Vertical curve length fitted to a fixed elevation at a fixed station
A sag curve must pass through an existing manhole rim at a set station and elevation. The required length comes out of a quadratic with two roots, only one of which puts the point on the curve.
Analyze· about 30 minutes by hand· 5 steps
Given
An equal-tangent parabolic vertical curve is to be designed at a PVI at station 48+00.00, elevation 512.00 ft.
Grade in g₁ = −2.00 percent; grade out g₂ = +3.00 percent.
An existing manhole rim at station 50+00.00 must be met exactly. Its elevation is 519.25 ft.
The PVI station, the PVI elevation and both grades are fixed by other constraints. Only the curve length may be varied.
Elevations to 0.01 ft.
Required
The curve length L that puts the finished profile through elevation 519.25 ft at station 50+00.00.
The stations and elevations of the BVC and the EVC for that length.
The low point, the K value and a grade sheet at full stations.
Work it through yourself before reading on - the solution below shows every step, so there is no way to skim it without giving the answer away.
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