I've incorporated a deceleration algorithm that allows us to show how much a following cyclist needs to decelerate in order to stay at or below his/her threshold if a leading cyclist drives the speed of the peloton too high for the following cyclist. This is a significant development over previous models, one of mine, and one by Erick Ratamero. Basically, I've incorporated the new deceleration algorithm into Ratamero's model, for a new model.
Ratamero's model is still sound because it models cyclists' overall energy expenditure in peloton conditions, while this new model allows us to see changing peloton dynamics as group speeds change throughout the course of a race. Nor is my earlier model invalidated, since it applied the same basic principle I use in the new model, except that the old model did not apply any actual speed, power or MSO data. That said, while I could defend the basic principles of my old model, we can now essentially discard it in favor of this new model.
To demonstrate the new model, first take a look at the link below of accelerated footage of the 2013 BC Championships women's Points Race. Pay attention to the oscillations between stretching (single-file) and compact formations. The accelerated motion of the video is about 2X normal speed. I hope the "Ride of the Valkyries" background music isn't too distracting!
Points race - accelerated
Keeping the dynamics of that race in mind, below is a simulated version of the same race, accelerated to about twice as fast again so you can see the whole race occur in a short time. I've incorporated the speed parameters that I derived at two timing places per lap, and encoded it into the simulation.You can see the speed changes according to the power graph to the lower right. When the power output spikes, you can see certain cyclists are forced to decelerate relative to others. When the speed relaxes, the peloton reintegrates and its density increases. This relaxation oscillation is well modeled by the new algorithm.
The numbers you see on the "backs" of the riders are their "maximal sustainable outputs" (MSOs), or their maximal sustainable power for a duration between 30 seconds and 5 minutes. These are derived from the cyclists' 200m sprint times, and multiplied by a value that reflects their sustained maximum output during the race for between 30s and 5 minutes.
simulated peloton 14 cyclists
With that fairly accurate simulation, we can try some experiments. For example, we can increase the size of the peloton. Here is a view of 50 cyclists with the same speed profile as for the 14 cyclists above.
simulated peloton 50 cyclists
Now let's take a look at 100 cyclists (link below). I've only included part of the video here, since the simulation runs slower with 100 cyclists, and the point is made with a slightly abbreviated version. Quite a bit more impressive, though, to see a much larger group and its dynamics, using the same speed profile as for the original 14 cyclists. What is interesting with 100 cyclists, which is not so easy to see with smaller the simulated pelotons, is that in the position profile graph we can see some evidence of the "convection" dynamic that I have spoken of in previous posts. It seems that it may be a dynamic that only clearly emerges at some threshold peloton size and speed. You can see this somewhat for 50 cyclists, but still it seems clearer in runs of 100 cyclists.
simulated peloton 100 cyclists
I am looking to have the new model published (with the same three collaborators on our last published paper: Richardson, Ratamero, Perc). In this new paper, we will show how the model demonstrates sorting of the peloton into groups, and some results to this effect.
In future, we still need to investigate and report more definitively on the convection dynamic. So that could be the subject of the next paper - or I am also interested in obtaining some more evidence of the hysteresis effect I observed a few years ago, and presented in principle at an AAAI conference.
I'm also now interested in developing a peloton solution to the tragedy of the commons (ToC), having been somewhat inspired by Francis Heylighen's recent efforts to show a self-organized solution to the ToC (not yet published).
Of course there is also some fluid dynamics analogies I want to develop, and recently I have been thinking about Stokes Law and particle settling as somewhat analagous to peloton sub-group sorting. Is there some sort of equivalency between the size of a particle moving through fluid, and the MSO of a rider?