In today’s Academic Minute, Dr. Francois Blanchette of the University of California Merced reveals the math behind the warmth of a penguin huddle.
Francois Blanchette is an associate professor of natural sciences at the University of California, Merced. He is an applied mathematician and primarily interested in problems involving fluid dynamics, but more recently, his work has involved describing the thermodynamics of penguin huddles. He holds a Ph.D. from the Massachusetts Institute of Technology.
Dr. Francois Blanchette – Warmth of the Penguins
One day when I didn’t feel like working, I decided to watch “The March of the penguins”. Looking at the penguins huddling against the cold wind, it occurred to me that these were truly amazing animals. Not only do they survive horrendous living conditions, but they also have to do it in a fair and equitable manner. If the strong penguins could stay sheltered in the center and the weak were left exposed on the edge of the huddle, the exposed penguins would die of exposure to the cold wind. The huddle would keep losing members, and, in time, disappear. Clearly, the law of the jungle doesn’t work in Antarctica. So with my colleagues, we decided to try to figure out how penguins managed to keep it fair.
We came up with a very simple model. Given a huddle, we computed the wind flow and temperature distribution around it. We then found the most exposed penguin, and had it relocate to the most sheltered position it could access without displacing any other penguin. By repeating this process, we saw that penguins peeled away from the windward side and piled up on the leeward side. But our model huddles didn’t quite look right; they had the wrong shape and were too perfectly smooth. To generate more realistic huddles, we had to add a fair amount of randomness in the system. This meant that although penguins followed the general principle that each individual tries to move to the warmest spot it can find, they applied that principle quite imperfectly.
The result was a fairly realistic looking huddle. Most importantly, every penguin eventually became exposed to the wind, as its live-penguin protection slowly eroded away. So it seems that the simple principle of every penguin for itself managed to produce a fair system… and that penguins are not purely rational, which I suppose is part of their charm.