Oh yes, that's a great insight. Traveling over the crest of a hill, a peloton might naturally stretch out, and then a second-order destabilizing effect could naturally split it into two. So I withdraw what I said, as long as you're only modeling the shape of the single peloton, and leaving breakaways for a more complex model. (You did write this at one point but most of the rest made it seem you wanted to model breakaways too.) It is not enough just to have some stronger riders who eventually diffuse to the front and catalyze a fission, because that is not a breakaway. Note that I distinguish between breakaways and "natural" divisions. The first is an intentional act of riders mostly as a psychology or manipulation strategy, whereas the other arises from riders pacing themselves differently out of necessity. (cc to Henry Baker) On Mon, Jul 12, 2010 at 10:04, Henry Baker <hbaker1@pipeline.com> wrote:
Robert:
You are certainly correct that energy management strategies have significant effects upon any real bike race.
However, I'm trying to find extremely simple models that account for some of the most obvious effects -- including the formation of a peloton in the first place. In an analogy to differential equations, I'm trying to find the equation _before_ forcing functions (e.g., strategy) are added in.
Even before strategies would be the effect of undulating terrain -- i.e., the elevation profile of the course. This type of "forcing function" could easily explain some of the fissioning of the peloton, as steeper terrain reduces the relative importance of the attraction force and the second-order wind resistance effect.
At 06:52 AM 7/12/2010, Robert Munafo wrote:
[...] Without
modeling them, your model with not exhibit the typical behaviour of a peloton (even ignoring breakaways) when it stretches and occasionally fissions or gives birth to small groups.
If you force the fissioning behaviour through changes to the simple model, you'll have a peloton that fissions for no relevant (strategic) reason, and therefore will split too often once an energy budget strategy model is added.
-- Robert Munafo -- mrob.com