Vertical and Horizontal Curves for Road and Railway

When designing road or railway alignment, we often use parabolic curve for vertical alignment and circular curve for horizontal alignment.

Depending on the gradient difference between the beginning and the end of curve, vertical curve can further be categorized as crest and sag curves. To determine the level of any point on vertical curve, we first determine its chainage measured from the beginning of curve. Then, we can calculate the elevation difference between it and the starting point based on the gradient and parabolic curve function. The level of a specific point is the sum of level at the beginning of curve and the calculated elevation difference.

A horizontal curve may be categorized into three types, namely simple curve, compound curve and reverse curve based on their configuration. When designing horizontal circular curve, we need to specify parameters such as the coordinate of tangents intersection point, curve radius, deflection angle, tangent length, curve length etc to ease the setting out process on site.

In this worked example, we are required to design for the vertical alignment for a 340m road section.

First, the target level is determined at some of its chainage. Based on this input, we know there are two vertical intersection points (VIP) for this section. Thus, we need to design for two vertical curves.

For each proposed vertical curve, we first need to check whether they are crest curve or sag curve. Then, we calculate the minimum vertical curve length (VCL) based on k value associated with the curve type. In our design, the proposed VCL should be greater than this value.

After that, we can find the chainages for the beginning and end of vertical curve (BVC & EVC). By taking BVC as our reference point, we can proceed with defining the reduced level along the vertical curve. In this example, level for every 10m chainage is determined.
Lastly, after all the levels are calculated, we can plot the vertical profile of this road section. Vertical curve data should be put at appropriate location in this plot for other engineers to understand the vertical curve design better.