Minimum railway curve radius

Minimum curve radii for railways are governed by the speed operated and by the mechanical ability of the rolling stock to adjust to the curvature.

[3] The sharpest curves tend to be on the narrowest of narrow gauge railways, where almost all the equipment is proportionately smaller.

More recent diesel and electric locomotives do not have a wheelbase problem, as they have flexible bogies, and also can easily be operated in multiple with a single crew.

For a line with a maximum speed of 60 km/h (37 mph), buffer-and-chain couplers increase the minimum radius to around 150 m (164 yd; 492 ft).

Common solutions include: A similar problem occurs with harsh changes in gradients (vertical curves).

Because freight and passenger trains tend to move at different speeds, a cant cannot be ideal for both types of rail traffic.

We start with the formula for a balancing centripetal force: θ is the angle by which the train is tilted due to the cant, r is the curve radius in meters, v is the speed in meters per second, and g is the standard gravity, approximately equal to 9.81 m/s²: Rearranging for r gives: Geometrically, tan θ can be expressed (using the small-angle approximation) in terms of the track gauge G, the cant ha and cant deficiency hb, all in millimeters: This approximation for tan θ gives: This table shows examples of curve radii.

A curve should not become a straight all at once, but should gradually increase in radius over time (a distance of around 40–80 m (130–260 ft) for a line with a maximum speed of about 100 km/h (62 mph)).

However, high-speed trains are sufficiently high-powered that steep slopes are preferable to the reduced speed necessary to navigate horizontal curves around obstacles, or the higher construction costs necessary to tunnel through or bridge over them.