Leonardo's rule, self-similarity and wind-induced stresses in trees

TL;DR

This paper proposes that Leonardo's rule about branch cross-sections in trees results from their self-similar structure and adaptive branch diameters that resist wind stresses, linking botanical observations with structural principles.

Contribution

It introduces a theoretical framework connecting Leonardo's rule with self-similarity and wind load adaptation in tree structures.

Findings

Leonardo's rule can be explained by self-similar tree structures.

Branch diameters are optimized to withstand wind-induced stresses.

The model links botanical observations with mechanical principles.

Abstract

Examining botanical trees, Leonardo da Vinci noted that the total cross-section of branches is conserved across branching nodes. In this Letter, it is proposed that this rule is a consequence of the tree skeleton having a self-similar structure and the branch diameters being adjusted to resist wind-induced loads.