The shortest distance

If you have done much running, then you are familiar with the concept of running tangents and please skip to the next paragraph.  It follows the idea that the shortest distance between two points is a straight line.  Instead of following the right or left hand side of the road/trail, look ahead and choose a path that goes straight through the curves.  I wouldn’t recommend this on a road unless it is closed off, but it works great on trails.

This season I’ve gotten back to running our local trail as the crushed gravel is easier on my joints and most of it is shaded.  It does wind a lot and I use that to practice running tangents.  It’s not that taking the inside of curve is complicated, but as you get more and more tired it is progressively easier to just stay on one side.

It would be easier for me if this was my personal trail and no one else was allowed.  Alas, that isn’t the case and I find myself having to dodge walkers, runners, dog owners and baby strollers.  Bicycles aren’t supposed to be on the trail (I’m not sure why), but they do allow baby strollers, even the double-wide model that takes up most of the trail.  I digress though, let me save that rant for another day!

It is an obvious decision, if the road curves to the right, to take a straight line and end up on the right side of the trail.  I’ve tried doing the math in my head while I run as to how much distance I’m saving.  At first I thought it was just twice the width of the trail.  I can’t imagine that is accurate or correct.  Perhaps I need to get out there with a tape measure.  I’m sure the other runners would appreciate that!

There is bound to be a mathematical formula to calculate the distance for staying in the lane vs. running the tangent.  I suspect it will require values for things I don’t know, such as the width, length and curve of the trail, which puts me back out there with my tape measure.  Instead, I resigned myself to the fact that I’m taking the shortest distance and not knowing by how much.

Here then is the real question, one I have posed to a math wiz, a math wiz runner, and my son who is burning up money at UT Austin as a computer science major:  What if the curve is just a little curve such that running a straight line wouldn’t cause you to change sides of the trail?  Maybe it just moves you out of your lane by a foot or so.  Taking the straight line would be shorter, but here is the interesting twist:  the trail on this sorter path isn’t as nicely worn as the outer part of the trail and it takes a bit more energy to run on it at the same pace.

This is where it would be helpful to know how much distance I was saving by running the tangent.  If I was saving 2 steps by running the tangent on the harder part of the trail it might be worth it, whereas if it was only a few inches it might not.

Everyone has their own opinion, but no one, even the math wiz runner, has one based on any sort of math.  Until I hear differently from someone who can speak with authority and a conviction I can believe, I’m going to stick with my gut and only run tangents when I think they will shorten my total run time.