Elevation Point of Vertical Curve Calculator

Vertical curves are important transition elements in geometric design for highways and its calculation has high importance in civil engineering.

Vertical curve calculator is developed for the ease of civil engineers and students. Engineers can use vertical curve calculator for surveying and other construction-related activities.

Let’s go through the definition of vertical curve, how to find vertical curve, and the formula to calculate the vertical curve in the sections below.

Vertical curve definition

The curve in a vertical alignment that is formed when two unalike gradients come across is known as vertical curves. There are two types of vertical curves. The curve leading to the bottom would be concave and to the top of an inclined plane would be convex.

Vertical curves are usually used in roads and canals. Horizontal curves are also used in railway tracks and roads according to the requirement.

Vertical curve formula

The vertical curve equation can be expressed as:

y = e_pvc + g₁x + [(g₂ − g₁) × x² / 2L]

Where,

y represents the vertical elevation of point,

e_pvc refers to initial elevation,

g₁ refers to initial grade,

g₂ is the final grade, and

x/L is the distance between the beginning and end of the curve.

How to find elevation point of vertical curve?

The elevation point of vertical curve can be calculated using the above formula. We will use an example to demonstrate the complete process to find the elevation point of vertical curve.

Follow the steps below for the detailed method:

• Identify and write down the values.
• Use the vertical curve equation and place the values.
• Simplify the equation to get the final result.

Example:

A road in construction has an initial elevation of 20 m and the length of the curve is 30 m. If the initial grade and the final grade are 3% and 7% respectively, find the elevation point of vertical curve?

Solution:

Step 1: Write down the values.

e_pvc = 20 m

x/L = 30 m

g₁ = 3%

g₂ = 7%

Step 2: Place the values in the elevation point of vertical equation.

y = e_pvc + g₁x + [(g₂ − g₁) × x² / 2L]

y = 20 + 3(30) + [(7% - 3%) × 30²/2(30)]

y = 21.5000 ~ 70.5381

The vertical tangent calculator above can save you from all of the above annoyance. If you are looking for connecting descending grades, checkout our SAG Vertical Curve Length.