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:

The power (or "mass", in your falling-through-air analogy) of the cyclists changes *over* *time* and from one cyclist to another due to their strategies. As in running and skating, etc., competitors apply a strategy to budget their energy over time. On-the-spot changes in strategy and psychological effects are usually involved (the tortoise and the hare).

These energy strategies are a large part of the cause of breakaways. 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.

On Mon, Jul 12, 2010 at 00:36, Henry Baker <hbaker1@pipeline.com> wrote:

...

[...] Anyone who has watched bike racing for more than a few moments quickly notices that most of the cyclists coalesce into blobs called "pelotons". This is because it is much more efficient (requiring perhaps only 66% as much wattage) to travel in groups, sharing the load of breaking the wind, than it is to travel individually. However, blobs occasionally break off ("break away") because they want to go faster, with larger groups being able to go faster more efficiently than smaller groups. [...] The problem is that any larger ensemble should almost _always_ fall faster than a smaller ensemble, which would eliminate the possibility of breakaways entirely.

Perhaps there are several different species of cyclist molecules, with different masses & attractive forces. (Assume for the moment that the cyclists don't form into color-coded teams!!) I.e., some cyclist molecules are "better"/"fitter", so they have slightly heavier masses (they have larger terminal velocities even when on their own) and slightly smaller attractive forces (they are more willing to break away). Then if statistically a group of these more massive, less attractive cyclists molecules found themselves together at the front of the peloton, then they could indeed "break away", and possibly fall faster than the larger peloton. [...]

-- Robert Munafo -- mrob.com