Railway Curve Superelevation Calculator
Railway civil design & track geometry: Calculate equilibrium superelevation (cant $E_a$), cant deficiency ($D$), uncompensated lateral centrifugal acceleration, and minimum spiral transition length.
Curve Geometry & Speed Specifications
Cant & Kinematic Acceleration Results
Equilibrium Cant $E_{eq}$
--
mm (zero lateral acceleration)
Cant Deficiency $D$
--
mm ($E_{eq} - E_a$)
Uncompensated Lateral Accel $a_{lat}$
--
$\text{m}/\text{s}^2$ (passenger body force)
Cant Excess $E$ (Slow Train)
--
mm (@ $V_{slow}$)
Min Transition Spiral $L_{trans}$
--
meters (clothoid transition)
Max Safe Speed $V_{max}$
--
km/h (@ max allowable $D$)
Track Superelevation & Centrifugal Force Balance
Superelevation tilts the track plane inwards. If $E_a < E_{eq}$, a net outward centrifugal acceleration ($a_{lat}$) pushes passengers towards the outside rail.
Superelevation Kinematics Formulation
Centrifugal force $F_c = m v^2 / R$ acting at the center of gravity is balanced by the horizontal component of gravity $F_g = m g \sin\theta \approx m g (E_a / G)$:
$$E_{eq} = \frac{G \, v^2}{g \, R} \approx \frac{11.82 \, V^2}{R} \quad [\text{mm for } G = 1500 \text{ mm, } V \text{ in km/h}]$$
$$D = E_{eq} - E_a, \quad a_{lat} = g \frac{D}{G} \approx \frac{D}{153} \; [\text{m/s}^2]$$
$$L_{trans} \ge \max\left( \frac{V \cdot E_a}{q_{cant}}, \frac{V \cdot D}{q_{def}} \right)$$
Under mixed passenger/freight traffic, cant cannot be optimized for high-speed trains without creating excessive cant excess ($E = E_a - E_{eq,slow}$) for slow freight trains, causing inner rail crushing.
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