Sag Vertical Curve Length for Headlight SSD (AASHTO)
The sag (valley) companion the crest tile hands off: a sag curve is limited at night by headlight reach, so its minimum length comes from 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 and source
L = 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.
The AASHTO A Policy on Geometric Design of Highways and Streets (the Green Book) sag vertical-curve headlight sight-distance minimums, by name.
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