**"The shortest distance between any two points is a straight line"**

I ran a 1/2 marathon over the weekend, part of which took place on a very wide 3-lane highway. I noticed that most of the runners were sticking to the far-right lane, as if they were driving in a car. This put them on the outside of some long sweeping corners.

However when they measure a course, they actually use the

**shortest path**.

How do you figure out the shortest path? Look far ahead to where you're ultimately trying to go and race toward it. This will typically mean making as straight a line as possible from the inside of one corner to the inside of the next.

Of course, you don't want to be cutting people off, so be aware of who is on your right or left... I'm looking at you, Mr. iPod!!!

**How much can this save?**

The better question is - how much is taking the long way costing you! Every extra step you take is a step away from your goal time, or worse, away from a Boston Qualifier.

The cost depends on the course - it is highest on a wide course or one with many corners, lowest on a narrow straight course. Once you have your mind dialed in to take the shortest path, though, you'll find you naturally gravitate toward it and it's really just "free speed".

## 14 comments:

Nice write up. I try to keep a strait line but it's usually a challenge at the start of any race. Too many people!

As much fun as it is to zig-zag through people collisions are not as much fun.

Jono: There was blurb in iRun magazine about this. It basically said if you had a circular 42.2km course that was 10 metres wide and you ran on the outside curve the whole way, you'd add less than 70 meters to the total distance. Usually not a big deal, but I met a guy at Vulture Bait who once missed qualifying for Boston by 22 seconds! Thet 70m would have helped in that case!

I wonder if it's possible to focus on your tangents so much that it drains your energy that you'd need later on in the race...

@Mo - that's interesting, I didn't read their article.

Did they say why they chose one large circle?? That's not the worst case scenario, the curve would be very gradual. A twisty course could be quite a bit worse...

Example: a college track is 400m in lane 1, 447m on the outside, a difference of more than 10%! Now THAT is an extreme example... :)

@Kieran - well my next post on Race Strategy will have to deal with not blowing up before the end!!! :)

In the most extreme case, a straight line could be 1/3rd the distance of following the right side of a path. here's my logic. The worst case is on a path that alternates 180 degrees of a circle going clockwise with 180 degrees of a circle going counter-clockwise. With a wide enough path, you could follow a straight line. The short route is the diameter of the circle, and the long route is 3.14 X the diameter of the circle. This really is academic though since such a course does not exist, and nobody except Kieran would likely take the long route.

Strange what goes through one's head while out there. I ran the full marathon same day and was absolutely perplexed by the long paths many/most took as you observed Jono. But maybe I am crazy - I stuck within the rumble strips on each side rather than the edge of the road as I figured the measuring device would not have crossed the strips and did not want to take shorter path than the official distance.

But would the measuring device have crossed the rumble strips and gone up to the guardrail?

computing dijkstra's algorithm while racing??? :-D

@Double Bellybuster - I'm not sure exactly how they deal with the shoulder... good question. I assumed it was part of the course and used it, and I bet the elites did too. If they won't DQ you for it, it's fair play! :)

The (theoretical) circular 42.2km is indeed the worst case scenario, in the sense that if you run the worst (outside) line the whole way you are always the maximum distance from the perfect (shortest, inside) line. In any other scenario, including the extremely twisty one, the worst and best lines intersect once for every 90 degree turn.

On, for instance, a two lane road course, the ratio of course width to race distance is much less than that of a 400m track, so the difference (as a percentage) between worst and best lines is much less significant in a marathon than in a 400m race.

Which isn't to say looking for the best line isn't of some value, but you have to weigh it's significance with things like shade, camber of the road, etc...

A twisty road is worse. In fact upon reflection, I was able to find a theoretical course with a 42.2k shortest path and an infinitely long path following a lane. :) Too much time on my hands.

Imagine these shoe laces are a race course...

http://img.alibaba.com/photo/50098135/Zig_Zag_Ric_Rac_.jpg

The shortest path is the straight line, the path hugging one side or the other is almost twice as long. If the bumps on the zigs and zags were made to be even larger, you would still have the straight line as the same length, but the person following the side would be going even further. Extend the bumps even more and you get to the theoretically infinitely long path...

A twisty road is much worse.

The theoretical 42.2K circular course mentioned is a bad example to use for a waste calculation. If you were running such a course, the arc would be so gradual that one would not even realize they are not running a straight line.

Check this out, Jon. The course certification states that we're to be running on the paved shoulder on the expressway:

http://www.acroad.ca/certificates/2016/ON-2016-007-DRY.pdf

Whhhaaaat? So I was cheating?? Lol

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