RESUMO
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. This formula theoretically explains why almost all plants exhibit a tapered form: it allows for a greater height at an earlier growth stage than a hollow cross-section.
RESUMO
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. We modeled a herbaceous plant as a cantilever with the ground side as a fixed end, and the greatest height was formulated considering the axial tension force from the turgor pressure. The scaling law describing the relationship between the height and diameter in terms of the turgor pressure was theoretically derived. Moreover, we proposed a plant classification rule based on stress distribution.
Assuntos
Plantas , MadeiraRESUMO
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. We modeled a plant a horizontally oriented thin-walled cylindrical cantilever with closed ends enclosing a cavity filled with water that is acted on by its own weight and by internal tension generated through turgor pressure. We derived an equation describing the plant's consequent deflection, introducing a dimensionless parameter to express the decrease in deflection associated with the action of turgor pressure. We found that the mechanical and physical characteristics of herbaceous plants that would appear to be counter-productive from a superficial perspective increase the deflection decreasing effect of turgor pressure.
RESUMO
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. We obtained a theoretical clarification of the effect of the weight distribution of heavy columns on the buckling behaviour. A widely applicable scaling law for trees was obtained. We found that an actual tree manages to distribute the weight of its trunk and branches along its vertical extent in a manner that adequately secures its critical height. The method and findings of this study are applicable to a wide range of fields, such as the simplification of complicated buckling problems and the study of tree shape quantification.
