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 S1 and grade out S2 (positive for ascending , negative for descending slopes), elevation of start point A of vertical curve HA
Solution: Elevation of point K at a distance x from curve start point A yK, grade value at point K SK
The vertical distance of point K from point A is calculated:
yK = (S1/100)*x + x2/(2*H)
The elevation of point K is calculated:
HK = HA + yK
Grade SK at point K calculation:
SK = S1 + (x/H)*100
S1 = 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%)
HA = elevation of start point A of vertical curve
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