Minimum railway curve radius - AbsoluteAstronomy.com

The minimum railway curve radius, the shortest design radius, has an important bearing on constructions costs and operating costs and, in combination with superelevation (difference in elevation of the two rails) in the case of train tracks, determines the maximum safe speed of a curve. Superelevation is not a factor on tramway track

Tramway track

Tramway track is used on tramways or light rail operations. Grooved rails are often used in order to make street running feasible...

s. Minimum radius of curve is one parameter in the design of railway vehicles

Railroad car

A railroad car or railway vehicle , also known as a bogie in Indian English, is a vehicle on a rail transport system that is used for the carrying of cargo or passengers. Cars can be coupled together into a train and hauled by one or more locomotives...

as well as tram

Tram

A tram is a passenger rail vehicle which runs on tracks along public urban streets and also sometimes on separate rights of way. It may also run between cities and/or towns , and/or partially grade separated even in the cities...

s .

History

The first proper railway was the Liverpool and Manchester Railway

Liverpool and Manchester Railway

The Liverpool and Manchester Railway was the world's first inter-city passenger railway in which all the trains were timetabled and were hauled for most of the distance solely by steam locomotives. The line opened on 15 September 1830 and ran between the cities of Liverpool and Manchester in North...

which opened in 1830. Like the trams that had preceded it over a hundred years, the L&M had gentle curves and gradients. Amongst other reasons for the gentle curves were the lack of strength of the track, which might have overturned if the curves were too sharp causing derailments. There was no signalling at this time, so drivers had to be able to see ahead to avoid collisions with previous trains. The gentler the curves, the longer the visibility.

In the early days, there was no information to help determine how sharp and steep lines could be, but over time curves did get sharper and gradients steeper.

Minimum radius

The sharpest curves tend to be on the narrowest of narrow gauge railways, where almost everything is proportionately smaller.
7000 m (22,966 ft) Typical China's high-speed railway network (350 km/h) 5500 m (18,045 ft) Typical China's high-speed railway network (250km/h~300km/h) 4000 m (13,123 ft) Typical high-speed railways (300 km/h) 3500 m (11,483 ft) Typical China's high-speed railway network (200~250km/h) 2000 m (6,562 ft) Typical high-speed railways (200 km/h)
Border Loop

Cougal Spiral (railway)

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...

- 240 m (787 ft) - 5000 LT (5,080.3 t; 5,600 ST) - 1500 m (4,921 ft)
Homebush triangle - 200 m (656 ft) - 5000 LT (5,080.3 t; 5,600 ST) - 1500 m (4,921 ft) Turkey

Transport in Turkey

-Railways:The TCDD - Türkiye Devlet Demir Yolları possess 10,984 km of gauge, of which 2,336 km are electrified . In 2004, Marmaray project started on a rail tunnel under the Bosphorus straits....

- 190 m (623 ft)
Zig Zag

Lithgow Zig Zag

The Lithgow Zig Zag was a zig zag railway built near Lithgow on the Great Western Railway of New South Wales in Australia which operated between 1870 and 1910, to overcome an otherwise insurmountable climb up the western side of the Blue Mountains...

- 160 m (525 ft) - 40km/h Batlow, New South Wales - 100 m (328 ft) - 500 LT (508 t; 560 ST) - 300 m (984 ft) - restricted to NSW Z19 class

New South Wales Z19 class locomotive

The Z19 class is a class of steam locomotive built for and operated by the New South Wales Government Railways of Australia.- History :...

steam locomotives - 85 m (279 ft) - Windberg Railway (:de:Windbergbahn) (between Freital

Freital

Freital is the biggest town in the Sächsische Schweiz-Osterzgebirge district, in the Free State of Saxony, Germany. It is situated on the small river Weißeritz, 8 km southwest of Dresden.- Geography :...

-Birkigt and Dresden

Dresden

Dresden is the capital city of the Free State of Saxony in Germany. It is situated in a valley on the River Elbe, near the Czech border. The Dresden conurbation is part of the Saxon Triangle metropolitan area....

-Gittersee) - restrictions to wheelbase - 200 ft (61 m) - London Underground

London Underground

The London Underground is a rapid transit system serving a large part of Greater London and some parts of Buckinghamshire, Hertfordshire and Essex in England...

Central line

Central Line

The Central line is a London Underground line, coloured red on the tube map. It is a deep-level "tube" line, running east-west across London, and, at , has the greatest total length of track of any line on the Underground. Of the 49 stations served, 20 are below ground...

(between White City and Shepherd's Bush) Sydney steam trams hauling 3 trailers - 25 m (82 ft) Chicago 'L'

Chicago 'L'

The L is the rapid transit system serving the city of Chicago and some of its surrounding suburbs. It is operated by the Chicago Transit Authority...

- 90 ft (27.43 m) Matadi-Kinshasa Railway

Matadi-Kinshasa Railway

The Matadi-Kinshasa Railway is a railway line in Bas-Congo Province between the port of Matadi and Kinshasa, the capital of Democratic Republic of the Congo.The Matadi-Kinshasa Railway was built from 1890 to 1898...

- 273 yd (819 ft; 250 m) - deviated line. Queensland Railways - 60 m (197 ft) Taunton Tramway

Taunton Tramway

The Taunton Tramway was an electric street tramway in Taunton, the county town of Somerset, England. It operated a fleet of six narrow gauge tramcars on a single route of between 1901 and 1921 when the tramway closed due to a dispute over the cost of electricity.-History:The Taunton and West...

- 35 ft (10.67 m) Bernina Railway

Bernina Railway

The Bernina Railway is a single track metre gauge railway line forming part of the Rhaetian Railway . It links the spa resort of St. Moritz, in the Canton of Graubünden, Switzerland, with the town of Tirano, in the Province of Sondrio, Italy, via the Bernina Pass...

- 45 m (148 ft) Matadi-Kinshasa Railway

Matadi-Kinshasa Railway

- 55 yd (165 ft; 50 m) - original line. Victorian Narrow Gauge

Narrow gauge lines of the Victorian Railways

The former Victorian Railways, the state railway authority in Victoria, Australia built a number of experimental narrow gauge railway lines around the beginning of the 20th century. Although all were closed by the early 1960s, parts of two have been reopened as heritage railways.- Background :A...

- 40 m (131 ft) 16 km/h (10 mph) on curves ; (32 km/h (20 mph) on straight ) Kalka-Shimla Railway

Kalka-Shimla Railway

The Kalka–Shimla Railway is a narrow gauge railway in North-West India travelling along a mostly mountainous route from Kalka to Shimla. It is known for breathtaking views of the hills and surrounding villages.- History :...

- 37.47 m (122.9 ft) or 48 degrees Darjeeling Himalayan Railway

Darjeeling Himalayan Railway

The Darjeeling Himalayan Railway, nicknamed the "Toy Train", is a narrow gauge railway from New Jalpaiguri to Darjeeling in West Bengal, run by the Indian Railways....

- 21.2 m (69.6 ft) Matheran Hill Railway

Matheran Hill Railway

Matheran Hill Railway is a heritage railway in Maharashtra, India. It was built between 1901 and 1907 by Abdul Hussein Adamjee Peerbhoy, financed by his father, Sir Adamjee Peerbhoy of the Adamjee Group at the cost of Rs.16,00,000...

- 18.25 m (59.9 ft); 1 in 20 (5%); (8 km/h (5 mph) on curve; 20 km/h (12 mph) on straight) Chicago Tunnel Company

Chicago Tunnel Company

The Chicago Tunnel Company built a narrow gauge railway freight tunnel network under the downtown of the city of Chicago. This was regulated by the Interstate Commerce Commission as an interurban despite the fact that it operated entirely under central Chicago, did not carry passengers, and was...

- 16 ft (4.9 m); 20 ft (6.1 m) in grand union

Grand union

A grand union is a rail track junction where two double-track railway lines cross at grade, often in a street intersection or crossroads. A total of sixteen railroad switches allow streetcars coming from any direction to take any of the three other directions...

s. Welsh Highland Railway

Welsh Highland Railway

The Welsh Highland Railway is a long restored narrow gauge heritage railway in North Wales, operating from Caernarfon to Porthmadog, and passing through a number of popular tourist destinations including Beddgelert and the Aberglaslyn Pass. At Porthmadog it connects with the Ffestiniog Railway...

- 50 m (164 ft) Welsh Highland Railway

Welsh Highland Railway

- 40 m (131 ft) on original line at Beddgelert

Beddgelert

Beddgelert, or in older English spelling often Bedgellert, is a village and community in the Snowdonia area of Gwynedd, Wales. It is reputed to be named after the legendary hound Gelert. Population 617.- History:...

Steam locomotives

As the need for more powerful (steam) locomotives grew, the need for more driving wheels on a longer, fixed wheelbase grew too. But long wheel bases are unfriendly to sharp curves. Various type of articulated locomotive

Articulated locomotive

Articulated locomotive usually means a steam locomotive with one or more engine units which can move independent of the main frame. This is done to allow a longer locomotive to negotiate tighter curves...

s Mallet

Mallet locomotive

The Mallet Locomotive is a type of articulated locomotive, invented by a Swiss engineer named Anatole Mallet ....

, Garratt, Shay

Shay locomotive

The Shay locomotive was the most widely used geared steam locomotive. The locomotives were built to the patents of Ephraim Shay, who has been credited with the popularization of the concept of a geared steam locomotive...

were devised to avoid having to operate multiple locomotives with multiple crews.

More recent diesel and electric locomotives do not have a wheelbase problem and can easily be operated in multiple with a single crew.

Transition curves

A curve should not become a straight all at once, but should gradually increase in radius over a transition

Track transition curve

A track transition curve, or spiral easement, is a mathematically calculated curve on a section of highway, or railroad track, where a straight section changes into a curve. It is designed to prevent sudden changes in centripetal force...

length of say 40 m - 80 m. Even worse than curves with no transition are reverse curves

Reverse curve

In civil engineering, a reverse curve is a section of the horizontal alignment of a highway or railroad route in which a curve to the left or right is followed immediately by a curve in the opposite direction....

with no intervening straight.

The super-elevation (aka cant

Cant (road/rail)

The cant of a railway track or a road is the difference in elevation between the two edges...

) must also be transitioned.

Example Garratt

gauge rails

main line radius - 175 metres (574 ft)
siding radius - 84 metres (276 ft)

Couplings

Not all couplers

Coupling (railway)

A coupling is a mechanism for connecting rolling stock in a train. The design of the coupler is standard, and is almost as important as the railway gauge, since flexibility and convenience are maximised if all rolling stock can be coupled together.The equipment that connects the couplings to the...

can handle very sharp curves. This is particularly true of the European buffer and chain couplers. The buffers get in the way.

Problem curves

The Australian Standard Garratt
Australian Standard Garratt
The Australian Standard Garratt was a Garratt steam locomotive designed in Australia during the Second World War, which was used on narrow gauge railway systems in Queensland, South Australia, Western Australia and Tasmania.- Overview :...

had flangeless leading driving wheels which tended to cause derailments on sharp curves.
Sharp curves on the Port Augusta
Port Augusta, South Australia
-Electricity generation:Electricity is generated at the Playford B and Northern power stations from brown coal mined at Leigh Creek, 250 km to the north...

to Hawker
Hawker, South Australia
Hawker is a town in the Flinders Ranges area of South Australia, 365 km north of Adelaide. It is in the Flinders Ranges Council, the state Electoral district of Stuart and the federal Division of Grey. At the 2006 census, Hawker had a population of 229....

line of the South Australian Railways
South Australian Railways
South Australian Railways built and operated railways in South Australia from 1854 to the incorporation of its non-urban railways into the Australian National Railways Commission in 1975, together with the former Commonwealth Railways and the former Tasmanian Government Railways...

caused derailment problems when bigger and heavier SAR X class
SAR X class
The South Australia Railways X class was a class of 2-6-0 tender locomotive engine. It was heavier than the class that it replaced, causing problems on the sharp curves on the Quorn railway, where the curves had to be eased....

locomotives were introduced, requiring deviations to ease the curves. curves on the Oberon railway line, New South Wales, limited steam locomotives to the 19 class.

High-speed rail

For high-speed rail

High-speed rail

High-speed rail is a type of passenger rail transport that operates significantly faster than the normal speed of rail traffic. Specific definitions by the European Union include for upgraded track and or faster for new track, whilst in the United States, the U.S...

much gentler curves are needed. A formula to calculate the minimum curve radius is:

where G is the rail gauge

Rail gauge

Track gauge or rail gauge is the distance between the inner sides of the heads of the two load bearing rails that make up a single railway line. Sixty percent of the world's railways use a standard gauge of . Wider gauges are called broad gauge; smaller gauges, narrow gauge. Break-of-gauge refers...

, v is speed (km/h), g is gravitational acceleration

Gravitational acceleration

In physics, gravitational acceleration is the acceleration on an object caused by gravity. Neglecting friction such as air resistance, all small bodies accelerate in a gravitational field at the same rate relative to the center of mass....

(9.8 m/s²), ha is cant

Cant (road/rail)

The cant of a railway track or a road is the difference in elevation between the two edges...

, and hb is cant deficiency

Cant deficiency

The term "cant deficiency" is defined in the context of travel of a rail vehicle at constant speed on a constant radius curve. Cant itself is a British synonym for the superelevation of the curve, that is, the elevation of the outside rail minus the elevation of the inside rail...

.

This table shows examples of curve radii. The values used when building high-speed railways varies, and depends on how much wear and safety desired.

Curve radius	≤ 120 km/h	≤ 200 km/h	≤ 250 km/h	≤ 300 km/h	≤ 350 km/h
Cant 160 mm, cant deficiency 100 mm, no tilting train Tilting train A tilting train is a train that has a mechanism enabling increased speed on regular rail tracks. As a train rounds a curve at speed, objects inside the train experience centrifugal force. This can cause packages to slide about or seated passengers to feel squashed by the outboard armrest due to... s	625 m	1800 m	2800 m	4000 m	5400 m
Cant 160 mm, cant deficiency 200 mm, with tilting train Tilting train A tilting train is a train that has a mechanism enabling increased speed on regular rail tracks. As a train rounds a curve at speed, objects inside the train experience centrifugal force. This can cause packages to slide about or seated passengers to feel squashed by the outboard armrest due to... s	450 m	1300 m	2000 m	no tilting trains planned for these speeds

History

Minimum radius

Steam locomotives

Transition curves

Example Garratt

Couplings

Problem curves

High-speed rail

See also