Check out the aerial footage of bicyclists competing in the annual Tour de France and you'll notice that riders tend to spontaneously group themselves into a diamond-shaped pattern. Jesse Belden, a researcher at the Naval Undersea Warfare Center, says such patterns emerge because riders are trying to stay close to their competitors while avoiding collisions.

Belden, an avid cyclist himself, described his work at a meeting of the American Physical Society's Division of Fluid Dynamics in Atlanta, Georgia. While watching coverage of the Tour de France, especially the aerial footage, he became fascinated by the formations of the group of cyclists. They resembled flocks of starlings or schools of fish—both examples of so-called "collective behavior" in nature. And he found himself wondering how one might model the behavior of riders in a peloton.

The study of swarming and other collective behavior in animals is a booming field, with scientists studying the group dynamics of murmurations of starlings, ubiquities of sparrows, swarms of midges, armies of fire ants, and schools of fish, among other examples in nature. The aim is to better understand the underlying mechanisms, with an eye toward identifying possible universal laws governing such behavior—a task made more difficult by the fact that there are slightly different mechanisms behind the collective behavior of each of the aforementioned groups.

Back in the 1980s, a computer graphics specialist named Craig Reynolds developed the "boids" program: an agent-based computer simulation to model collective behavior. The program treats each individual in a swarm as a dot (or particle) that starts out moving in a straight line at constant speed. Then a few simple rules are added. If two particles get too close, they must move away to avoid a collision, for example, and must move closer if they get too far apart. Tweak those rules, and you'll get something resembling a swarm of midges or a raft of fire ants. Collective behavior in the form of a flocking pattern will emerge once there is a sufficient density of individual units.

Belden and his colleagues studied hours of aerial footage of the Tour de France and noticed a similarity to circulation in a fluid, marked by two distinct types of waves. The first are longitudinal waves, moving back and forth along the peloton, usually caused when a rider slows to avoid a collision or brakes suddenly. The second are transverse waves, produced as riders swerve left or right to avoid obstacles or find a more advantageous position. Those two wave types hold the key to why peloton riders so often form diamond patterns during a race.

Belden initially thought the diamond pattern arises because each rider is trying to gain an aerodynamic advantage by catching the tailwinds of other nearby riders. He reasoned there would be more of an aerodynamic advantage at the edges of the diamond. But this factor was less relevant than he had assumed. "It turns out that, inside a large peloton, that consideration is satisfied no matter where you are in the group," he says, because the riders are always so close together. This is supported by a recent Dutch study employing wind tunnels and simulations of 120 riders to study the aerodynamics at play during a peloton.

"By orienting themselves in this diamond structure, the rider immediately in front is now offset farther away."

The primary driving factor appears to be rider vision. According to Belden, world-class cyclists rely on something called "preattentive visual sensory processing" to avoid collisions. Each rider is trying to maintain a position with his or her nearest neighbors at the optimal distance where they are most sensitive to slight perturbations in motion, the better to avoid collisions. "These are not conscious decisions they're making," he says. "These are embedded reactions that probably have [developed] over many, many miles riding this close to each other."

And that's what is driving the emergence of the diamond formation. The longitudinal waves triggered by a rider slowing or braking spread twice as fast as the transverse waves triggered by riders moving side to side. "By orienting themselves in this diamond structure, the rider immediately in front of me is now offset farther away," he says. "And my two flanking neighbors are within plus or minus 30 degrees." That's the optimal range for the near-peripheral field of vision. A rider in this position will have more time to react to a sudden braking motion by the rider in front. And riders shifting side to side are less of an immediate threat, because there is more space to maneuver to avoid collision.

Professional cyclists who compete in the Tour de France are so skilled at maintaining a balance between these dynamics that they can ride extremely close to each other without crashing.

Belden also teamed up with Utah State University scientist Tadd Truscott to study a group of high-level amateur cyclists riding in certain formations. They didn't ride nearly as close together as the average Tour de France cyclists.

Looking at how pelotons form is not just about helping cyclists become better competitors. The ultimate goal behind studying collective dynamics is to identify nature's fundamental interaction principles between agents—the rules of engagement, if you will—in order to apply them to human-made systems, such as traffic flow and crowd management, the power grid, or self-driving cars.

It's a daunting challenge, particularly when human behavior is factored in. "It's been so hard just to identify what the interaction rules are in, for example, a school of fish," says Belden. "But what's becoming clear as we study more is that the rules can and will change, given different operating conditions."

DOI: Journal of Wind Engineering and Industrial Dynamics, 2018. 10.1016/j.jweia.2018.06.011 (About DOIs).