Comment on "Critical wind speed at which trees break"

Role of the crown in tree resistance against high winds

Rather than using wooden sticks to simulate the breakage of trees in high winds as in most research, we employ fresh samples from camphor and Formosa gum with branches and leaves to certify the crucial role of the tree crown. By using a blowdown wind tunnel with a maximum wind speed of 50 m/s, we purposely reduce the number of leaves and show that the drag force will drop by as much as two thirds when half pruned. Based on real observations, we model the leaf by an open and full cone in the presence of light and strong winds, and calculate how their corresponding cross-sectional area A and drag force F vary with wind speed v. Different slopes before and after the formation of a full cone are predicted and confirmed when these two quantities are plotted in full-log scale. Compared to the empirical value, our simple model gave α=2/5 and 2/3 for A∝v^{-α} and β=4/5 and 2/3 for F∝v^{β} at low and high winds. Discrepancies can be accounted for by including further details, such as the reorientation of open cones and the movement of branches.

Controlling fracture cascades through twisting and quenching

Fracture fundamentally limits the structural stability of macroscopic and microscopic matter, from beams and bones to microtubules and nanotubes. Despite substantial recent experimental and theoretical progress, fracture control continues to present profound practical and theoretical challenges. While bending-induced fracture of elongated rod-like objects has been intensely studied, the effects of twist and quench dynamics have yet to be explored systematically. Here, we show how twist and quench protocols may be used to control such fracture processes, by revisiting Feynman's observation that dry spaghetti typically breaks into three or more pieces when exposed to large pure bending stresses. Combining theory and experiment, we demonstrate controlled binary fracture of brittle elastic rods for two distinct protocols based on twisting and nonadiabatic quenching. Our experimental data for twist-controlled fracture agree quantitatively with a theoretically predicted phase diagram, and we establish asymptotic scaling relations for quenched fracture. Due to their general character, these results are expected to apply to torsional and kinetic fracture processes in a wide range of systems.

Wind loads and competition for light sculpt trees into self-similar structures

Trees are self-similar structures: their branch lengths and diameters vary allometrically within the tree architecture, with longer and thicker branches near the ground. These tree allometries are often attributed to optimisation of hydraulic sap transport and safety against elastic buckling. Here, we show that these allometries also emerge from a model that includes competition for light, wind biomechanics and no hydraulics. We have developed MECHATREE, a numerical model of trees growing and evolving on a virtual island. With this model, we identify the fittest growth strategy when trees compete for light and allocate their photosynthates to grow seeds, create new branches or reinforce existing ones in response to wind-induced loads. Strikingly, we find that selected trees species are self-similar and follow allometric scalings similar to those observed on dicots and conifers. This result suggests that resistance to wind and competition for light play an essential role in determining tree allometries.

Tree branches follow allometric scalings between length, thickness and dry mass. Here, Eloy and colleagues develop a functional-structural model that shows how such allometries in tree architecture can emerge through evolution as a result of competition for light, wind biomechanics, and wind sensing.

Reply to "Comment on 'Critical wind speed at which trees break' "

In the preceding comment [A. Albrecht et al., Phys. Rev. E 94, 067001 (2016)10.1103/PhysRevE.94.067001], Albrecht et al. argue that important biomechanical ingredients are missing in our model about the wind speed at which trees break [Phys. Rev. E 93, 023001 (2016)10.1103/PhysRevE.93.023001]. Here we wish to emphasize that our model is an idealization, which primarily aims at evidencing the dominant ingredients of the problem. Since it captures both observed trends and orders of magnitude, we believe that the essential parameters in tree breakage have been identified, a useful step to make further progress and more detailed descriptions.