| Radius (m) | Speed (km/h) | Gauge (mm) | Provided cant (mm) | Equilibrium cant (mm) | Deficiency (mm) | Adopted transition (m) |
|---|---|---|---|---|---|---|
| 600 | 90 | 1435 | 110 | ~136 | ~26 | ~79 |
| 350 | 80 | 1435 | 120 | ~207 | ~87 | ~86 |
| 1200 | 110 | 1435 | 130 | ~145 | ~15 | ~94 |
- Equilibrium cant (mm): e = (G × V²) / (127 × R)
- Cant deficiency (mm): D = max(0, e − ea)
- Cant excess (mm): E = max(0, ea − e)
- Allowable speed (km/h): V = √(127 × R × (ea + Dmax) / G)
- Transition by gradient (m): L = (ea × N) / 1000
- Transition by rate (m): L = (V(m/s) × ea) / ROC
- Enter radius, speed, and gauge for the curve.
- Provide cant and the allowable limits used on site.
- Set cant gradient and rate-of-change for transitions.
- Press Calculate to view results above the form.
- Download CSV or PDF to attach to design submittals.
Purpose of cant on curves
Cant (superelevation) raises the outer rail or edge so part of the lateral acceleration is balanced by gravity. This reduces wheel unloading, improves comfort, and lowers rail or pavement wear at operating speed. For mixed traffic, the chosen value is a compromise between slow and fast movements. The calculator helps quantify the resulting cant, deficiency, and transition needs.
Key inputs and typical ranges
Radius and speed drive the demand for cant. Track gauge affects the equilibrium relationship, while allowable cant and allowable deficiency are set by the adopted standard and rolling stock. Consider using the design or posted speed, not temporary restrictions. If inputs are uncertain, run sensitivity cases to understand the effect of speed or radius changes. Construction teams often work in millimeters for cant and meters for transition length, matching survey and as-built records.
Equilibrium cant and cant deficiency
Equilibrium cant is the cant that perfectly balances lateral acceleration at a given speed and radius. If provided cant is lower than equilibrium, the difference is cant deficiency, indicating residual lateral load and a comfort or wear penalty. Persistent high deficiency can raise maintenance demand on fast corridors. If provided cant exceeds equilibrium, cant excess can increase low-speed forces and drainage concerns.
Transition design and ride comfort
Cant should not change abruptly. Transition length can be controlled by a cant gradient limit (mm per meter) and by a rate-of-change criterion tied to speed (mm per second). The governing length is the larger of the two, supporting smooth vehicle roll-in and reducing dynamic amplification in track or slab systems. Where space is limited, revisit speed or cant limits.
Construction checks and reporting
Use outputs to prepare a field checklist: target cant, permissible min/max, predicted deficiency, and transition length. During installation, verify twist and cross-level at regular chainages, and document deviations with corrective actions. Confirm drainage and fastening tolerances before opening to traffic. Exported CSV and PDF summaries are useful for approvals, audits, and handover dossiers.
FAQs
1) What is the difference between cant and superelevation?
They describe the same concept: a cross-slope on a curve. In rail, cant is the height difference between rails. On roadway or slab, it is the outer-edge elevation that creates a banking effect.
2) Why can cant deficiency be allowed?
Allowing some deficiency lets higher speeds operate without excessive cant at low speeds. Standards limit deficiency to control comfort, wheel unloading, and wear, especially for passenger vehicles and lightly loaded equipment.
3) Which transition length should I adopt?
Use the larger length from the cant-gradient criterion and the rate-of-change criterion. The governing value is typically the comfort-based rate at higher speeds and the gradient limit in constrained construction zones.
4) What units should I enter for speed and radius?
Enter speed in kilometers per hour and radius in meters, as shown on the form. Cant-related values are in millimeters. Keeping consistent units avoids scaling errors that can significantly distort equilibrium cant and transition length.
5) How do I choose allowable cant limits?
Start with the project’s governing specification, then confirm with vehicle type, maintenance capability, and drainage requirements. For rehabilitation, also consider existing geometry and the tolerance you can realistically achieve during lining and tamping.
6) Does this replace a detailed design standard check?
No. It is a calculation aid. Always confirm outputs against your applicable standard, verify assumptions, and coordinate with track, civil, and operations teams before issuing final drawings.