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Trees break at a nearly constant critical wind speed

The speed is surprisingly insensitive to a tree's height, diameter, or elasticity.

What's the maximum load a piece of wood can sustain before breaking? The question has a star-studded history, with contributions from Leonardo da Vinci, Galileo Galilei, the Bernoulli family, and Leonhard Euler, among others. The topic is one of practical importance, with applications in shipbuilding and curve fitting as well as in architecture and engineering. Christophe Clanet and colleagues at École Polytechnique in Palaiseau, France, and ESPCI Paris Tech have now looked at its implications for the ability of live trees to withstand wind. Examining data from the storm Klaus that hit southwest Europe in 2009, the team observed significant overlap between the areas of strongest wind and the areas of most broken trees. Where local wind speeds topped roughly 42 m/s, fewer than half the trees survived, whether softwood pines or hardwood oaks. To explore that connection, the researchers took quite different samples—meter-long beech rods and centimeters-long pencil leads—held them horizontally from one end, and added weight to the other end until they broke. They found that the critical radius of curvature at which the rods broke was independent of length and scaled with the 3/2 power of the diameter. That's consistent with having stress-concentrating defects whose typical sizes scale with the rod diameter. Back outside, the wind's bending force is distributed over a tree's length and width. Indeed, one would expect tall, skinny trees to break more readily than short, thick ones. But trees tend not to be both tall and thin simultaneously; rather, they top out at about 1/4 of their self-buckling height. Incorporating that allometric relationship, the researchers obtained a formula for the critical wind speed that depends only weakly on tree size. Further accounting for wind gusts yields a value for that critical wind speed suggestively close to what was actually observed. (E. Virot et al., Phys. Rev. E. 93, 023001, 2016.)

Trees break at a nearly constant critical wind speed - figure 1

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