Hi MathBane:

I used to actually do this in real life. I was a surveyor for road and bridge construction contractors and this is how vertical curves are laid out.

We would use 50 foot stations though and 25 foot for fine grade.

The beginning of the vertical curve is called the PVC, Point of Vertical Curvature.

Where it ends is called the PVT, Point of Vertical Tangency.

The intersection point, where a straight line off of the curves intersects is called the PVI, Point of Vertical Intersection.

I wrote a program years back for my calculator that works these grades. But we used to use an HP-48GX with the Construction V software that done the calculations in the field for traversing, horizontal curves, vertical curves, or whatever was needed. They are obsolete now. Technology has advanced since thos days.

Using 0+00 as the PVC, its elevation is 1067.29

1+00 is elev. 1068.32

2+00 is elev. 1068.726

part d,The high point is at station 2+15.43 with elev.1068.733

2+50 is the PVI with elev. 1070.64, but the road elevation at that point is

1068.696. There is a 1.94 foot difference in the PVI elevation and the road elevation at that point.

Note as we round the top of the curve the grades are very similar.

3+00 is elev. 1068.511

4+00 is elev. 1067.674

5+00 at the PVT is elev. 1066.215

Here are the grades to shoot for when using your formula.

You can find the high or low point by using calc or the vertex of a parabola method. Afterall, that is what it is.