Tuesday, April 2, 2013


           Energy savings by following others occurs throughout nature. For example, it is well-established that birds save energy by flying in vee formations [1], fish save energy in a school [2], young dolphins save energy by swimming next to their mothers [3], penguins save energy by huddling [4], ducklings save energy by paddling behind their mother [5].
         In bicycle pelotons, or groups of cyclists, following behind other cyclists is called drafting. Drafting allows a following rider to save considerable energy relative to a non-drafting cyclist who is riding "in the wind". While cyclists are keenly aware of the benefits of drafting, perhaps not all are aware how drafting, when combined with other factors, causes pattern formation in pelotons.
          Below is photo from a race in Victoria, B.C. It shows a criterium, a race on a loop around a few city blocks. Courses are usually about 1 km to make a lap, and cyclists must complete many laps of the course.   For the footage of that race, I rented a 45 foot boom lift and set it on one of the course corners.

A peloton. Men's Cat 1,2 Bastion Square Criterium, 2012.
      Of course there is nothing new about the concept of energy savings. By their very definitions, notions of efficiency or optimization involve the least use of energy and resources to produce maximum payoff for any given activity. These concepts confront us every day in many ways and contexts. Indeed, we can imagine that most sorts of cooperative behavior is likely to involve mutual energy savings.  However, while notions of efficiency, optimization, and cooperation are commonplace in our lexicon and well studied generally, I have found that there is little research and understanding of how energy savings within systems results in pattern formation; what those patterns are, whether they are visually obvious patterns, or mathematical ones that are hidden in the structure of the system and its behavior.
      I am largely concerned with how following others in some way or another reduces energy expenditure not only for the follower, but also where coupling of some kind occurs that results in mutual energy savings. So, while my frame of reference and the focus of my research is the bicycle peloton and its dynamics, I hope to explore where in nature similar principles of energy savings and their patterns arise. I hope to show that pattern formations in pelotons are driven by universal principles that apply to many other human, biological and non-biological systems. I will seek evidence for the presence of these universal principles in other systems, and hope to show either by my own original research or by reference to the research of others, where these principles occur, and their implications. For me this process is becoming a kind of lifelong quest; a search for universal principles and their manifestations in nature.

What, a bunch of birds on the water? A peloton?
American coots on Elk Lake near Victoria, B.C.

What the devil? A skunk cabbage spadix? Surely Hugh's out to lunch now!
What, praytell, is this?
What does this have to do with anything?
That's it, Hugh's really gone off his rocker. 
The quest that I embark upon takes me deeply into the field of study known as complexity theory. Complexity theory has its origins as a branch of physics [6], but it is now viewed more broadly as encompassing the study of the dynamics of any collection of interacting components. 
      In his book [7],"Why Society is a Complex Matter" (2012), Phillip Ball says:

Definitions vary, but there is a general consensus that a complex system is one  made up of many components (which might or might not be identical) that interact strongly with one another. When these components are autonomous entities that can make decisions - representing animals, people, institutions and so forth - they are often called agents.

The Peloton 
      As noted, cyclists save energy by drafting. Energy expenditure is reduced by approximately 18% at 32 km/hr (20 mph), 27% at 40 km/hr (25 mph), when drafting a single rider [8]. If among a group of eight riders, energy savings is as much as 39% at 40 km/hr; energy saved by drafting is negligible at speeds lower than 16 km/hr [8]. From these figures we can see that a reasonable approximation of the energy savings due to drafting for a cyclist drafting one other is 1 % per mile an hour, at speeds greater than 10 mph (16 km/h), as I show in the figure below.

Power requirements for cyclist in non-drafting position and cyclist in drafting position. Curve for non-drafting cyclist based on 75kg (bicycle and rider); rolling friction coefficient 0.004 dimensionless;  0.00 gradient; air-density 1.226kg/m3; drag co-efficient of 0.5; frontal surface area of 0.05m2 (parameters from www.analyticcycling.com). Curve for drafting cyclist based on approximate 1% savings per mile/hr (Hagberg and McCole 1990; Burke, 1996; Figure adapted from [9]).

      When riders draft, or alternate between non-drafting and drafting positions, they may be said to be coupled. Coupling means that they mutually interact; that the actions of one influences the actions or the properties of another, and vice-versa. When coupling occurs between a cyclist and her immediate surrounding neighbours, they may be said to be "locally" coupled or interacting. When a larger group of cyclists displays patterns of behavior due to the effects of local coupling, the whole group may be said to be globally coupled. In the parlance of complexity science, when global behaviors occur due to principles of local coupling, the global behavior is said to "emerge". Global behaviors are "emergent" or show "emergent behavior" or "emergent patterns".
      There are many emergent patterns in pelotons. They occur within certain ranges of cyclists' power output and speed. Power output and speed are independent of each other in cycling, because a cyclist might at one time be going uphill very slowly while exerting maximum power. Or he might be going very fast downhill, and exerting very little power. So, it is more accurate to think of emergent patterns as occurring within certain power-output ranges. However, as the cycling uphill example demonstrates, drafting benefit is a function of both power output and speed. This is because a cyclist might be riding at maximum up a very steep hill and deriving no drafting benefit at all. It is not until the course levels out and the cyclists can travel at higher speeds that a following rider may head for the slipstream of her compatriot for relief. As a result, in my discussions I will refer sometimes to power separately from speed, and sometimes to both speed and power as necessarily connected.
      So there's an introduction. In the course of these posts, I will often delve into speculative analysis that does not currently have much research in support, but I hope to support it with as much sound reasoning and evidence as I can. Occasionally, I may post something that is not necessarily in sequence or in context of another post that immediately precedes, but I will attempt to tie the relevance of the post to the general aims of this blog.

Next: peloton "phases". 
Notes and references

1. Weimerskirch H., Julien M., Clerquin Y., Alexandre P., Jiraskova S. 2001. Energy Saving in Flight Formation, Nature, 413, 697-698; Cutts C., Speakman J. Energy Savings in Formation Flight of Pink-footed Geese, 1994, J. Exp. Biol. 189, 251–261, citing Lissaman and Shollenberger, 1970; Badgerow and Hainsworth 1981.

2. Herskin J., Steffensen F. 1998. Energy Savings in Sea Bass Swimming in a School: Measurements of Tail Beat Frequency and Oxygen Consumption at Different Swimming Speeds, Journal of Fish Biology, Vol 53, Issue 2, 366–376.

3. Weihs, D. 2004. The Hydrodynamics of Dolphin Drafting, Journal of Biology, 38(8), 1-23.

4. Gilbert C., Blanc S., Le Maho Y., Ancel A. 2008. Energy Savings Processes in Huddling Emperor Penguins: From Experiments to Theory, Journal of Experimental Biology 211, 1-8.

5. Fish, F. 1995. Kinematics of Ducklings Swimming in Formation: Consequences of Position, The Journal of Experimental Zoology 273:1-11.

6. For example: Waldrop, M. 1992. Complexity - The Emerging Science at the Edge of Order and Chaos. A Touchstone Book. New York. "This is a book about the science of complexity - a subject that is still so new and wide-ranging that nobody knows quite how to define it..."

7. Ball, P. with a contribution by Dirk Helbing. 2012. Why Society is a Complex Matter. Springer-Verlag, Berlin Heidelberg.

8.  McCole S.D, Claney K., Conte J.C., Anderson, R., Hagberg J.M. 1990. Energy expenditure during bicycling. Journal of Applied Physiology. 68:748-753.

9.Trenchard, H. 2010. Hysteresis in competitive bicycle pelotons. Complex Adaptive Systems – Resilience, Robustness and Evolvibility: Papers from AAAI Fall Symposium FS-10-03 130-137

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