### Solution: Vertical Curves Set 2

#### Problem (1)

PVI station and elevation are 41+00.00 and 1262.00 ft. Incoming and outgoing grades are -2.50% and +3.00%. What is the curve length if it must pass through an elevation of 1268.00 ft at station 42+50.00?

Because it's 150 ft from the PVI to the design point, curve length must be 687.22.

#### Problem (2)

A +1.75% grade intersects a -2.25% grade at 32+50.00 and elevation 1015.00. An existing overpass is located at station 31+56.50. Its underside elevation is 1022.50 ft. What is the minimum curve length which will provide 12.00 ft of clearance under the overpass?

Length = 908.25 ft, *computations are left to the reader.*

(The design elevation is 1022.50 - 12.00 = 1010.50 ft)