Transition (Spiral) Curve Length

Length of transition / spiral curve based on radial acceleration, superelevation runoff, and empirical terrain formula. Units: km/h, m, %, m/s³.

1. Basic data & design mode

Design / operating speed on the curve.
Radius of the circular curve to which the spiral is attached.
Only needed in Check mode. Compared against governing Ls,min.

2. Criterion A – Rate of change of radial acceleration

If left blank, C is taken as 80/(75+V) with limits 0.5–0.8 m/s³. Length by this criterion: Ls,A = 0.0215·V³ / (C·R)

This criterion controls passenger comfort by limiting the rate at which lateral (centrifugal) acceleration builds up.

3. Criterion B – Superelevation runoff

Full superelevation on the circular curve. Leave blank to ignore this criterion.
Total width being rotated (for both directions if applicable).
Additional widening on the curve. Default 0.0 m.
1:N is the rate of introduction of superelevation (e.g. N = 150 for 1:150). Criterion formula: Ls,B = e·N·(W + We)/2.

4. Criterion C – Empirical (terrain based)

Plain/rolling: Ls,C = 2.7·V² / R, Mountainous: Ls,C = V² / R (V in km/h, R in m).

Final recommended spiral length Ls,min is taken as the maximum of A, B and C (where applicable).