A reversed curve is a horizontal alignment consisting of two consecutive circular curves that bend in opposite directions and are joined directly without an intervening tangent; its engineering significance lies in the abrupt reversal of centrifugal force acting on vehicles, which can reduce riding comfort and compromise safety if not properly designed. Because drivers must immediately adjust steering in the opposite direction, reversed curves are generally avoided on high-speed facilities unless adequate transition curves, proper superelevation development, and sufficient sight distance are provided. When unavoidable due to terrain or right-of-way constraints, careful geometric design is essential to minimize operational hazards and ensure smooth vehicle maneuvering.
Reverse Curve with Parallel Tangents
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Reverse Curve with Converging Tangents
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Reverse Curve with Intermediate Tangent
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Problem: Reversed Curve with Parallel Tangents
The perpendicular distance between two parallel tangents is equal to 8 meters. These tangents are connected by a reversed curvature such that the central angle is 8º and the radius of curvature of the first curve is equal to 175m. Find the radius of the second curve of the reversed curvature.
Problem: Reversed Curve with Parallel Tangents and Connected by Intermediate Tangent
Two parallel tangents have directions of due east and are 200 meters apart. They are connected by a reversed curve having the same degree of 1.4º. PC of the curve is on the upper tangent while the PT of the curve is at the lower tangent. If the horizontal distance parallel to the tangent from the PC to the PT of the reversed curve is 800m, determine:
a. The distance of the intermediate tangent between the two curves.
b. The distance between the centers of the reversed curvature.
c. The stationing of PT if the stationing of PC is 10+200.
Problem: Reversed Curve with Converging Tangents
A reverse curve connects two converging tangents with an angle of intersection of 32º. The distance from PI of the second curve to this point of intersection is 180m. The deflection angle of the common tangent from the back tangent is 22º and the degree of curve of the 2nd curve is 5º.
a. Determine the radius of the 2nd curve.
b. Determine the tangent distance of the 2nd curve.
c. Determine the degree of curve of the 1st curve by arc basis.
d. If the stationing of PC is 3+600, determine the stationing of PT.
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