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Superelevation Calculator

Description

On a real curve, the outer rail is built up higher than the inner rail so gravity leans the train slightly inward, offsetting some of the outward pull it feels running the curve at speed — the same banking idea as a banked highway on-ramp. The amount that exactly balances a given speed is called equilibrium superelevation, and it depends on the track's gauge, the curve's radius, and how fast the train is moving.

The default mode gives you that prototype superelevation directly from a speed and radius. The other two modes work backward: enter a target superelevation (prototype railroads typically cap it well under 10 inches) and either a radius or a speed, to find the matching speed limit or minimum curve radius.

Prototype superelevation is almost always too small to matter once scaled down — a few inches of real rail height becomes a fraction of a millimeter in most model scales — so this calculator also converts the result into your scale, mainly so you can see just how small it really is. Modelers who do add visible superelevation for appearance are choosing a cosmetic amount, not this calculated one.

Sources

Equilibrium superelevation comes directly from the physics of circular motion applied to a railway: the outer-rail rise needed so gravity's inward component balances a train's centripetal acceleration at a given speed, E = G·V²/(g·R). This is standard railway/civil-engineering derivation (the same relationship AREMA practice expresses via an approximate degree-of-curve constant) — not a modeling-specific standard, so there's no separate citation needed for the formula itself, the same reasoning this site uses for its Grade & Elevation Calculator. Scale ratios for the model-equivalent conversion come from the same sources as the Scale Converter:

Disclaimer: this is theoretical equilibrium superelevation, not a specific railroad's actual engineering practice — real applied superelevation also accounts for mixed freight/passenger speeds and other factors. Always verify against your specific prototype or reference if precision matters.