Basic biomechanics of self-supporting plants: wind loads and gravitational loads on a Norway spruce tree

Abstract

Mechanical constraints are major determinants of size and shape of self-supporting plants, for instance upright stems will become mechanically unstable due to their own weight if too slender (Euler buckling). Both gravitational forces and wind loads induce bending moments which the structure has to be able to withstand. Straightforward is the computation of gravitational loads on side branches and stems leaning to various degrees, provided that the geometrical parameters like their tapering mode and the number and size of primary and secondary branches is known. The limit of the structure is reached if at any point the bending moment induced is larger than the critical bending moment. This in turn depends on structural parameters (the geometry of the cross-section) and properties of the material (the modulus of elasticity and the critical stresses at which failure occurs). In many cases, depending on the root–soil interaction, the bending moment on the trunk may lead to root lodging. Most important also from an economical point of view is the assessment of wind loads. It requires an estimate of the effective sail-area (which due to the flexibility of the branches will depend on the wind speed) and the drag coefficient and particularly the knowledge of the wind profile, which may be very different for a solitary tree than for a tree within a dense stand. Flexibility combined with viscoelastic behaviour is the plant’s answer to dynamic wind loads. Although our comprehension may still seem fragmentary, one general conclusion emerges from a comparison of biomechanical calculations with empirical data: plants are often structured in such a way that they approach their biomechanical limits within controlled safety margins. This safety factor applies to ‘normal’ environmental loads, either gravitational loads or wind loads and may be overruled by excessive snow loads or by extreme winds like hurricanes. For a biologist it is a challenge to trace the ‘principle of constant safety factors’ to adaptive growth as response to mechanical stimuli. The phenomenon has been demonstrated qualitatively, but neither the mechanoreceptor nor the signal transduction chain has as yet been identified.