# Horseshoe curve

The horse shoe shape gives the curve its name.
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.

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 Måbødalen gorge, a complex system of horseshoe curves and tunnels on Norwegian National Road 7.
The Flåm Line, 1926 shortly after construction
Credit: Anders Beer Wilse
• 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.

### 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.