There’s something about the immense beauty and mystery of nature that just can’t help but make you think: math. Take‚ for example‚ a new study in which an international team of researchers have figured out the previously unknown formulas behind flocking – or at least‚ some small part of the phenomenon – allowing us to at long last harness the ingenuity of nature for our own mechanical purposes.“This area of research is important since animals are known to take advantage of the flows‚ such as of air or water‚ left by other members of a group to save on the energy needed to move or to reduce drag or resistance‚” explained Leif Ristroph‚ an associate professor at New York University’s Courant Institute of Mathematical Sciences and the senior author of the paper‚ in a statement.The team restricted their study to birds moving in a column – those formations in which groups of flyers will line up directly behind each other – rather than attempting some of the more adventurous murmurations achieved by some species of bird. That shouldn’t be seen as a shortcoming‚ by the way – those movements can be so complex as to resemble the quantum dynamics of superfluid helium‚ and even collecting sufficient data to model equations from can be prohibitively difficult.In fact‚ previous work on the math behind flocking has considered even fewer birds: only two‚ in a paper from the same team some five years ago. But the new paper has shown just how important expanding the study was to understanding the movements of these groups of animals – because as it turns out‚ the effects of the dynamics involved actually depend on the size of the group.“The aerodynamic interactions in small bird flocks help each member to hold a certain special position relative to their leading neighbor‚” explained Sophie Ramananarivo‚ an assistant professor at &;Eacute;cole Polytechnique Paris and one of the paper’s authors. “But larger groups are disrupted by an effect that dislodges members from these positions and may cause collisions.” This observation was confirmed with a “mock flock” – mechanical replica wings‚ created by the team and driven through water to model the air flow around real birds in flight. The cut-off point‚ they discovered‚ was about four: fewer flyers than that‚ and the aerodynamic interactions are a help to each individual relative to the others‚ Ristroph explained. “If a flyer is displaced from its position‚ the vortices or swirls of flow left by the leading neighbor help to push the follower back into place and hold it there‚” he said. “This means the flyers can assemble into an orderly queue of regular spacing automatically and with no extra effort‚ since the physics does all the work.”More than that‚ however‚ and staying in formation gets difficult. “[The] flow interactions cause later members to be jostled around and thrown out of position‚ typically causing a breakdown of the flock due to collisions among members‚” Ristroph said. “This means that the very long groups seen in some types of birds are not at all easy to form.”Essentially‚ the team discovered‚ each bird is affected by the bird in front – but is unable to exert any reciprocal effect back to its predecessor. These waves‚ dubbed “flonons” by the researchers‚ add up through the column‚ so by the time we get to the back of the queue‚ birds can be oscillating wildly: they “likely have to constantly work to hold their positions and avoid crashing into their neighbors‚” Ristroph explained.But while that’s all very interesting‚ is it particularly helpful for those of us without feathers&;#63; Well‚ in fact‚ yes. “Our findings […] raise some interesting connections to material physics‚” pointed out Joel Newbolt‚ an NYU graduate student in physics at the time of research. “[The] birds in an orderly flock are analogous to atoms in a regular crystal.”And the study might have some more immediate real-world implications‚ too‚ Ristroph added. “Our work may also have applications in transportation – like efficient propulsion through air or water‚” he suggested‚ “and energy‚ such as more effectively harvesting power from wind‚ water currents‚ or waves.”The study is published in the journal Nature Communications.