Figure 1.
Overhead view of the proposed branching system scheme.
A mother branch has several daughter branches, here labelled as A, B, and C. The branch's spatial arrangement is within a horizontal plane. The weight of daughter branches is defined as WA, WB, and WC and the distances between the center of gravity and the base of each daughter are gA, gB, and gC. The branching angles of each daughter are θA, θB, and θC and the distances between the branching point and the measurement points are mA, mB, mC, and mM.
Figure 2.
Daughter/mother ratios based on assumptions of the uniform stress model for two daughters.
Daughter/mother ratios based on assumptions of the uniform stress model plotted in palette maps. The range of values for daughter/mother ratios is represented by a range of colors. Values greater than 3 are shown in yellow. This plot shows two daughters (A and B) with weights denoted by WA and WB. The weight of daughter B is fixed at 10 kg, and the weight of daughter A is set to vary from 0 to 10 kg. mM and mi are 1 cm. (A) θB was fixed at zero, θA was set to vary from 0.1 to 90°. (B) The angles of daughter A and B are set as θA = θB and to vary from 0.1 to 90°.
Figure 3.
Daughter/mother ratios based on assumptions of the uniform stress model for three daughters.
Daughter/mother ratios based on assumptions of the uniform stress model for three daughters: A, B, and C. Different values of the daughter/mother ratio are represented by different colors. Values greater than 3 are shown in yellow. The angles of daughters A and C are set as θA = θC and to vary from 0.1 to 90°. The weight of daughter B is fixed at 10 kg, and the weights of daughters A and C are set as WA = WC and to vary from 0 to 10 kg. mM and mi are 1 cm.
Figure 4.
Daughter/mother ratios based on assumptions of the elastic similarity model for two daughters.
Daughter/mother ratios based on the assumptions of the elastic similarity model for two daughters, A and B, with weights WA and WB. Different values of the daughter/mother ratio are represented by different colors. Values greater than 3 are shown in yellow. The weight of daughter B is fixed at 10 kg and the weight of daughter A is set to vary from 0 to 10 kg. (A) θB was fixed at zero, θA was set to vary from 0.1 to 90°. (B) The angles of daughter A and B are set as θA = θB and to vary from 0.1 to 90°.
Figure 5.
Daughter/mother ratios based on assumptions of the elastic similarity model for three daughters.
Daughter/mother ratios based on assumptions of the elastic similarity model for three daughters, A, B, and C. Different values of the daughter/mother ratio are represented by different colors. Values greater than 3 are shown in yellow. The angles of daughters A and C are set as θA = θC and to vary from 0.1 to 90°. The weight of daughter B is fixed at 10 kg, and the weights of daughters A and C are set as WA = WC and to vary from 0 to 10 kg. mM and mi are 1 cm.
Figure 6.
Daughter/mother ratios vs. daughters' degrees of deviation.
Daughter/mother ratios vs. daughters' degree of deviation in (A) Fagus crenata and (B) Abies homolepis. The number of daughters branching from a mother branch is two in Fagus crenata, and two (open circles), three (filled circles), and four to five (open squares) in Abies homolepis.
Figure 7.
Indices of the uniform stress model vs. daughters' degrees of deviation.
Indices of the uniform stress model vs. daughters' degrees of deviation in (A) Fagus crenata and (B) Abies homolepis. The theoretical value of the index is 1.0, independent of daughters' degrees of deviation.
Table 1.
Constants of the regression equations (y = Ax+B) and correlation coefficients (r) in Figs. 6, 7, and 8.
Figure 8.
Elastic similarity model indices relative to daughters' degrees of deviation.
Elastic similarity model indices plotted against daughters' degrees of deviation in (A) Fagus crenata and (B) Abies homolepis. The theoretical value of the index is 1.0 independent of daughters' degrees of deviation.
Table 2.
Biases and standard errors of estimates (SEE) of daughter/mother ratios estimated in compliance with the assumptions of each model.
Figure 9.
Changes in strain values of branches after bending, freed from their own weights.
Changes in strain values (με) for three branches of Fagus crenata and four branches of Abies homolepis after being freed from their own weights, plotted against the distance from the fixed end of each branch. The lines are drawn to connect the points of each branch. Legends show individual numbers of each branch.