crash modification factor for horizontal curves

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crash modification factor for horizontal curves

My local jurisdiction is located in the Sierra Nevada mountains and foothills we deal extensively with roadways with horizontal curves. Many of our improvement projects in the past have addressed this issue by increasing the radius and reducing the length of curves. Chapter 10 of the HSM deals with the predictive method for two lane rural roads. On page 10-27 there is a formula for determining the crash modification factor for horizontal curves (10-13). This formula uses curve length and radius to determine the CMF. Using the formula, we am coming up with the result where a longer curve has a better (lower) CMF than a shorter curve given the same radius.

For example – a curve with a radius of 500’ and a length of .1 mile has a CMF of 2.03 while a curve with radius 500’ and length of .2 miles has a CMF of 1.52. This is a significant improvement by doubling the length of the curve. Another example -- a curve with radius 500’ with a length of 0.2 mile has the same CMF as a curve with a radius of 1000’ with a length of 0.1 mile.

In a test of the formula, a project that reduced overall curve length and increased curve radius the calculations show a higher CMF after the project. This result is counter intuitive. Any assistance that you could provide in helping us understand the formula would be appreciated.
sholloway

Posts: 1
Joined: Thu Feb 10, 2011 12:06 pm

Re: crash modification factor for horizontal curves

Sholloway wrote: “a longer curve has a better (lower) CMF than a shorter curve given the same radius.” He also wrote: “In a test of the formula, a project that reduced overall curve length and increased curve radius the calculations show a higher CMF after the project. This result is counter intuitive.”

About the first comment, we should not forget that CMFs are the representative of crash risks per length of highway segments. It means that even though from two curves with the same radius the longer one has smaller CMF it does not mean that the longer curve carries less crash risk in total. In the calculations of the predicted number of crashes the length of segments are multiplied by the CMFs. One theory behind the fact that by increasing the length of the curve you decrease the crash risk per length of highway is that the sources of crash risk on curve sections are two. One source is the action of “entering into and exiting out of the curve” and the other is the action of “driving along the curve” (I’ve heard this from Ezra Hauer but I am not sure if it originally his). If we consider two curves with the same radius but different lengths, the part of the crash risk that comes from the second source (driving along the curve) would be the same (if we consider the risk per length of highway). However, the part of the risk that comes from the first source would be the same for whole length of curves but smaller per length of the curve for the longer curve. Therefore, in the average the risk of the crash per length of highway is smaller for the longer curve.
With respect to the second comment, in any project we also need to remember that with any curve flattening we increase the length of the curve sections but, we also decrease the lengths of the adjacent tangents. Therefore, in our comparisons we also need to consider the decreases in crashes that come from decreasing the length of adjacent tangents. The conclusion is that for any fair comparison we need to compare the total number of predicted crashes for the curve and adjacent tangents of different alternatives, not just the curve sections crashes. In sholloway’s example the overall curve length is reduced and the curve radius is increased. In real projects this cannot happen. If we are talking about the same project but different curves as alternatives for the same deflection, as we increase the radius of the curve the length of the curve would increase as well and the lengths of adjacent tangents decrease. As a matter of fact as we increase the curve radius the total length of the project affected by this (lengths of adjacent tangents plus the length of the curve) would decrease slightly. 