# Effect of Dimensional Variables on the Behavior of Trees for Biomechanical Studies
## 3 Results and Discussion  
### Deflection  
#### 3.1.1 Comparison with Literature  
Comparing deflection values using literature is complex because different authors use different measurement methodologies. Some of them consider only the inclination of the root plate [15; 17], and others consider the inclination of the root plate and the deflection of the stem together [26; 33; 43], as in this study (Figure 2). Furthermore, the deflection is influenced by geometric tree parameters such as height, diameter, and taper [24], and also by mechanical properties of the trunk and root wood, as modulus of elasticity [15]. Therefore, the comparison with literature is focused on the analysis of the general order of magnitude of the values obtained and the coherence of behavior, considering geometric parameters of the trees and properties of the wood adopted by different authors.  
In ref. [43] uses two trees with the same height (\(H\) = 20 m) and diameters at breast height (\(DBH\) = 24.5 cm and 24.8 cm), both same species with density 300 kg\(\cdot\)m\({}^{-3}\) and modulus of elasticity in bending 3584 MPa. The horizontal pulling force, with a magnitude much lower (maximum 2.25 kN and 1.65 kN) than those used in this research (5 kN to 15 kN), was applied at 12.23 m and 12.20 m (about 60% \(H\)). The closest condition to compare our data is in scenario 1, where the tree with \(H\) = 20 m (Table 1) was subjected to a horizontal load of 5 kN at 55% \(H\) (Table 4). For a horizontal load of 1.65 kN, the average displacement at the point of load application obtained by [43] was 1.5 m. If we apply a composition of differences of \(DBH\) (24.7 cm/91 cm = 0.27) and modulus of elasticity (3584 MPa/10387 MPa = 0.34) calculated by multiplying these differences (0.09), the expected displacement (0.14 m) will be of the same order of magnitude as those obtained in this paper (0.293 m in Table 4).  
In ref. [34] simulated a tree with \(H\) = 8 m, \(DBH\) = 0.40 m, and horizontal force applied at 5 m (62.5% \(H\)). The simulated horizontal forces ranged from 5 kN to 75 kN. There is no information about the modulus of elasticity of the stem and root used in the model. The closest condition in this research is in scenario 2 for slender = 16, where \(H\) = 7.5 m and \(DBH\) = 0.47 m (Table 1) with horizontal load applied at 63.3% \(H\). For this condition, the deflection in the horizontal-load position was 0.027 m (horizontal load = 5 kN (Table 4)), 0.028 m (horizontal load = 10 kN (Table 5)), and 0.029 m (horizontal load = 15 kN (Table 6)). For these load levels, [34] obtained 0.02 m, 0.03 m, and 0.04 m, with the same order of magnitude as our results.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \(H\) & \(\lambda\) & \(T\) & \(\delta_{M}  
In ref. [33] modeled, using the structural theory of a cantilever beam, the behavior of eight trees with H ranging from 9.6 m to 13.2 m subjected to large deflections using a pulling test. The modulus of elasticity of the trees' wood was 2000 to 6400 MPa, and the diameter (\(D\)) was measured at 2 m from the base of 10 cm to 19.2 cm. The horizontal load was applied at about 70% \(H\). The deflection of the trees ranged from 2 m to 6 m and showed positive dependence on the modulus of elasticity and diameter. The mean deflection of two trees (\(H\)  
The results of the comparisons show that although at first glance, the deflections obtained with the proposed model are very small, the values obtained by adjusting the diameter and modulus of elasticity are within the expected order of magnitude.