Shape of the vertical curve: Parabolic

A vertical curve is a curve that is used to provide a smooth transition between two different grades on a road or railway. It is designed to ensure a comfortable and safe ride for vehicles and trains by eliminating sudden changes in elevation. The shape of the vertical curve is generally provided as a parabolic curve.

Explanation:
A vertical curve consists of two grades: the incoming grade and the outgoing grade. The incoming grade is the slope or grade of the road or railway before the vertical curve, and the outgoing grade is the slope or grade after the vertical curve.

The shape of the vertical curve is determined by the design criteria and standards set by transportation authorities. The most commonly used shape for vertical curves is the parabolic shape. The parabolic shape is chosen because it provides a smooth transition between the two grades, minimizing the discomfort and safety risks associated with sudden changes in elevation.

The parabolic shape is a mathematical curve that is defined by a quadratic equation. It has a smooth, rounded shape that allows for a gradual change in elevation. The curve starts with a gentle slope, gradually increases in steepness, and then decreases again to match the slope of the outgoing grade.

The parabolic shape of the vertical curve is designed to meet certain criteria, such as the maximum allowable rate of change in grade and the minimum sight distance requirements. These criteria ensure that the vertical curve provides a comfortable and safe transition for vehicles and trains.

In addition to the parabolic shape, there are other shapes that can be used for vertical curves, such as circular, spiral, and elliptical curves. However, the parabolic shape is the most commonly used shape due to its simplicity, ease of calculation, and ability to meet the design criteria.

In conclusion, the shape of the vertical curve that is generally provided is a parabolic curve. This shape is chosen to ensure a smooth and safe transition between two different grades on a road or railway.