Abstract
From the point of the optimal theory, the relationship between the branching structure and the mechanical characteristics of a tree was analysed in reference with such parameters as circum-ference, weight, bending moment, branch length and-branching angle, The study was based on a hypothesis that the optimal structure of a tree agrees the minimum energy loss.The total energy loss is the sum of the energy required for the construction which is proportional to the wood' volume of the branches and the energy consumption for supporting the weight of the branches and leaves which is equal to the elastic. strain energy. Results derived theoretically from the hypothesis are as follows : 1) The Maximum bending stress at each branching point is constant.2) The relation between the circurmference (C) at some point and the bending moment (T) acting on the branch is, T∝C3. 3) The relation between the weight (W) of all the parts of the tree peripheral to some branching point and C is, W∝C2.5. 4) The relation between T and W is, W∝T5/6. 5) The relatlon between the branch length (l) and C is, l2 ∝C. 6) When C0, C1, C2 are the circumferences of the mother and daughter branches and θ1, θ2 are their branching angles, the following optimal conditions for a dichotomy are derived;
C02.5= C12.5+C22.5 and C13/ sinθ2=C23/ sinθ1.
These relations were examined, by measuring the varying size of branches, 76-286 in all, on seven different kinds of trees, and the very good agreements between the theoreiical and actual relations were confirmed.
