(Phil henshaw) "What kind of information might indicate the approach of common resource limits? How would that be different from evidence that other users are breaking their agreements? As independent users of natural resources tend to have less information about, or interest in, each other's particular needs than, say, cyclists in a peloton, how would they begin to renegotiate their common habits when circumstances require it?"
Here is a short essay that looks at Phil's questions of resource consumption from the perspective of a peloton analog. It doesn't seek to answer the questions, but rather proposes a model in which to analyze them. It may be rather simplistic against the backdrop of sophisticated economic theory, but as a very real system, I suggest the dynamics of pelotons may provide insight into them. The scope of my essay may also be overly broad, and in that respect, incomplete, but my hope is that there are a few kernels that may assist Phil's analysis, or are at the very least, interesting. Information exchange, resource consumption and sharing in bicycle pelotons: a model for analyzing competitive systems Hugh Trenchard Bicycle racing is by definition competitive, and involves strategies for the cooperative distribution and exploitation of individual and collective resources. Individual resources exist in the form of energy available for consumption within a rider's body, either in the form of glucose stored in rider's livers and muscles, or body fats, and the physiological mechanisms which allow riders to expend that energy. Rate of individual resource consumption may be reduced by drafting, which occurs when riders are positioned in zones of lower air pressure, either directly behind others riders', or at angles to the wind direction. Riders in drafting positions reduce energy expenditure by as much as 30 - 40% over a rider in front at 40km/hr, depending on positioning within the peloton (Hagberg and McCole, 1990). Reduction of energy expenditure in drafting positions is also a collective, or shared resource. It is a collective resource when riders in competitive situations either cooperate or exploit this resource to maximally reduce their own individual resource expenditure or the expenditure of allies. Allies may be team-mates, but are also frequently competitors from different teams who cooperate when a peloton has split into groups, thereby temporarily becoming allies to achieve specific objectives, before again becoming competitors. The relative and continuous balance between cooperation and exploitation occurs most notably when a peloton has split into groups of two or more, and the objective of group(s) ahead is to remain ahead of following groups, while the reverse objective exists for groups behind, which is to reintegrate groups ahead. In situations like these, free-riders, quite literally, are prevalent, repleat with a number of modes of punishment. A more detailed account of that, however, is beyond the scope of this discussion. In the course of their resource consumption, the information cyclists receive or generate is largely visual. There is also vocal information, and, at the highest levels there is nearly always communication exchanged between riders within the peloton and sources outside the peloton (coaches or "director sportifs"), via radio contact - an advancement in racing tactics that has developed and been allowed in races for roughly 20 years now. Generally riders have limited global information due to obstructed viewing (i.e. blocked by riders surrounding them) and primarily receive only local information about the riders immediately surrounding them. One reason (albeit a secondary reason) for advancing or falling back within a peloton is to gather information about the positions of competitors. Some of this information may be relayed verbally through information links within the peloton (other cyclists), or riders acquire the information by visual observation, or through radio contact. The information riders seek is primarily threefold: 1 competitor positioning 2 apparent rider resource consumption 3 course constraints 1. Competitor positioning This is determined by a. local observation of riders in immediate 360 degree visual field, where course topography is flat b. partial or complete global observations of peloton where elevation and course configuration allow visual information to be obtained from higher or lateral vantage points (e.g. if a cyclist is near the rear of a descending peloton on an open road, the rider has a clear view of cyclists' positions ahead); c. positional information may also be gleaned by implication, namely if a cyclist is at the front, he or she knows all her competitors are behind, and will see them if they try to pass. Similarly, but more anxiety causing, if a cyclist is at the back, he will know all competitors are ahead of him. 2. Resource consumption Information about resource consumption is evidenced by competitors' apparent discomfort, such as facial contortions, body positions, or by other indicators such as failures to take pulls at the front (during cooperative situations), struggling to hold minimal distances between wheels, deteriorating pedalling form, poor gear ratio selection, or observations about fluid intake or food consumption during the race. For example, if a rider has lost his water bottle at a critical point, others will have exploitative information about his sugar levels. 3. Course constraints This refers to the physical course and its changes: is there a hill approaching, is there an obstacle approaching, is there a bend in the course; how strong is the wind, and from what direction is it coming? In road racing, courses may be out-and-back or point-to-point, and change continuously and, aside from general course information obtained before commencing the race, course predictability is relatively low; in road circuit races, which may consist of several loops of a course of, say, 1 km to 15km or more, the course repeats regularly and so there is a greater degree of course predictability, in addition to information obtained before hand; a track course is oval, is either 250m or 333m long and is banked, and thus is highly regular and allows the greatest degree of predictability and available global information. All of these factors provide clues as to when individual and shared resource limits are approaching. These limits arise primarily in the following situations: 1. Shared resources are lost, such as during sufficiently steep hill climbs, when speeds fall to a point when drafting advantage is negligible (<16km/h (Swain, 1990)) and differentials between cyclists'respective power output capacities overwhelm the equalizing effects of any drafting advantage; 2. Shared resources are not-negotiated, such as during a final sprint for the finish line, or other situations when speeds are beyond a certain threshold between sets of rider causing peloton disintegration** 3. Shared resources are too dangerous, such as on high-speed descents, where collisions with others, obstacles or proceding on trajectories outside physical course parameters (e.g. plummetting over a cliff on the outside of a hairpin turn!) are avoided by maintaining distances outside of drafting range). Applying the peloton model A peloton may thus be viewed as a basic resource sharing system which may provide clues as to how resources are shared and consumed in other systems, especially competitive ones - which arguably most such systems involving resource consumption are. I suggest that, in principle, when we investigate the question of how to re-negotiate resource sharing, we can first seek to understand the nature of these categories of information: competitor positioning, apparent resource consumption, and course constraints. These factors by themselves are nothing new, but applying a peloton model to other systems, at least in any rigourous fashion, is new. When information about these factors is not available globally, as is most often the case, we can examine features exhibited by other systems of resource sharing that may be analogous to what occurs in pelotons. For example, energy in a peloton is reduced, essentially, by following the paths of other riders. Any natural system in which path following serves to reduce energy expenditure is analogous to a peloton. As a simple example, when a forager tramples a path through snow to a food source, that forager expends more energy than all that follow in the established pathway. Forager dynamics may be examined against the model of peloton dynamics and its pattern thresholds. In pelotons, thresholds exist where observable collective emergent behaviours are exhibited, described by the following phases: Phase 1 Transitional As cyclists set off at the beginning of a race, there is a period during which the speeds are sufficiently low for cyclists to have no physiological necessity to draft one another, as they are all well below individual pain thresholds or maximal power output capacity. The phase is characterized by roughly random internal peloton movements, or low-pattern formation within the peloton. Phase II Rotational As speeds increase, a transition occurs whereby resource sharing becomes necessary as cyclists approach (but remain below) pain and maximal output thresholds, and when the collective drafting resource is exploited. In this phase, a balancing occurs between energy expenditure and optimal position within the peloton. Because it is a competitive situation, it is better to be positioned as close to the front as possible. As this is a continuous imperative, rotational movements occur within the peloton, when riders move up and down the peloton, or are caught in "eddies" whereby they advance for relatively short distances within the peloton, before being shifted backward again, and then attempt to move forward again. These movements occur while riders attempt to use as little energy as possible to advance. So, where there are riders who shift to the outside of the pack (facing the wind by doing so), other riders will follow in their draft. The result is a rotational pattern whereby riders advance up the sides for relatively long stretches, while riders drop back within the peloton, and while within the peloton there are smaller-scale rotations, or eddies. The rotational patterns which emerge are analogous to the roiling effects of boiling liquid, as riders "heat up" by greater energy expenditure in moving forward, and cool down by reduced energy expenditure in moving backward through the peloton. Incidentally, this pattern is also similar to rotational patterns observed in emperor penguin huddles (Ancel, et al., 1997; Stead, 2003). Phase III Stretching A third phase transition occurs when the pace shifts up beyond another threshold, whereby the speeds are too high for there to be continuous rotational movement within the peloton, and the peloton stretches into a single line. This phase, while easily observable, is a precurser to a final transition where the peloton begins to splinter: individual riders fall off the back, or separations occur in the line of riders which following riders cannot bridge, resulting in regions of peloton instability and loss of cohesion. Phase IV Disintegration In this last phase riders fall outside of drafting range, and cooperation (or coupling between cyclists) disintegrates as cyclists become either in direct competition with the each other. This phase is analogous to the phase change between liquid and gas, as cyclists move outside of drafting range, thereby de-coupling. In bicycle racing this phase is usually temporary, however, as speeds drop quickly, and, through a series of agglomerations, the entire peloton either reintegrates or sub-groups form which cooperate internally but which are also in direct conflict with each other. In the case of sub-groups in conflict, it is the objective of chasing groups to reintegrate groups ahead, while it is the objective of groups ahead to stay ahead of chasing groups. Conclusion Although a peloton is a resource sharing system consisting of human agents with competitive human objectives, it is also an energetically dynamic system that exhibits self-organized thresholds and emergent patterns. It is reasonable to speculate that when we look at other natural systems in which resources are shared and exploited, there are analogous patterns which emerge at certain energy consumption thresholds. The physical manifestations of such thresholds and emergent patterns may not be easy to identify, but here we have a microcosmic model of a competitive, self-organizing system which may provide some clues. ____________________________ References Hagberg, J., McCole, S. The Effect of Drafting and Aerodynamic Equipment on Energy Expenditure During Cycling, 1990, Cycling Science, 2, p. 20 Swain, D. Cycling Uphill and Downhill. Sportscience 2(4), sportsci.org/jour/9804/dps.html, 1998 (2682 words) **which threshold I have previously argued on the basis of a coupling model, having called it the peloton convergence ratio (PCR). PCR =(Wa-Wb/Wa)/D where Wa is the maximum power output (watts) of cyclist A at any given moment; Wb is the maximum power output of cyclist B at that moment (assuming Wa>Wb), and D is the percent energy savings due to drafting at the velocity travelled: Trenchard, H., Mayer-Kress, G. Self-Organized Oscillator Coupling and Synchronization in Bicycle Pelotons During Mass-start bicycle racing. Book of Abstracts, International Conference on Control and Synchronization of Dynamical Systems, Oct 4-7, 2005, Leon, Gto, Mexico. Ratios of =<1 and cyclists remain coupled; >1 and cyclists de-couple, when points of instability in pelotons occur and peloton disintegration begins. Ancel, A., Visser, H., Handrick, Y., Masman, D., Le Maho, Y. Energy Saving in huddling penguins. Nature, Vol. 385. 23 Jan 1997; Stead, G. An Artificial Life Simulation to Investigate the Huddling Behaviour of Emperor Penguins. Submitted in partial fulfillment for the degree of MSc in software systems technology. ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org
