## 3 Results
### Characteristics of the Aeroelastic Model Tree
#### 3.3.1 Crown Morphology  
The main geometry dimensions of the aeroelastic model match these of the prototype according to the target length scale 1:6, as shown in Table 1.  
The drag coefficient (C\({}_{f}=\frac{2F_{D}}{\rho A_{U}\mu L^{2}}\), where \(F_{D}\) is the drag, \(\rho\) is the air density, \(A_{U}\) is the frontal area and \(U\) is the wind speed) of the aeroelastic model was measured in the Boundary Layer Wind Tunnel II (BLWT II) at Western University, Canada. Because the upstream terrain of the prototype is close to flat, the simulation of the turbulent atmospheric boundary layer (ABL) flow was determined by comparing the full-scale wind speed profile given by ESDU 85020 [66] (2008). Vertical profiles of the mean velocity and turbulence intensity of the aforementioned ABL flows are shown in Figure 9a. The mean velocity profile of the wind tunnel terrain is similar to that of full-scale terrain along the tree height. Because the ratio between the crown area and trunk area is 2.82-9.12, the aerodynamic force of the model is mainly caused by crown. The similarity of the turbulence intensity profiles at the crown height between the wind tunnel terrain and the full-scale terrain meets the requirement of the wind tunnel test, except below the crown, close to ground, where the turbulence intensities are too high. The power spectral density (PSD) functions of streamwise velocities at reference height (\(z=0.85\) H) for the ABL flow in the wind tunnel terrain is similar to that for the theoretical full-scale ABL flow, as shown in Figure 9b. It is worth noting that the dimensionless integral length scale (\(L_{x}/D_{ crown}\), where \(L_{x}\) is integral length scale, and \(D_{ crown}\) is the crown diameter projected to the ground) of the wind tunnel terrain (1.68) is significantly smaller than that of the full-scale ABL flow (26.86), which is caused by the primary issue when using relatively larger scale models in typical boundary layer wind tunnels. This mismatch will lead to a crown response that is underestimated. However, because the large-scale gusts are in the quasi-steady range, the effect is similar to there being a slightly lower mean wind speed. In other words, while the displacements of the crown are accurate for the particular gust speeds in the wind tunnel simulation, larger gust speeds and deflections would be observed in the true terrain. In contrast, the higher turbulence levels acting on the trunk, close to the ground, may lead to small changes in the trunk response given the relatively small turbulence levels (between 10-12%). Figure 10a depicts relationships between drag coefficients and wind speed of the model for cases C1 to C8, in which the wind speed was converted into full scale according to velocity scale 1:2.45 [5], and other typical broad-leaved trees, including rose of Sharon [67], poplar  
Figure 9: (**a**) The profiles of non-dimensional mean velocity and turbulence intensity, and (**b**) the PSD function of streamwise velocities at reference height, for the wind tunnel terrain and the theoretical full-scale terrain from ESDU. trees [25], black cottonwood, trembling aspen, red alder, paper birch and bigleaf map [68]. The drag coefficients for case C1 are 0.22 to 0.18 at wind speeds of 3.9 m/s to 9.3 m/s, while for case C2, the drag coefficients dramatically increase to 0.40-0.36 at the same wind speeds, which indicates that the crown frame greatly changes the aerodynamic shape of the model. The drag coefficients increase rapidly with increased numbers of leaf clusters (for cases C3 to C4) and tend to be steady when there are relatively more leaf clusters (for cases C5 to C8). The former is mainly caused by the initial increased number of leaves significantly changing the aerodynamic shape of the model, while the latter indicates that the aerodynamic shape of the model changes more slowly with more leaves. The variation of drag coefficients generally overlap those reported for the typical broad-leaved trees.