Minimum railway curve radius

90-foot (27.43 m) radii on the elevated 4 ft 8 ¹⁄₂ in (1,435 mm) Chicago 'L'. There is no room for longer radii at this street intersection

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 tracks. Minimum radius of curve is one parameter in the design of railway vehicles^[1] as well as trams ^[2].

History

The first proper railway was the Liverpool and Manchester Railway 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.^[3][4]

• 1,435 mm (4 ft 8 ¹⁄₂ in) 7,000 m (22,966 ft) Typical China's high-speed railway network (350 km/h)
• 1,435 mm (4 ft 8 ¹⁄₂ in) 5,500 m (18,045 ft) Typical China's high-speed railway network (250km/h~300km/h)
• 1,435 mm (4 ft 8 ¹⁄₂ in) 4,000 m (13,123 ft) Typical high-speed railways (300 km/h)
• 1,435 mm (4 ft 8 ¹⁄₂ in) 3,500 m (11,483 ft) Typical China's high-speed railway network (200~250km/h)
• 1,435 mm (4 ft 8 ¹⁄₂ in) 2,000 m (6,562 ft) Typical high-speed railways (200 km/h)

• 1,435 mm (4 ft 8 ¹⁄₂ in) Border Loop - 240 m (787 ft) - 5,000 long tons (5,100 t; 5,600 ST) - 1,500 m (4,921 ft)

• 1,435 mm (4 ft 8 ¹⁄₂ in) Homebush triangle - 200 m (656 ft) - 5,000 long tons (5,100 t; 5,600 ST) - 1,500 m (4,921 ft)
• 1,435 mm (4 ft 8 ¹⁄₂ in) Turkey - 190 m (623 ft) ^[4]

• 1,435 mm (4 ft 8 ¹⁄₂ in) Zig Zag - 160 m (525 ft) - 40km/h
• 1,435 mm (4 ft 8 ¹⁄₂ in) Batlow, New South Wales - 100 m (328 ft) - 500 long tons (510 t; 560 ST) - 300 m (984 ft) - restricted to NSW Z19 class steam locomotives
• 1,435 mm (4 ft 8 ¹⁄₂ in) - 85 m (279 ft) - Windberg Railway (de:Windbergbahn) (between Freital-Birkigt and Dresden-Gittersee) - restrictions to wheelbase
• 1,435 mm (4 ft 8 ¹⁄₂ in) - 200 ft (61 m) - London Underground Central line (between White City and Shepherd's Bush)
• 1,435 mm (4 ft 8 ¹⁄₂ in) Sydney steam trams hauling 3 trailers - 25 m (82 ft)
• 1,435 mm (4 ft 8 ¹⁄₂ in) Chicago 'L' - 90 ft (27.43 m)
• 1,067 mm (3 ft 6 in) Matadi-Kinshasa Railway - 273 yd (819 ft; 250 m) - deviated 1,067 mm (3 ft 6 in) line.
• 1,067 mm (3 ft 6 in) Queensland Railways - 60 m (197 ft)
• 1,067 mm (3 ft 6 in) Taunton Tramway - 35 ft (10.67 m)
• 1,000 mm (3 ft 3 ³⁄₈ in) Bernina Railway - 45 m (148 ft)
• 762 mm (2 ft 6 in) Matadi-Kinshasa Railway - 55 yd (165 ft; 50 m) - original 762 mm (2 ft 6 in) line.
• 762 mm (2 ft 6 in) Victorian Narrow Gauge - 40 m (131 ft) 16 km/h/10 mph on curves ; (32 km/h/20 mph on straight )
• 762 mm (2 ft 6 in) Kalka-Shimla Railway - 37.47 m (122.9 ft) or 48 degrees
• 610 mm (2 ft)  Darjeeling Himalayan Railway - 21.2 m (70 ft)
• 610 mm (2 ft)  Matheran Hill Railway - 18.25 m (59.9 ft); 1 in 20 (5%); (8 km/h/5 mph on curve; 20 km/h/12 mph on straight)
• 610 mm (2 ft)  Chicago Tunnel Company - 16 ft (4.9 m); 20 ft (6.1 m) in grand unions.
• 600 mm (1 ft 11 ⁵⁄₈ in) Welsh Highland Railway - 50 m (164 ft)
• 600 mm (1 ft 11 ⁵⁄₈ in) Welsh Highland Railway - 40 m (131 ft) on original line at Beddgelert

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 locomotives Mallet, Garratt, Shay 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 length of say 40 m - 80 m. Even worse than curves with no transition are reverse curves with no intervening straight.

The super-elevation (aka cant) must also be transitioned.

K class garratt

The TGR K Class was

• 610 mm (2 ft)  gauge
• 99 ft (30 m) radius curves

Example Garratt

• 1,000 mm (3 ft 3 ³⁄₈ in) gauge
• 25 kg/m (50.40 lb/yd) rails
• main line radius - 175 metres (574 ft)
• siding radius - 84 metres (276 ft) ^[5]

0-4-0

• GER Class 209
• 1,435 mm (4 ft 8 ¹⁄₂ in)

Couplings

Not all couplers 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 had flangeless leading driving wheels which tended to cause derailments on sharp curves.
• Sharp curves on the Port Augusta to Hawker line of the South Australian Railways caused derailment problems when bigger and heavier SAR X class locomotives were introduced, requiring deviations to ease the curves. ^[6]
• 5-chain (101 m; 330 ft) curves on the Oberon railway line, New South Wales, limited steam locomotives to the 19 class.

High-speed rail

For high-speed rail much gentler curves are needed. A formula to calculate the minimum curve radius is:

$r=\frac{G\left(\frac{v}{3.6}\right)^2}{g(ha+hb)}$

where G is the rail gauge, v is speed (km/h), g is gravitational acceleration (9.8 m/s²), ha is cant, and hb is cant deficiency.

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 trains	625 m	1800 m	2800 m	4000 m	5400 m
Cant 160 mm, cant deficiency 200 mm, with tilting trains	450 m	1300 m	2000 m	no tilting trains planned for these speeds

See also

Category:Articulated locomotives Degree of curvature, civil engineering Heaviest trains

Lateral motion device Longest trains Matheran Hill Railway

Radius of curvature (applications) Railway systems engineering Track transition curve Turning radius

References

1. ^ Guide to Railcars, showing the minimum radii that each freight car is able to negotiate
2. ^ Canadian Light Rail Vehicle able to negotiate a 36 ft (10.973 m) radius curve
3. ^ http://www.wis.co.uk/andy/16mm/minimumcurveradius.html
4. ^ ^{a b} Jane's World Railways 1995-1996 p728
5. ^ http://www.garrattmaker.com/history.html
6. ^ Australian Railway History September 2008, p291.