Safe Curve Speed from Radius and Superelevation
The maximum safe speed a curve supports from its radius, superelevation (bank), and side-friction factor.
Example
You enter
- Curve radius R (ft) 1500
- Superelevation e (e.g. 0.08) 0.08
- Side-friction factor f 0.11
You get
- Maximum safe speed 65.4 mph
Checked against published worked examples from: Montana DOT.
Details, formula, and sources
ScopeThe maximum safe speed a curve supports from its radius, superelevation (bank), and side-friction factor, V = sqrt( 15 R (e + f) ) mph. A 1,500 ft radius at e 0.08 supports about 65 mph with f 0.11, the AASHTO side-friction factor at 65 mph (the 60 mph f of 0.12 would overstate it at 67 mph). Use the AASHTO f for the resulting speed band (f decreases with speed; iterate once). Point-mass model; ignores grade and the transition. A design/check aid; the civil engineer governs.
Formula or tableV = sqrt( 15 R (e + f) ) mph, the inverse of the AASHTO point-mass e + f = V^2/(15 R). R in ft.
Source and editionThe AASHTO A Policy on Geometric Design of Highways and Streets (the Green Book) point-mass curve model, solved for the speed, by name.
Free accessThe AASHTO point-mass relation is published in the Green Book; the side-friction design factors are in its speed table. AHJ, state DOT design manual, and the licensed civil engineer of record govern.
What governsEstimate. AHJ and licensed professional govern.
API field namesR_ft, e, f, v_mph
- Point-mass model V = sqrt( 15 R (e + f) ), V in mph and R in ftAASHTO Green Book
- Side-friction factor use the AASHTO f for the resulting speed band (about 0.20 at 30 mph to 0.08 at 80 mph); iterate onceAASHTO Green Book speed table
- Not a runoff/spiral design ignores grade, the transition/spiral, and driver comfortscope of this tile