Growth patterns and bending mechanics of branches

This paper describes a simple model that calculates the evolution of branch shape as the result of growth patterns and weight variations. Experimental data concerning growth parameters were collected on a 23-year-old maritime pine tree (Pinus pinaster Ait.). Results are analysed in the first part of the study. Linear relationships are found between length and diameter, length and weight, and finally between the weight of branchwood and the square diameter. The analysis of vertical distribution of weight in the crown shows that the amount of branchwood main axis only remains lower than the amount of foliage needles and laterals in the upper whorls, whereas for older branches the relative amount of foliage tends to decrease. These results provide baseline data for computer simulation of branch growth. The theoretical bases of the model are presented in the second part of this work. The effects of growth parameters increase in length, diameter and weight and mechanical properties of the branch on the final shape are analysed. As expected, among all parameters, branch diameter has the greatest influence on the bending deflection. On the other hand, orthotropic growth of the terminal shoot tends to reduce the maximum bending moment in the branch. The distribution of weights in the branch also affects the deflection and maximum bending moment. These results are of interest for further analysis of branch form as an optimization problem based on biological growth.