Pavements & traffic · Road geometry
Horizontal curve: radius, superelevation, transition, sight clearance calculator
Minimum radius for the design speed from maximum superelevation and side friction; the side friction demanded on the proposed radius and superelevation; transition (spiral) length from the rate of change of centripetal acceleration; superelevation development length from the maximum relative grade; and the lateral clearance to an obstruction needed for stopping sight distance round the curve.
Standard: Austroads Guide to Road Design Part 3 Sec 7: V² = 127R(e + f), transition length, superelevation development, horizontal sight distance (M = R(1 − cos(28.65S/R)))
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Inputs in the worked example
The live calculator starts with these values; change any of them and every result, check and diagram updates instantly.
| Input | Value | Unit |
|---|---|---|
| Design speed | 90 | km/h |
| Proposed radius | 400 | m |
| Superelevation | 6 | % |
| Maximum superelevation | 7 | % |
| Maximum side friction | 0.12 | |
| Rate of change of centripetal acceleration | 0.6 | m/s³ |
| Width rotated (lane width × lanes) | 3.5 | m |
| Maximum relative grade | 0.5 | % |
| Normal crossfall | 3 | % |
| Sight distance required | 170 | m |
Worked example — results
| Result | Value | Unit |
|---|---|---|
| Minimum radius (emax + fmax) | 336 | m |
| Side friction demanded on R with e | 0.099 | |
| Transition (spiral) length | 65.0 | m |
| Superelevation development length | 63.0 | m |
| Lateral clearance for sight distance M | 9.00 | m |
- ✓ R ≥ minimum radius — 400 vs 336 m
- ✓ Side friction demand ≤ fmax — 0.099
- ✓ e ≤ emax
Method, formulas and assumptions
- V² = 127R(e + f): Rmin = V²/[127(emax + fmax)]; f demanded = V²/(127R) − e.
- Transition length L = 0.0214V³/(R·C) with C the rate of change of centripetal acceleration (0.3–0.9 m/s³).
- Superelevation development = width rotated × (e + normal crossfall)/maximum relative grade.
- Horizontal sight clearance M = R[1 − cos(28.65S/R)] (degrees), measured from the inside lane centreline.
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For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.