Why the grain in tree trunks spirals: a mechanical perspective

Abstract

The trunks of Ponderosa pine are curiously designed: their grain spirals around the trunk. The natural question arises: why does the evolution lead to such complication in the design? Here, we attempt to find the answer considering the morphology of a trunk as a result of the optimization of a mechanical construction. We model the trunk as an anisotropic cylinder with helicoidal symmetry, compute the stresses, and optimize the angle of the grain’s inclination using a strength criterion. When the structure of the tree is optimized only for the strength, the objective remains practically neutral to the variation of the angle of spiraling if the angle does not exceed a limit, then the strength declines. The measured angle in the Ponderosa pine corresponds to this limit. Another biological factor must be considered: the transportation of the fluid from the roots to the branches. The spiraling is needed to achieve the uniform watering of the branches across the trunk even if the roots grow from one side only. The analysis of the stresses in the anisotropic cylinder with helicoidal symmetry under bending and compression loads is performed by introducing elastic potentials which generalize the potentials for cylindrical anisotropy.