Thursday, November 21, 2013

A Peloton Palette

In August I took video of a number of track races at the B.C. Provincial championships. I was able to get very good video of two races in particular, the women's points-race, and the women's scratch race.  

                               Figure 1. Women's points race. 2013 B.C. Provincial championships

The two graphs below contain data from the women's points race. The top graph shows the positional changes for each of fourteen cyclists; the lower graph shows peloton speed.

The values on the left indicate the relative position of the rider: the closer to 1, the farther toward the back of the pack the cyclist is.  The closer to 0, the closer to the front the cyclist is. So, we can imagine the pack as facing downward on the page.  Ignoring the letters at the top for now (which indicate peloton phases, which I do not discuss in this post), we can see that regions where curves are most dense are periods when there was high positional change among the riders.  The regions where curves are straight and horizontal are periods when the riders maintained stable positions (i.e. they "held" their positions during these periods). 

The graph tracks very nicely how riders within the group shifted their positions relative to each other, determined simply by counting the number of riders ahead, not counting riders directly beside each other, divided by the total for a ratio <1. It is a very useful method of indicating phases of peloton dynamics. The graphs combined are a very nice static representation of an entire race, and if we follow each curve individually or pick one or two at random, we get a good sense of how they moved in the pack over the course of the race. 

    Figure 2. Top graph shows positional change among 14 cyclists. Letters at top indicate phases and sub-
    phases (not discussed in this post). The squiggly arrow at the top shows a rider who had been lapped.

Now below is a positional change graph for 16 cyclists from my Peloton 5.5. simulation. (See Figure 8 for an enlarged view of a typical simulated peloton). We can see similar regions of high positional change and periods of stability. Here the periods of stability are comparatively long-term.

     Figure 3.  Positional change for 16 simulated cyclists (PCR .49) for roughly 7 minutes of run time.

For context, below is a graph tracking one single cyclist's positional change looks like. The circle shows the cyclist being tracked, and the red graph in the middle shows its positional change over time. The curve shows how the rider started near the front of the group, gradually shifted toward the back, and then gradually shifted toward the front again. 

    Figure 4. Tracking positional change of one simulated cyclist.  There are 200 simulated riders in the
    peloton above. Red curve shows positional change of rider in circle. 

Below is a similar graph tracking 50 of 60 simulated cyclists. It is much richer, and again we can clearly see regions of high positional change and period of stability, as well as mixed phases. 

Figure 5. Positional change for 48 simulated cyclists. 

To me it is somewhat reminiscent of a Jackson Pollock abstract painting, perhaps a little like the one in Figure 6. Interestingly, Jackson Pollock paintings have been found to contain fractal patterns. Here is a link to Marcus du Satoy's discussion of this topic.

                                            Figure 6. Jackson Pollock painting 

In Figure 5 and 7 (below), we may consider mixed phases as containing "eddies", in that there are subsets of cyclists within the group who are exchanging positions, while others are holding their positions. There are gaps in the graph, which indicate regions when riders were side-by-side. As in the real life graph (Fig 2), when cyclists were directly side-by-side, they were not counted as being ahead or behind. So side-by-side riders have the same position value - these appear as "holes" is in the graph. Where we see regions of long-range diagonal movement among most of the cyclists, this indicates whole peloton rotations, much like the convection pattern I have spoken of in previous blogs, and as Erick Ratamero presented evidence for in his paper (3).


  Figure 7. Positional change for 50 of 60 cyclists, roughly 10 minutes of run time. Note the clear transitions
  between periods of high positional change periods of stability.

                                Figure 8. Enlarged view of typical peloton from my Peloton 5.5
                                model (version slightly modified from that presented in my paper "Peloton phase

I believe we are bound to see similar kinds of patterns and transitions of high positional change and low positional change in a large variety of collective phenomena. What palettes of positional change may we find among other such collectives? Where else will find the Jackson Pollocks of nature, embedded deeply within the patterns of collective interaction?

Of particular interest to me of course are American coot collectives, and I hope to do some additional research regarding coots this winter. The challenge for natural collectives like coots, or flocks of starlings or geese, for example, is in obtaining video or other data that can be accurately analyzed for positional change among flock members. Not easy among three dimensional flocks from great distances, but possible with the right conditions.

                               Figure 9. Coots on Elk lake (5)


1. Marcus du Satoy

2. Pollock, Jackson. 1952.  "Blue-Poles"

3. Ratamero, Erick. 2013. MOPED : an agent-based model for peloton dynamics in competitive cycling
In: International Congress on Sports Science Research and Technology Support, 2013, Vilamoura, icSPORTS 2013

4. Trenchard, H. 2013. Peloton phase oscillations. Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena, pp. 194-201

5. Trenchard, H. American Coot Collective On-water Dynamics. Nonlinear Dynamics, Psychology, and Life Sciences, Vol. 17, No. 2, pp. 183-203.

Thursday, November 14, 2013

Video demonstration of Peloton 5.5

In the video link below I discuss and demonstrate my Peloton 5.5 model, using Netlogo.  The model includes a few refinements over the version I presented in my recently published paper [1]. In that paper I apply my “peloton convergence ratio" (PCR) equation and examine peloton phase changes as a function of fractions of PCR. In that paper I also incorporate a “passing principle” whereby I suggest that when there is a significant power output differential between front and drafting riders, it is inevitable that drafting riders with greater relative energy stores will pass those ahead, but this passing capacity falls as riders approach maximal sustainable outputs.
          In Peloton 5.5 I break down PCR into its constituent elements: a fixed power output for a front non-drafting rider, a variable drafting rate -- which returns a correspondingly reduced power output for drafting riders relative to a riders in front positions -- and a variable MSO (“maximal sustainable output”).  I set an arbitrary output for the front rider, and allow the other variables to be adjusted returning a PCR that describes the output relationships between the front and the following riders.  
        With this I demonstrate two extreme peloton phases: the low-density stretched phase in which PCR approaches 1 in which little or no passing occurs, indicating that the power output of the following rider approaches her maximal sustainable output; a high density, high passing phase in which PCR is closer to zero. I then go on to show  mid-range of PCR in which we see oscillations between phase states as well as simultaneous occurrences of them.

In a subsequent post I hope to discuss a recent peloton model created by Erick Ratamero (University of Warwick), which he presented at a conference in September.  He, myself, and Ash Richardson (University of Victoria), are in the stages of preparing a collaborative paper in which we look at the data I've obtained from two track races at the recent B.C. track championships.

Trenchard, H. 2013 Peloton Phase Oscillations. Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena, pp. 194-201