马蹄弯

马蹄弯是道路的一种爬行弯道，在拐点处翻转两次，最高可到达180度翻转。

类似的弯道也可以在铁路见到但常用于道路上. 因为其特色的U型弯道酷似马蹄，故名为马蹄弯。有些道路上的弯道，因为转弯幅度过于狭小，故又有称为发夹弯的变种。

## 原理

马蹄弯是一种以加长上升或下降坡度，从而减少路线最大坡度的方法。坡度定义为上升距离除予长度或距离，原则上类似的弯道增加长度时，为保持坡度一样，同样的上升距离（海拔）也会随之添加。就像展线环绕山丘或爬升越过环绕的山峰那样。

如果一段两点之间的路途因太陡而难以爬升，迂回的线路会让距离增加，使两地水平面可以以长一点的轨道（或道路）达到平衡。马蹄弯不像螺旋，它并不包括跨越它自己的轨道，且一个完整的马蹄弯包括两条相对的直线线段。

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

### 欧洲

<image>

<image>

- 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, 标准铁轨, single track.
- 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 普罗斯纳河。
- Between 耶莱尼亚古拉 and 什克拉尔斯卡-波伦巴 in Poland there is a five-times, elongated horseshoe curve (50°51′19"N, 15°34′17"E). Map
- 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 莱茵-鲁尔城市快铁 in 德国 has a horseshoe curve in Neviges, 费尔贝特 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 苏格兰 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 图尔钱斯凯特普利采 railway track and on the railway from 兹沃伦 to 图尔钱斯凯特普利采. More than 20 tunnels and couple of horseshoe curves were built to overcome rough terrain and elevation differences.

### 北美洲

- The first ever, and most famous is the four tracks built by the 宾夕法尼亚铁路 (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
- 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)
- 66° curve; Moro Castle, Colorado; Uintah Railway; 3英尺（914毫米） gauge (abandoned)
- Balloon Loop; Columbine, Colorado; Uintah Railway; 3英尺（914毫米） gauge (abandoned)
- Hairpin Curve and Muleshoe Curve; McAndrews, Colorado; Uintah Railway; 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 圣路易斯-奥比斯保 to Cuesta Pass, a route owned by the 联合太平洋铁路 and used by Amtrak's 海岸星光号 (Los Angeles, CA to Seattle, WA).
- The Cantara Loops between 邓斯缪尔 and 芒特沙斯塔. Map
- East of Oakridge, Oregon on the Cascade Line.
- Notch Hill, on 加拿大太平洋铁路'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运输'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 坎伯兰 and 弗罗斯特堡, Maryland, at Cash Valley Road; former 西马里兰铁路 Connellsville Extension, now the 西马里兰观光铁路.
- Swain, New York; Pittsburg, Shawmut, & Northern Railroad (abandoned)
- Richburg, New York; Pittsburg, Shawmut, & Northern Railroad (abandoned)

### 亚洲

- 日本东日本旅客铁道的釜石线在上有住站至陆中大桥站之间有 horseshoe curve ("down" on the elevation and registration of direction of the line).
- 中国的南昆铁路 , inside 宜良县, located in the east of Yiliang Town.

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.

### 澳洲

- 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.