Name: calculating elevations on a vertical curve
Uploaded: 2025-03-26T15:36:53.000Z
Duration: 1 min 23 s
Channel: JoVE

A vertical curve connects two grade lines, ensuring a smooth highway transition. The curve length, grades, P.V.I. location, and P.V.I. elevation are provided to calculate the curve’s elevations at specified stations.&nbsp;The P.V.C. and P.V.T.&nbsp;stations, marking the start and end of the curve, are calculated by subtracting and adding half the curve length to the P.V.I. station.Using the given grades, P.V.I. elevation, and half the curve length, the elevations at P.V.C. and P.V.T. are determined.For each station, the grade line elevation is computed by combining the grade and the horizontal distance from the P.V.C. or P.V.T.Next, the midpoint elevation of the long chord and the curve's midpoint elevation are determined to calculate the offset at P.V.I.This offset and the horizontal distance from the P.V.C. or P.V.T. are used to calculate tangent offsets for each station based on the curve length.Finally, the curve elevations at the stations are obtained by subtracting the tangent offsets from the grade line elevations.The computed elevations represent the vertical profile of the curve.

vertical curve: problem solving

Vertical curves provide the transition between two roadway grades, ensuring safety, comfort, and functionality. Calculating elevations at specific stations along the curve involves several systematic steps based on the curve's geometry and provided design parameters.The vertical curve is defined by its length, grades, Point of Vertical Intersection (P.V.I.) location, and P.V.I. elevation. The stations of the Point of Vertical Curvature (P.V.C.), where the curve begins, and the Point of Vertical Tangency (P.V.T.), where the curve ends, are determined by subtracting and adding half the curve length to the P.V.I. station. The elevations at P.V.C. and P.V.T. are calculated using the grades and P.V.I. elevation.The grade line elevation is computed for each station along the curve using the grade at the P.V.C. or P.V.T. and the horizontal distance to the station. This calculation provides the linear elevation profile before accounting for the curve's parabolic shape. The elevation at the midpoint of the long chord and the curve’s midpoint are determined to calculate the offset at the P.V.I. This offset, derived from the curve's parabolic geometry, represents the vertical distance between the grade line and the curve at the P.V.I.Using the P.V.I. offset and the horizontal distance from the P.V.C. or P.V.T., tangent offsets are computed for each station. These offsets reflect the deviation from the grade line caused by the curvature of the roadway. The curve elevation at each station is then obtained by subtracting the tangent offset from the grade line elevation. The calculated elevations at specified stations form the vertical profile of the curve, which is critical for designing smooth transitions, ensuring proper drainage, and maintaining safety standards. These computations enable engineers to create roadways that balance functionality with driver comfort.

Vertical Curve: Problem Solving

Vertical curves provide the transition between two roadway grades, ensuring safety, comfort, and functionality. Calculating elevations at specific ...

Education

JoVE Core

Civil Engineering

Unit 1

Horizontal and Vertical Curves

KEY TERMS AND CONCEPTS

calculating elevations on a vertical curve

Vertical curves connect two roadway grades and help make the road safer, smoother, and more functional. To find the elevation at specific stations on the curve, engineers follow a set of steps based on the curve length, the grades, the Point of Vertical Intersection, or P.V.I., and the P.V.I. elevation.

The first step is to locate the Point of Vertical Curvature, or P.V.C., and the Point of Vertical Tangency, or P.V.T. The P.V.C. marks the start of the curve, and the P.V.T. marks the end. Their stations are found by subtracting and adding half the curve length from the P.V.I. station. The elevations at the P.V.C. and P.V.T. are then calculated from the grades and the P.V.I. elevation.

Next, the grade line elevation is found at each station along the curve. This uses the grade at the P.V.C. or P.V.T. and the horizontal distance to the station. The result gives the straight-line elevation profile before the parabolic curve shape is applied. Engineers then find the elevation at the midpoint of the long chord and the curve’s midpoint to determine the offset at the P.V.I.

That offset comes from the curve’s parabolic geometry. It is the vertical distance between the grade line and the actual curve at the P.V.I. Using the P.V.I. offset and the horizontal distance from the P.V.C. or P.V.T., tangent offsets are calculated for each station. These offsets show how far the roadway curve deviates from the grade line.

The final curve elevation at each station is found by subtracting the tangent offset from the grade line elevation. These station elevations form the vertical profile of the roadway. They are important for smooth transitions, proper drainage, and safety, while also helping the road remain comfortable for drivers.

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Vertical curves connect two roadway grades and help make the road safer, smoother, and more functional. To find the elevation at specific stations on the curve, engineers follow a set of steps based on the curve length, the grades, the Point of Vertical Intersection, or P.V.I., and the P.V.I. elevation. The first step is to locate the Point of Vertical Curvature, or P.V.C., and the Point of Vertical Tangency, or P.V.T. The P.V.C. marks the start of the curve, and the P.V.T. marks the end.

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key terms and concepts

Learn how to calculate elevations on a vertical curve using P.V.C., P.V.T., P.V.I., grade line elevation, and tangent offsets in roadway design.

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JoVE Core Civil Engineering offers a foundational exploration of essential construction materials such as bricks, stones, steel, wood, and concrete, along with fluid mechanics topics like flow over immersed bodies, open channel flow, and dimensional modeling. It also covers key surveying concepts, including leveling, traverse adjustments, curve design, topographic mapping, and geospatial technologies (GPS & GIS). Science-in-action videos showcase laboratory research on materials, fluids, and surveying practices in real-world engineering systems.

civil engineering

Calculating Elevations on a Vertical Curve

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