Combined Vertical and Horizontal Curves

1. A section of highway has vertical and horizontal curves with the same design speed. A vertical curve on this highway connects a +1% and a +3% grade and is 420 ft long. If a horizontal curve on this highway is on a two-lane section with 12-ft lanes and has a central angle of 37 degrees and a superelevation of 6%, what is the length of the horizontal curve?

2. A section of a two-lane highway (12-ft lanes) is designed for 75 mi/h. At one point a vertical curve connects a −2.5% and +1.5% grade. The PVT of this curve is at station 36 + 50. It is known that a horizontal curve starts (has PC) 294 ft before the vertical curve’s PVC. If the superelevation of the horizontal curve is 0.08 and the central angle is 38 degrees, what is the station of the PT?

3. Two straight sections of freeway cross at a right angle. At the point of crossing, the east-west highway is at elevation 150 ft and has a constant +5.0% grade (upgrade in the east direction), and the north-south highway is at elevation 125 ft and has a constant −3.0% grade (downgrade in the north direction). Design a 90-degree ramp that connects the northbound direction of travel to the eastbound direction of travel. Design the ramp for the highest design speed (to nearest 5 mi/h) with the constraint that the minimum allowable value of D is 8.0. (Assume that the PC of the horizontal curve is at station 15 + 00, and the vertical curve PVIs are at the PC and PT.) Give the stationing and elevations of the PC, PT, PVCs, and PVTs.

4. A crest vertical curve and a horizontal curve on the same highway have the same design speed. The equal-tangent vertical curve connects a +3% initial grade with a +1% final grade and has a PVC at 101 + 78 and a PVT at 106 + 72, The horizontal curve has a PI at 150 + 10 and a central angle of 75 degrees. If the superelevation of the horizontal curve is 8% and the road has two 12-ft lanes, what is the stationing of the PT?

5. West and east highway segments are separated by 600 ft horizontally. The west segment has a +2% grade and the east segment has a +1% grade. The west-grade segment ends at a higher elevation than the east segment and the two segments are connected by a joining sag and crest curve combination (so PVTs = PVCc). If the road is designed for 45 mi/h, what is the elevation difference between the west and east highway segments?