If you’ve been watching the Tour de France recently, you may have wondered why cyclists move in such tight formations. In fact, they are borrowing a technique used by many animals in nature, as Professor Michael Shelley of New York University explained in his lecture at the School of Mathematics and Statistics on Monday. By working collectively, the cyclists are able to take advantage of the slipstream of the cyclist in front to decrease the air drag that they need to work against. Flocking birds and schooling fish use the same technique to fly and swim more efficiently. 

Professor Shelley is the 2015 Australian Mathematical Sciences Institute (AMSI) Lecturer, and will be touring Australia over the next three weeks to talk about his research on complex phenomena arising in biophysics, computational science, and the fluid dynamics of flying and swimming. Run in conjunction with the Australian and New Zealand Industrial and Applied Mathematics (ANZIAM) society, the AMSI Lecture series gives the Australian public and the research community an opportunity to learn from eminent mathematical researchers from around the world.  

An enormous range of swimming and flying behaviour can be described with a single mathematical quantity called the Reynolds number. Named after the physicist Osborne Reynolds, the Reynolds number measures the of viscosity, or “syrupy-ness”, of a fluid. Honey has a higher viscosity than water, which in turn has a higher viscosity than air. The higher the viscosity of a fluid, the harder it is to swim through. But the size and inertia of the swimmer matters too. A bacterium swimming through water has to work as hard as a human trying to swim in custard. The Reynolds number measures the relative importance of viscosity and inertia in the equations of motion describing fluid dynamics. 

Nature has evolved some ingenious strategies for moving through fluids. Tiny algae and spermatozoa have a low Reynolds number, which means that they need to wriggle, corkscrew, or undulate to overcome the effect of viscosity. Fish and birds have a high Reynolds number and move by imparting momentum to the fluid to push themselves forward. Cycling is another example of a high Reynolds number fluid phenomenon. 

Things become even more complicated when swimmers and flyers move collectively. In his talk, Professor Shelley described some of the fascinating ways in which individual swimmers and flyers work together to move more quickly and efficiently through a fluid. A familiar example is when birds fly in a V-formation. Like cyclists, the birds can take advantage of the slipstream of the bird flying at the front of the flock. But birds have another advantage that cyclists don’t. By flapping its wings, the bird in front also helps to create an updraft for the birds flying behind, who in turn create an updraft for the birds behind them. This strategy can increase the speed of the flock by a factor of two or more. So it seems that birds of a feather have plenty of good reasons to stick together. 

(Words: Shane Keating)