Fundamentals of Transportation/Horizontal Curves/Solution

TProblem

Problem:

A given curve was very poorly designed. The two-lane road used has a lower-than-average coefficient of friction (0.05), no superelevation to speak of, and 4-meter lanes. 900 kg vehicles tend to go around this curve and are stylistically top heavy. County engineers have warned that this curve cannot be traversed as safely as other curves in the area, but politicians want to keep the speed up to boost tourism in the area. The curves have a radius of 500 meters and a design speed of 80 km/hr. Because the vehicles using the curve are top heavy, they have a tendency to roll over if too much side force is exerted on them (the local kids often race around the curve at night to get the thrill of "two-wheeling"). As an engineer, you need to prove that this curve is infeasible before an accident occurs. How can you show this?

Example

Solution:

The stated speed is 80 km/hr. The easiest way would be to prove that this is too high. We will look at the innermost lane, since forces will be greater there. Using the general curve radius formula and solving for v, we find:

$R={\frac {v^{2}}{g\left({e+f_{s}}\right)}}={\frac {v^{2}}{9.8\left({0.05+0}\right)}}=500-(4/2)\,\!$

$v=15.62\ m/s=56.23\ km/hr\,\!$

80 km/hr is much greater than 56.23 km/hr, which by default means that more force is being exerted on the vehicle than the road can counter. Thus, the curve's speed limit is dangerous and needs to be changed.