Sag Vertical Curve Comfort and Drainage (AASHTO)
The comfort and drainage limits on a sag vertical curve - the two controls beyond headlight sight distance.
Example
You enter
- Algebraic grade difference A (%, |g2-g1|) 4
- Design speed V (mph) 60
You get
- Comfort minimum length L 309.677
- Rate of vertical curvature K 77.419
- Drainage maximum length (K<=167) 668
Checked against published worked examples from: Indiana DOT.
Details, formula, and sources
ScopeThe AASHTO comfort criterion L = A V^2/46.5 (A in %, V in mph) is the length that holds the vertical acceleration on the sag to about 1 ft/s^2, giving K = L/A = V^2/46.5; the drainage maximum K <= 167 (a 0.30% minimum grade within 50 ft of the low point, 50/0.30) caps the length at 167 A on curbed sections. A 4% break at 60 mph wants at least a 310 ft curve (K 77.4) for comfort and no more than 668 ft for drainage. Comfort is far less restrictive than headlight SSD; a licensed civil engineer's design governs.
Formula or tableComfort: L = A V^2 / 46.5 (A in %, V in mph, L in ft), K = L/A = V^2/46.5. Drainage maximum K <= 167 (a 0.30% minimum grade within 50 ft of the low point, 50/0.30 = 166.7), so the drainage-max length is 167 A.
Source and editionThe AASHTO A Policy on Geometric Design of Highways and Streets (the Green Book) sag vertical-curve comfort and drainage controls, by name.
Free accessThe AASHTO sag-curve comfort and drainage relations are published in the Green Book and mirrored in state DOT design manuals. 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, V_mph, L_ft, K_ft_per_pct, L_drainage_max_ft
- Comfort criterion L = A V^2 / 46.5 limits the vertical acceleration to about 1 ft/s^2; the 46.5 embeds that acceleration limit with V in mph and L in ftAASHTO Green Book
- Drainage maximum K <= 167 from a 0.30% minimum grade within 50 ft of the low point (50/0.30 = 166.7); the drainage-max length is 167 A, applicable to curbed sectionsAASHTO Green Book
- Not the SSD control the headlight stopping-sight-distance criterion (the governing sag stopping control) is a separate check, typically the most restrictivescope of this tile