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The minimum railway curve radius has an important bearing on constructions costs and operating costs and, in combination with superelevation (difference in elevation of the two rails), determines the maximum safe speed of a curve. Minimum radius of curve is one parameter in the design of railway vehicles.

Contents

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.[1]

  • 1,435 mm (4 ft 8+12 in) 4,000 m (13,123 ft) Typical High Speed Railways (200km/h)

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.

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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+38 in) gauge
  • 25 kg/m (50.40 lb/yd) rails
  • main line radius - 175 metres (574 ft)
  • siding radius - 84 metres (276 ft) [3]

0-4-0

Couplings

Not all couplers can handle very sharp curves. This is particularly true of buffer and chain couplers. The buffers get in the way.

Problem curves

High-speed rail

For high-speed rail much gentler curves are needed. A formula to calculate the minimum curve radius is r=(v/3.6)^2 * rail gauge / (g * (ha+hb)), where 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

References


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