Tour de France and the dynamics of bicycle pelotons

After spending three months in Durham, England, and taken a vacation from blogging for six weeks (amazing what it does to the hit count on a blog!!), I thought that I'd restart with a look at the dynamics of the peloton that plays such a role in bicycle competitions since tonight is the next to final day of the Tour de France. Kudos to the apparent victor, British Bradley Wiggins!

I found a very interesting paper "The self-organized complex dynamics of bicycle pelotons," by Hugh Trenchard.  I do not have not got a citation for this paper, it appears to be a book chapter submission under revision, and is available here on the WWW. The link to the author on the top of the first page says that he's interested in self-organized complex adaptive systems, with special emphasis on the pelotons.  An eclectic interest and a very interesting paper. I hope that it does get published!

Briefly, a peloton is a group of cyclists riding in a group.  It can consist of as few as two cyclists, but amongst the competitive cycling community, it usually means a large group of cyclists riding in (frighteningly close) proximity. An indication of the massiveness and effects of the peloton was indicated today by a radio commentator who was at the roadside as the cyclists emerged from the French Pyrenees, describing the strong wind that they generated as the blew by and the smell of burning rubber from the hundreds of cyclists all using their brakes at the same time!

Cyclists in the front and, to a certain extent, on the sides, experience the highest air pressure and resistance to their motion, and cyclists behind the leaders or inside the periphery experience a reduced air pressure. Riders who are behind the leaders are "drafting." According to Trenchard's paper, the energy saved by being in a drafting position is reduced by 18% at 20 mph, 27% at 25 mph, and 39% at 40 km/hr for a peloton of eight riders. Cycling is an incredibly strategic competition, and stage races like the Tour de France that extend of many days and weeks are a complex mix of individual and team strategies. No rider can sustain the lead forever, and so riders on a team change leads frequently. If one individual has been designated as the team leader who all others are to support in order that the victory be his/hers, then team members subordinate their own desire for individual victory to support a team victory. This has had some interesting dynamics in the last days of the current Tour.

Trenchard presents two models for the dynamics of the peloton. The first is an energetic model that looks at individual, coupled, and globally-coupled energy output thresholds. The second is an economic model that incorporates competition and cooperation dynamics, using basic game theory.

Without going into any detail, I'll summarize a bit of the results of the energetic model.  Phase I ("Disordered-relaxed") begins immediately upon start of the race as the cyclists begin to accelerate in a pack.The pack is fairly disordered, low density, unstable, and undergoing increasing speeds and pack density. This phase can occur during the outset of a race or during temporary relaxations after periods of high energy output.  This phase can last only a few seconds in some instances before the onset of Phase II ("Peloton rotation/convection rolls"). In this phase, speed, power output and energy expenditure also increase but are not at the physiological thresholds of the riders. In this phase, the group has a maximum density. The system exhibits convection roll dynamics called "peloton rotations," not unlike the rotation of Emperor Penguins in the Antarctic or convection in Rayleigh-Bernard heating. This phase is stable and comprises the largest proportion of time during a typical race.

In Phase III ("Single paceline, synchronized") speeds are synchronized and riders align in single file. This is a phase of high power output and energy expenditure and riders are very near their physiological thresholds.

In Phase IV ("Disintegrated") riders are exhausted and the peloton disintegrates. There is a low density but still fairly high energy output. This phase is unstable, and may lead to a reintegration through phase I dynamics.