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Curve Vertical Grade Example Calculation Elevation # Calculation example – Elevation calculation and grade along a profile vertical curve

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Determine the elevation and grade value of an unknown point K which lies along a profile vertical curve (convex in this example).

*Commonly in profile vertical curves, a parabola is applied as an approximation to circular curve, considering that for large radius values and target precision, these elements practically coincide.

**Known values: **Curvature radius H^{~}R (positive for concave, negative for convex vertical curve), grade in **S _{1} **and grade out

**Solution:** Elevation of point K at a distance **x **from curve start point A **y _{K}**, grade value at point K

The vertical distance of point K from point A is calculated:

**y _{K} = (S_{1}/100)*x + x^{2}/(2*H)**

The elevation of point K is calculated:

**H _{K} = H_{A} + y_{K}**

Grade **S _{K}** at point K calculation:

**S _{K} = S_{1} + (x/H)*100**

Where:

S_{1} = grade in value at start point A of vertical curve

x = horizontal distance of point K from point A

H = curvature radius at peak of vertical curve (where grade s = 0%)

H_{A} = elevation of start point A of vertical curve

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