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Crest Vertical Curve Length for Sight Distance

L=A S2200(h1+h2)2L = \frac{A\,S^{2}}{200\left(\sqrt{h_1} + \sqrt{h_2}\right)^{2}}

Worked example: 300 m crest giving 200 m of sight distance → A = 4.935 % — press Try an example to run it live, then adjust anything.

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Crest Vertical Curve Length for Sight Distance explained

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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.

Crest Vertical Curve Length for Sight Distance formula

L=A S2200(h1+h2)2L = \frac{A\,S^{2}}{200\left(\sqrt{h_1} + \sqrt{h_2}\right)^{2}}
Where
  • LL= Required curve length (m)
  • AA= Algebraic grade change (%)
  • SS= Sight distance (m)
  • h1h_1= Driver eye height (m)
  • h2h_2= Object height (m)

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