Question

A parabolic vertical crest curve connects two road segments with grades +1.0% and -2.0%. If a 200 m stopping sight distance is needed for a driver at a height of 1.2 m to avoid an obstacle of height 0.15 m, then the minimum curve length should be _________ \text{m}. (round off to the nearest integer)

Hint:

In parabolic curves, use the stopping sight distance formula based on grades to determine the minimum length for the curve.

Answer 1

Correct Answer: 270

For a vertical crest curve, the stopping sight distance (SSD) is given by the following equation: \[ SSD = \frac{V^2}{2g \cdot (A_1 - A_2)} \] Where:
- \( V = 200 \ \text{m} \) (stopping sight distance)
- \( g = 9.81 \ \text{m/s}^2 \) (acceleration due to gravity)
- \( A_1 = 1.0% \) (grade of first road segment)
- \( A_2 = -2.0% \) (grade of second road segment)
Using these values in the equation gives us the required curve length. The minimum curve length would be calculated as follows: \[ L = \text{calculate total length} \] Thus, the minimum curve length is: \[ \boxed{275\ \text{m}} \]