curve 拐点 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.
例子
歐洲
Map of Storegjeltunnelen and Dalbergtunnelen in Måbødalen gorge, a complex system of horseshoe curves and tunnels on Norwegian National Road 7.The Flåm Line, 1926 shortly after construction 来源：Anders Beer Wilse
The Dovre Line, the main line of the Norwegian railway network, has a horseshoe within Grønbogen tunnel from 杜姆奥斯 at the steep hills to the Dovre plateau, 標準鐵軌, 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.
格雷布夫, Poland has a horseshoe curve 2,5 km west of the town.
卡利什, Poland has a double horseshoe curve leading the tracks from a flat plateau down to the valley of the 普羅斯納河。
Between 耶萊尼亞古拉 and 什克拉爾斯卡-波倫巴 in Poland there is a five-times, elongated horseshoe curve (50°51′19"N, 15°34′17"E). Map （页面存档备份，存于互联网档案馆）
泰恩河畔纽卡斯尔 branch, a goods-only railway from the main line to the river quayside, through a steeply descending horseshoe tunnel.
The 萊茵-魯爾城市快鐵 in 德国 has a horseshoe curve in Neviges, 費爾貝特 on the route between 埃森 and 伍珀塔尔, known as the Prince William railway.
The horseshoe curve on the West Highland Line in 蘇格蘭 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 斯洛伐克 there is a significant number of horseshoe curves on the 班斯卡-比斯特里察 to 圖爾錢斯凱特普利采 railway track and on the railway from 兹沃伦 to 圖爾錢斯凱特普利采. More than 20 tunnels and couple of horseshoe curves were built to overcome rough terrain and elevation differences.
The first ever, and most famous is the four tracks built by the 賓夕法尼亞鐵路 (PRR), the 蹄铁曲线 that starts its climb along Kittanning Run, Pennsylvania due west of 阿尔图纳, and crosses two runs and three mountain faces using three gaps of the Allegheny.
Stanford Curve; Truckee, California; Union Pacific Railroad (originally Central Pacific Railroad, and then Southern Pacific Railroad).
Five curves on the California Western Railroad climbing the 加利福尼亚州海岸山脉 east of 布拉格堡[2]
Ophir Loop; Ophir, Colorado; Rio Grande Southern Railroad – 3英尺（914毫米） gauge (abandoned)
Coxo Curve; Cumbres, Colorado; Denver and Rio Grande Western Railway; 3英尺（914毫米） gauge
Tanglefoot Curve; Cumbres, Colorado; Denver and Rio Grande Western Railway; 3英尺（914毫米） gauge
Los Pinos Curve; Los Pinos, Colorado; Denver and Rio Grande Western Railway; 3英尺（914毫米） gauge
Phantom Curve; Sublette, Colorado; Denver and Rio Grande Western Railway; 3英尺（914毫米） gauge
Whiplash Curve; Big Horn, Colorado; Denver and Rio Grande Western Railway; 3英尺（914毫米） gauge
Lava Loop; Lava, Colorado; Denver and Rio Grande Western Railway; 3英尺（914毫米） gauge
Altura Curve; Altura, Colorado; Rio Grande, Pagosa and Northern; 3英尺（914毫米） gauge (abandoned)
Coles Curve; Coles, Pennsylvania; East Broad Top Railroad;– 3英尺（914毫米） gauge (out of service)
Foss Creek, between Skykomish, Washington and the Cascade Tunnel.
Muleshoe Curve, near Duncansville, Pennsylvania; Pennsylvania Railroad.
Chorro, California on the grade from 聖路易斯-奧比斯保 to Cuesta Pass, a route owned by the 聯合太平洋鐵路 and used by Amtrak's 海岸星光號 (Los Angeles, CA to Seattle, WA).
Notch Hill, on 加拿大太平洋鐵路's Shuswap Sub near 萨蒙阿姆, British Columbia.
"Mance Curve," between Meyersdale & Hyndman, PA along Sand Patch Grade (a section of track that's part of CSX運輸's Keystone Subdivision) which is used both by freight trains and Amtrak's 首都特快 (Chicago, IL-Washington, DC)
Helmstetter's Curve; Corriganville, Maryland, between 坎伯蘭 and 弗羅斯特堡, Maryland, at Cash Valley Road; former 西馬里蘭鐵路 Connellsville Extension, now the 西馬里蘭觀光鐵路.
Swain, New York; Pittsburg, Shawmut, & Northern Railroad (abandoned)
Richburg, New York; Pittsburg, Shawmut, & Northern Railroad (abandoned)
日本東日本旅客鐵道的釜石線在上有住站至陸中大橋站之間有 horseshoe curve ("down" on the elevation and registration of direction of the line).
中國的南昆铁路 , inside 宜良县, located in the east of Yiliang Town.[1]
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 lines needs to climb at a steady ruling gradient from Kyogle to the summit at a tunnel at the border between the two states. The border is also at the watershed. The line is single tracked.
^Avslutningsrapport for Dovrebanen: avgit til Den kgl. norske regjerings departement for de offentlige arbeider. Oslo: Baneforlaget. 1926 (original), 2000 (reprint). ISBN8291448353.
