Vertical Curve

1. A 400-ft equal-tangent sag vertical curve has its PVC at station 100 + 00 and elevation 500 ft. The initial grade is −4.0% and the final grade is +2.5%. Determine the elevation of the lowest point of the curve.

a) 495.077 ft b) 495.250 ft c) 485.231 ft d) 492.043 ft

3.63 A horizontal curve is being designed around a pond with a tangent length of 1200 ft and central angle of 0.5211 radians. If the PI is at station 145 + 00, determine the station of PT.

a) 168 + 45.44 b) 156 + 45.44 c) 173 + 94.00 d) 156 + 72.72

2. A car is traveling over a 1400-ft vertical curve. One of the passengers decides to calculate the current offset from the PVC. By looking at the onboard navigation device, the passenger knows that the car is 750 feet from the PVC. The initial grade is +5.5% while the final roadway grade is +3.0%. What is the current offset?

a) 4.38 ft b) 17.50 ft c) 17.08 ft d) 5.02 ft

3. You are designing a highway to AASHTO guidelines on rolling terrain where the design speed will be 65 mi/h. At one section, a +1.25% grade and a −2.25% grade must be connected with an equal-tangent vertical curve. Determine the minimum length of curve that can be designed while meeting SSD requirements.

a) 864.30 ft b) 645.00 ft c) 674.74 ft d) 673.43 ft