Vertical Curve Calculator

What is a Vertical Curve?

A vertical curve is like a smooth hill or valley on a road. It connects two slopes gently, making it easier and safer for cars to drive up or down. Imagine rolling a ball down a slide that curves at the bottom - that's similar to how a vertical curve works!

How to Calculate a Vertical Curve

Calculating a vertical curve is like solving a puzzle. We use special formulas to figure out how high or low the road should be at any point along the curve. It's a bit like drawing a smooth line between two straight lines!

Formula

The main formula for a vertical curve is:

\[ y = \frac{G_2 - G_1}{2L}x^2 + G_1x + E_{BVC} \]

Where:

• \(y\) is the elevation at any point on the curve
• \(G_1\) is the initial grade (slope) in percent
• \(G_2\) is the final grade (slope) in percent
• \(L\) is the length of the curve
• \(x\) is the distance from the beginning of the curve
• \(E_{BVC}\) is the elevation at the beginning of the vertical curve

Calculation Steps

1. Determine the initial grade (\(G_1\)) and final grade (\(G_2\))
2. Measure the length of the curve (\(L\))
3. Find the elevation at the beginning of the curve (\(E_{BVC}\))
4. Choose a point along the curve (\(x\))
5. Plug these values into the formula to find the elevation (\(y\)) at that point

Example and Visual Representation

Let's look at a vertical curve with these values:

• \(G_1 = 2\%\) (going uphill)
• \(G_2 = -3\%\) (going downhill)
• \(L = 200\) feet
• \(E_{BVC} = 100\) feet

We'll calculate the elevation at \(x = 100\) feet (halfway along the curve):

\[ y = \frac{-3 - 2}{2(200)}(100)^2 + 2(100) + 100 \]

\[ y = -0.00625(10000) + 200 + 100 = 237.5\text{ feet} \]

Here's what this vertical curve looks like:

In this picture, you can see how the vertical curve smoothly connects the uphill and downhill slopes. The blue line shows the curve, and the red dot marks the midpoint we calculated at (100, 237.5).