Work out track curvature radius instantly with clear inputs, formula shown and shareable results.
Radius is found from a chord and its versine: R = chord squared divided by eight times the versine. That is the basis of track measurement in the field. From the radius and speed follow the lateral acceleration and the equilibrium cant that would balance it.
Versine method
R = C^2 / (8 x versine); equilibrium cant = 1500 x V^2 / (R x g) mm for 1435 mm gauge
Rail results are planning estimates only. Verify against the infrastructure manager's rule book, approved braking curves and applicable railway safety regulations.
A chord and its mid-offset can be measured directly on the rail with a string line, while the radius cannot. Versine is also what track recording cars record.
The North American measure: the central angle subtended by a 100 ft chord. It is roughly 1746 divided by the radius in metres.