Crest Vertical Curve Length for Sight Distance

Over a crest, the pavement itself blocks the view, and the geometry of a sightline grazing a parabola gives this result. The two heights are policy decisions, not measurements: AASHTO uses a driver eye height of 3.5 ft and an object height of 2.0 ft (1.08 m and 0.60 m in metric), and those numbers have drifted over the decades. Eye height fell from 3.75 ft as cars got lower, and the object height was once 6 in, on the theory that a driver should be able to see a small obstacle, before it was raised to represent a vehicle's tail lights. Substitute the American values and 200(√3.5 + √2)² collapses to 2,158, the constant printed in every US design manual; the metric pair gives 658.

A worked example: a 4 % grade change with 600 ft of required sight distance needs L = 4 × 600²/2158 = 667 ft of crest curve. The formula assumes S is shorter than L; when the required sight distance overruns the curve a different expression applies, and design manuals give both. Always check the assumption after computing: if S came out longer than L, you used the wrong case.