The Physics of a Wind-Shattered Tree

French physicists offer cautionary calculations.

Michael Byrne

Michael Byrne

Image: Rob and Stephanie Levy/Wikimedia/Wikimedia

I live at the base of Wind Mountain in Washington state, which is also a quarter mile from its companion Wind River, and would you even believe that it is windy as shit here nearly all of the time? It's true!

Shredded trees are just a fact of life in my little valley. The mornings after a good blow, which are most of them in the wintertime, will find local roads and trails coated in a fresh carpet of pine scraps and even some full-sized trees. It's spooky just being out and about when the wind is really ripping because it seems like just about any tree might be the next to snap with a shotgun report and tumble. You can hear them up above, creaking and moaning. Maybe the next one will be destined for my skull.

It turns out that there are some interesting physics at work in the process of wind-caused tree felling. As researchers from France's École Polytechnique write in the current Physical Review E, all trees, irrespective of size and species, will fall in the presence of wind blowing at the same critical speed.

To reach this conclusion, the physicists had help from an even better laboratory than my own: Cyclone Klaus. Klaus, which killed 26 and left many millions without power, hit Western Europe in 2009 backed by hurricane force winds. In a few days time, the storm leveled millions of trees of all types.

The group behind the current study was led by David Quéré and Christophe Clanet, the principles behind École Polytechnique's Interfaces and Co. lab. Their study revolves around the physics of liquids interacting with solids and gases—related topics are wide-ranging and include superhydrophobicity, the Leidenfrost effect, and sports physics.

In their paper, Quéré and Clanet note that the study of wind interfacing with wood is as old as physics itself. Leonardo studied it, and came up with the relationship D2/L, where D is the diameter of a wooden beam or cylinder and L is its length. This was the critical mass at which wood would break, he concluded. A couple of centuries later, Galileo determined that it was more like D3/L, and, finally, in 1740 the French mathematician and naturalist Comte de Buffon refined it to D2.6/L1.1.

Which brings us to now, 2016, where we're still trying to fully understand the falling of trees, or their "loss of verticality." The phenomenon is known more properly as lodging.

Image: Quéré et al

"The storm Klaus in France (January 24th, 2009) gives precious data on the vulnerability of trees in a large territory hosting many types of forest," Quéré and Clanet write. "The map of maximal wind speed and the map of trees broken after the storm suggest that strong winds fit with high percentages of damage. This result seems independent of the tree characteristics, as shown in areas A and B, where trees are respectively pines (softwood) and oaks (hardwood)."

The group arrived at their conclusions via three broad physical concepts: Hooke's Law (how forces interact with elastic materials), Griffith's criterion (how cracks propagate through a material), and tree allometry (quantitative measurements of trees, basically). "A closer look at the shape of tree trunks, foliages, and wind unsteadiness leads to a more precise estimation of the absolute value of critical wind speed, found to be on the order of the maximal wind speeds expected on the Earth ( ≃50 m/s)," the paper concludes. "Hence our results might contribute to understanding why trees are such old living systems."

As the authors note, the conclusion is hardly trivial in a changing climate. More storms means more wind, and this has obvious implications for, well, not getting crushed by trees, but also for how we design and build structures. Your world may soon enough look a lot more like mine.