## Help wanted for interesting "Road Curves" project

Hi All:

I'm working a road engineering project (of sorts), and a critical part of the project is attempting to come up with a formula or method for objectively quantifying the "twistiness" of a given stretch of road.

By "twistiness," I mean the "curviness" of the road—not just the number of curves (which in itself would be hard to judge, because what do you count as a curve?)...but the overall degree of "deviation" of the curves from a straight line.

I confess I'm a complete math idiot—I'm a writer by trade (so that pretty much says it all, LOL).

I initially thought I could use the following equation for a given stretch of road:

Road distance (start to finish) / Straightline distance (start to finish).

This seemed like a logical way to do it. But then a friend said "What if the road loops around, and the finish is right next to the start?" He's right—that would render the above equation's result worthless!

So I thought, okay, perhaps I could establish some sort of precondition, like "The equation only works on roads that over their length don't stray beyond "x" degrees to either side of a straight line...but then I know that's starting to sound very vague and unscientific.

Another issue I thought of is this: What if one road section is 60 miles long...and a different road section is only 5 miles long...but they both have the same "twistiness factor?" Does that impact the equation at all? (Or would the result be universal regardless.)

I don't know if this is a good place to post this question...but a math forum seemed like a good place to start! I further don't know what type of math this kind of question involves—Geometry? Trigonometry? Algebra? All of the above?

Even not being a math person, this seems like a thorny challenge, because roads by their very nature vary wildly in their "curviness."

My end goal (if possible) is to come up with a nice neat equation that will spit out a number or percentage that allows me to quantify a road's "twistiness" and then use that number to compare the twistiness of many roads.

If anyone has any ideas on how to approach this challenge, I'd be grateful. And if there any better places to post this kind of question, please let me know! (It sounds like it could be a great math project for a high school or college student!)

Thanks,
Scott