So, stepping back...what do I mean by running the tangents? Well, to understand that, one must understand how a race is calculated by the race director. A race is measured by the shortest distance along the route. This rarely follows the drive a car would take on the road.
Its natural to run in a "lane", but this encourages many racers run a longer distance and thus increase their time for the race. A tangent is a straight line that just touches a curve. In other words, its the shortest distance possible between point A and point B while staying within the confines of the road/course marks. When a race-course is measured and certified, the course follows the tangents to the curves, and by running those tangents, you run the measured distance. If you don't run the tangents, you run a longer distance. Look at the diagram that follows:
The black line clearly delineates the road. A car/bike will follow the green (assuming you are not in England!). If you want to minimize the distance you are running, you should run the red line.Strangely, I was running the tangents, or so I thought. I remember several moments during the race where it felt as if I was the ONLY person doing so....so I can only imagine how long of a run most raced!
Now, why would you NOT want to run the tangent? There are some obvious benefits to not adhering to this rule 100%. Some prefer to run the yellow line...its not cambered at all. So, there is less chance of knee injury, but then again, it can be slippery (more of an issue for the barefoot runner). Also, running the tangent can be riskier since its often more crowded and there is more debris, and since its more crowded you can't always see the debris that you shoud be dodging!
Obviously, you don't want to run more than you need to if you are running for time...and who isn't in a race! At the time you save is not as important as caring for your safety....so its a balancing act.