# Fundamentals of Transportation/Vertical Curves/Homework

## Homework

1. Which conic section forms the basis of vertical curves?

2. A section of a roadway goes up a 6% incline and includes no horizontal curves. Point A, which lies along this incline, has a station marker. Using a wheel measure, you measure the distance along the centerline from point A to the next PVC and find it is 880 meters. If point A is at Station 0+700, what is the station of the PVC?

3. Identify 4 criteria used to set the minimum length of a sag vertical curve (4 points), place them in order from most to least important (1 point):

4. An equal tangent sag vertical curve joins a –0.5 % grade with a +3.0% grade. Assume H=0.6, headlights are aimed upward at an angle of 1 degree

If the PVI of the grades is at metric station 10+100 and has an elevation of 300 meters, using the headlight criterion determine the station elevation of the PVC and PVT for a design speed of 100 km/hr and a coefficient of friction of 0.30. Draw a diagram with the values of your solution.

5. A crest vertical curve on a 2-way, 2-lane road is designed for 100 km/hr. The grades are 1.6% and – 1.4%. If the tangents intersect at metric station 2 + 000.00 (where 2 represents 2 km and 000.00 is 0 meters) and at an elevation of 100 meters above sea level, determine the stopping sight distance, the length of the curve, and the stations and elevations for the Beginning and End of the Vertical Curve. Assume h1 = 1.1 m and h2 = 0.15 m, perception reaction time is 2.5 seconds, f=0.30.

Draw a diagram with the values of your solution.

6. An equal tangent sag vertical curve joins a -2.5% grade with a +3.0% grade. Assume H=0.67, headlights are aimed upward at an angle of 1 degree. If the PVI of the grades is at metric station 5+750 and has an elevation of 0 meters, using the headlight criterion determine the station elevation of the PVC and PVT for a design speed of 120 km/hr and a coefficient of friction of 0.31. Draw a diagram with the values of your solution.

7. You have been asked to design an equal-tangent vertical curve to connect grades of the +1.0% and -2.0%. The design speed is 113 km/h. Assume a value of 3.4 m*s-2 for deceleration rate, a value of 2.5s for reaction time, and a value of 9.807m*s for gravitational constant.

A. Calculate the Stopping Sight Distance (SSD) if we assume vehicles travel at the design speed.

B. If we take this SSD as the required minimum Sight Distance, determine the minimum length of curve. (According to AASHTO, we assume a driver eye height, H1, of 1.08m and a roadway object height, H2, of 0.6m).