馬蹄彎

馬蹄彎是道路的一種爬行彎道，在拐點處翻轉兩次，最高可到達180度翻轉。

類似的彎道也可以在鐵路見到但常用於道路上. 因為其特色的U型彎道酷似馬蹄，故名為馬蹄彎。有些道路上的彎道，因為轉彎幅度過於狹小，故又有稱為髮夾彎的變種。

## 原理

馬蹄彎是一種以加長上升或下降坡度，從而減少路線最大坡度的方法。坡度定義為上升距離除予長度或距離，原則上類似的彎道增加長度時，為保持坡度一樣，同樣的上升距離（海拔）也會隨之添加。就像展線環繞山丘或爬升越過環繞的山峰那樣。

如果一段兩點之間的路途因太陡而難以爬升，迂迴的線路會讓距離增加，使兩地水平面可以以長一點的軌道（或道路）達到平衡。馬蹄彎不像螺旋，它並不包括跨越它自己的軌道，且一個完整的馬蹄彎包括兩條相對的直線線段。

curve 拐點 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

- The Dovre Line, the main line of the Norwegian railway network, has a horseshoe within Grønbogen tunnel from 杜姆奧斯 at the steep hills to the Dovre plateau, 標準鐵軌, 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
- 泰恩河畔紐卡斯爾 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 德國 has a horseshoe curve in Neviges, 費爾貝特 on the route between 埃森 and 伍珀塔爾, 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 茲沃倫 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.

### 北美洲

- The first ever, and most famous is the four tracks built by the 賓夕法尼亞鐵路 (PRR), the 蹄鐵曲線 that starts its climb along Kittanning Run, Pennsylvania due west of 阿爾圖納, 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 加利福尼亞州海岸山脈 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 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).
- The Cantara Loops between 鄧斯繆爾 and 芒特沙斯塔. Map
- East of Oakridge, Oregon on the Cascade Line.
- Notch Hill, on 加拿大太平洋鐵路's Shuswap Sub near 薩蒙阿姆, 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)

### 亞洲

- 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).
- 中國的南昆鐵路 , inside 宜良縣, 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.