Plant strategies for greatest height: tapering or hollowing.

The tapered form and hollow cross-section of the stem and trunk of wild plants are rational mechanical approaches because they facilitate the plant simultaneously growing taller for photosynthesis and supporting its own weight. The purpose of this study is to clarify the advantages and disadvantages of tapering and hollowing from the perspective of the greatest probable height before self-buckling. We modelled woody plants using tapering or hollow cantilevers, formulated the greatest height before self-buckling, and derived a theoretical formula for the greatest probable height considering tapering and hollowing.

Mechanics-based classification rule for plants.

The height of thick and solid plants, such as woody plants, is proportional to two-thirds of the power of their diameter at breast height. However, this rule cannot be applied to herbaceous plants that are thin and soft because the mechanisms supporting their bodies are fundamentally different. This study aims to clarify the rigidity control mechanism resulting from turgor pressure caused by internal water in herbaceous plants to formulate the corresponding scaling law.

Rigidity control mechanism by turgor pressure in plants.

The bodies of herbaceous plants are slender, thin, and soft. These plants support their bodies through the action of turgor pressure associated with their internal water stores. The purpose of this study was to apply the principles of structural mechanics to clarify the underlying mechanism of rigidity control that is responsible for turgor pressure in plants and the reason behind the self-supporting ability of herbaceous plants.

Mathematical modelling to determine the greatest height of trees.

This study aimed to analyse the critical height of a column whose weight varies vertically in order to obtain a simple scaling law for a tree where the weight distribution considered. We modelled trees as cantilevers that were fixed to the ground and formulated a self-buckling problem for various weight distributions. A formula for calculating the critical height was derived in a simple form that did not include special functions.