Vertical Curve Elevations
Equal-tangent parabolic elevations and the high or low point of a vertical curve.
Example
You enter
- Incoming grade g1 (percent) 3
- Outgoing grade g2 (percent) -2
- Curve length L (ft) 400
- PVI station (ft) 5000
- PVI elevation (ft) 100
- Evaluate at station (ft, optional) 5040
You get
- Bvc elev (ft) 94
- Turning elev (ft) 97.6
Checked against published worked examples from: AASHTO Green Book / FM 5-233 (by name).
Details, formula, and sources
Formula or tableEqual-tangent parabola from the BVC: elev(x) = bvc_elev + (g1/100)*x + ((g2-g1)/100)/(2L)*x^2, x in ft from BVC. Turning point at x = -g1*L/(g2-g1) when it lies in [0, L].
Source and editionEqual-tangent parabolic vertical-curve elevations and the high/low-point location per the AASHTO Green Book vertical-alignment relations and FM 5-233, by name; first-principles.
Free accessFM 5-233 is public-domain US Government work, free at US Army publication archives. The design of record governs.
What governsEstimate. Engineer of record governs the design and acceptance. Verify against the project structural drawings and the manufacturer's published capacity / chart.
API field namesg1_pct, g2_pct, length_ft, pvi_station_ft, pvi_elevation_ft, eval_station_ft, bvc_elev_ft, turning_elev_ft
- Symmetric curve equal-tangent (symmetric) parabola; unequal-tangent curves out of scopemethod