodland and ran passenger service until 1941 and freight service into the 1960s.

The South Pacific Coast Railroad (SPC) was a 3 ft narrow gauge steam railroad running between Santa Cruz, California and Alameda, with a ferry connection in Alameda to San Francisco. The railroad was created as the Santa Clara Valley Railroad, founded by local strawberry growers as a way to get their crops to market in San Francisco and provide an alternative to the Southern Pacific Railroad. In 1876, James Graham Fair, a Comstock Lode silver baron, bought the line and extended it into the Santa Cruz Mountains to capture the significant lumber traffic coming out of the redwood forests. The narrow-gauge line was originally laid with 52-pound-per-yard (26 kg/m) rail on 8-foot (2.44 m) redwood ties; and was later acquired by the Southern Pacific and converted to 4 ft 8 12 instandard gauge.

The Colorado and Southern Railway was an American Class I railroad in the western United States that operated independently from 1898 to 1908, then as part of the Chicago, Burlington and Quincy Railroad until it was absorbed into the Burlington Northern Railroad in 1981.

Standard gauge was favored for railway construction in the United States, although a fairly large narrow-gauge system developed in the Rocky Mountains of Colorado and Utah. Isolated narrow-gauge lines were built in many areas to minimize construction costs for industrial transport or resort access, and some of these lines offered common carrier service. Outside Colorado, these isolated lines evolved into regional narrow-gauge systems in Maine, New York, Pennsylvania, Ohio, Iowa, Hawaii, and Alaska.

The Utah Division of the former Denver & Rio Grande Western Railroad (D&RGW) is a rail line that connects Grand Junction, Colorado and Salt Lake City, Utah in the Western United States. It is now incorporated into the Union Pacific Railroad (UP) system as its Green River and Provo Subdivisions, forming a portion of the Denver-Nevada Central Corridor. Daily passenger service is provided by Amtrak's California Zephyr, and the BNSF Railway and Utah Railway have trackage rights over the line.

The Central Corridor is a rail line operated by the Union Pacific Railroad from near Winnemucca, Nevada to Denver, Colorado in the western United States. The line was created after the merger with the Southern Pacific Transportation Company by combining portions of lines built by former competitors. No portion of the line was originally built by the Union Pacific; in fact, some portions were built specifically to compete with the Union Pacific's Overland Route. The line is known for significant feats of engineering while crossing the Wasatch Mountains of Utah and the Rocky Mountains of Colorado. The line features numerous tunnels, the longest and highest of these is the Moffat Tunnel.

The Pittsburgh Line is a rail line that is located in state of the Pennsylvania and it is owned and operated by the Norfolk Southern Railway. The Pittsburgh Line is Norfolk Southern Railway's primary east–west artery in its Pittsburgh Division and Harrisburg Division across Pennsylvania and it is part of the Amtrak-Norfolk Southern combined rail corridor, the Keystone Corridor.

The Alamosa–Durango line or San Juan extension was a railroad line built by the Denver and Rio Grande Western Railroad, following the border between the U.S. states of Colorado and New Mexico, in the Rocky Mountains. The line was originally built as a 3 ft narrow-gauge line between Alamosa, Colorado, and Durango, Colorado. Portions of the route survive to this day: the now standard-gauged segment from Alamosa to Antonito, Colorado, and a narrow-gauge portion from Antonito to Chama, New Mexico.

## 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.
• Clark, Ken (2016). Pittsburg, Shawmut, & Northern Railroad. arcadia publishing. pp. 20, 37. ISBN   978-1-4671-1726-5.