Sag Vertical Curve Length for Headlight SSD (AASHTO)
The minimum length of a sag (valley) vertical curve, which at night is limited by headlight reach.
Example
You enter
- Algebraic grade difference A (%, |g2-g1|) 4
- Stopping sight distance S (ft) 400
You get
- Minimum sag curve length L 350
- Rate of vertical curvature K 88 ft/% (K = L/A)
Checked against published worked examples from: Michigan DOT.
Details, formula, and sources
ScopeFrom the AASHTO headlight criterion L = A S^2/(400 + 3.5 S) for S<=L, L = 2 S - (400 + 3.5 S)/A for S>L, with K = L/A (400 and 3.5 embed the 2.0 ft headlight height and 1-degree beam). A 4% grade break needing 400 ft SSD wants a 350 ft sag curve (K 87.5). Headlight-SSD control only; comfort (A V^2/46.5) and drainage (K<=167) are separate. A design aid, not a substitute for a licensed civil engineer's design.
Formula or tableL = A S^2 / (400 + 3.5 S) for S <= L; L = 2 S - (400 + 3.5 S)/A for S > L; K = L/A. 400 and 3.5 embed the 2.0 ft headlight height and 1-degree beam divergence.
Source and editionThe AASHTO A Policy on Geometric Design of Highways and Streets (the Green Book) sag vertical-curve headlight sight-distance minimums, by name.
Free accessThe AASHTO sag-curve headlight-criterion equations are published in the Green Book. The AHJ, state DOT design manual, and the licensed civil engineer of record govern.
What governsEstimate. AHJ and licensed professional govern.
API field namesA_pct, S_ft, L_ft, K_ft_per_pct
- Headlight criterion L from the 2.0 ft headlight beam reaching the road on the far grade; the 400/3.5 constants are the beam-height and 1-degree-divergence geometryAASHTO Green Book
- Branch selection L = A S^2/(400 + 3.5 S) when S <= L, else L = 2 S - (400 + 3.5 S)/A; the governing branch is chosen by the S vs L comparisonAASHTO Green Book
- Headlight SSD only the comfort (A V^2/46.5) and drainage (K <= 167) criteria are separate checksscope of this tile