Crest Vertical Curves

1 A 520-ft long equal-tangent crest vertical curve connects tangents that intersect at station 340 + 00 and elevation 1325 ft. The initial grade is +4.0% and the final grade is −2.5%. Determine the elevation and stationing of the high point, PVC, and PVT.

4 An equal-tangent crest vertical curve is designed for 70 mi/h. The high point is at elevation 1011.4 ft. The initial grade is +2% and the final grade is −1%. What is the elevation of the PVT?

5 An equal-tangent crest curve has been designed for 70 mi/h to connect a +2% initial grade and a −1% final grade for a new vehicle that has a 3 ft driver’s eye height; the curve was designed to avoid an object that is 1 ft high. Standard practical stopping distance design was used but, unlike current design standards, the vehicle was assumed to make a 0.5g stop, although driver reactions are assumed to be the same as in current highway design standards. If the PVC of the curve is at elevation 848 ft and station 43 + 48, what is the station and elevation of the high point of the curve?

6 A vertical curve is designed for 55 mi/h and has an initial grade of +2.5% and a final grade of −1.0%. The PVT is at station 114 + 50. It is known that a point on the curve at station 112 + 35 is at elevation 245 ft. What is the stationing and elevation of the PVC? What is the stationing and elevation of the high point on the curve?

7 An equal-tangent crest vertical curve is designed for 65 mi/h. The initial grade is +3.4% and the final grade is negative. What is the elevation difference between the PVC and the high point of the curve?

8 An equal-tangent crest vertical curve has a 50- mi/h design speed. The initial grade is +3%. The high point is at station 33 + 40.76 and the PVT is at station 37 + 24.66. What is the elevation difference between the high point and the PVT?

9 An equal-tangent crest curve connects a +2% initial grade with a −1% final grade and is designed for 55 mi/h. The station of the PVI is 233 + 40 with an elevation of 1203 ft. What is the elevation of the curve at station 234 + 00?

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