The Unsymmetrical Vertical Parabola

by Robert P. Vreeland,

Serial Information: Journal of the Surveying and Mapping Division, 1968, Vol. 94, Issue 1, Pg. 61-66

Document Type: Journal Paper


An unsymmetrical vertical curve is occasionally required in the geometric design of highways, particularly at interchanges. The usual procedure in such cases makes use of two parabolas with vertical axes and a common tangent. This results in an abrupt change in curvature, and acceleration, at this point of compound curvature. A method is suggested using one parabola with its axis inclined. The elevations as a function of stationing are computed in non dimensional form in terms of three parameters: the two grades and the ratio between the horizontal projections of the tangent lengths.

Subject Headings: Curvature | Paraboloid | Geometrics | Interchanges | Case studies | Parameters (statistics)

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