Superelevation Calculator: Simplified Curve Balance
Estimate bank rate or signed side-friction demand from speed and curve radius using a stated simplified balance, in metric or US units.
Explore the simplified balance between curve banking and side-friction demand for a vehicle following a circular path. Solve a bank rate from an assumed friction contribution, or calculate the signed friction demand for an existing bank.
How to use this tool
- Select the unknown: bank rate or side-friction demand.
- Enter speed and path radius with their units.
- Supply the known signed bank percentage or assumed friction factor.
- Read the result as a simplified balance and compare any proposed design separately with applicable criteria.
Formula
e + f ≈ v² / (gR); e = bank percentage / 100
The calculation converts speed to m/s and radius to metres, using g = 9.80665 m/s². Positive contributions act toward the curve centre. Common road formulas use rounded conversion constants such as 15 for mph/feet, so small differences are expected. This is a small-rate approximation, not the full force balance at arbitrary banking angles.
Example
At 72 km/h on a 200 m radius, speed is 20 m/s and centripetal acceleration is 2 m/s². With an assumed inward friction factor of 0.10, e = 2 / 9.80665 − 0.10, giving approximately 10.394324% bank. That arithmetic result is not a selected design rate.
Frequently asked questions
Why can friction demand be negative?
At low speed on a positively banked curve, friction may need to act outward to balance the inward bank contribution. The sign describes direction.
Is the friction input a measured tire coefficient?
It is a signed contribution in this simplified model. Road design friction criteria also consider comfort and operating conditions; available tire grip is a separate question.
Can this set a safe speed or approve a road?
No. It does not check rollover, drainage, transitions, pavement conditions, sight distance or agency limits. Those require a complete design assessment.
Sources
Last updated: 2026-10-30