## 3 Results
### Mechanical Properties
#### 3.1.2 Modulus of Elasticity  
Descriptive statistics of the MOE are presented in Table 6. The MOE and air-dry density were strongly correlated in spruce (0.761) and pine (0.752). The differences in variation between the species and between the log types were more minor than in density. The differences in the MOE between the burned trees and reference trees in both species corresponded to the differences in density. The highest MOE was observed in the pine sapwood of the burned trees in the butt logs and the smallest in the spruce heartwood of the burned trees in the butt logs.  
In the linear mixed model for the MOE, significant fixed factors differed between the species. Density was the most significant factor for both species (\(p<0.01\)) (Table 7). Height class was very significant for spruce and significant for pine (\(p<0.01\)). The radial position was a significant factor for pine but had no statistical significance for spruce. Fire damage class was not a significant factor for either species, although the significance was close to 0.05 in spruce. The interaction between the radial position and density was very significant for pine (\(p<0.001\)) but did not have any significance for spruce.  
The fixed coefficients of the models for the MOE are presented in Table 8. A higher density indicates a higher MOE. In both spruce and pine, the MOE was the lowest in the top logs and the highest in the middle logs. In pine, the MOE was higher in sapwood than in heartwood. The positive interaction between the radial position and density in pine indicated that density had a more substantial positive effect on the sapwood MOE than on heartwood. However, fire damage did not have any significant effect on the MOE. In spruce, the RMSE and proportion of stand-level variation (83.0%) of the total random variation were high. Most of the random variation in pine was residual (51.8%), and the RMSE was smaller.  
\begin{table}
\begin{tabular}{l c c c c c c} \hline  & & **Norway Spruce** & & **Scots Pine** & \\ \hline
**Wood Material** & **Butt Log** & **Middle Log** & **Top Log** & **Butt Log** & **Middle Log** & **Top Log** \\ \hline Sapwood, heavily burned side & 8.0 (1.6) & 9.2 (1.6) & 7.7 (1.6) & 12.3 (1.7) & 9.1 (1.4) & 8.9 (1.2) \\ Sapwood, slightly burned side & 8.5 (1.9) & 9.3 (1.0) & 8.0 (0.4) & 11.6 (2.0) & 9.7 (1.6) & 9.3 (1.4) \\ Heartwood, burned trees & 5.4 (1.3) & 7.0 (0.8) & – & 9.4 (1.4) & 9.1 (1.2) & – \\ Sapwood, reference trees & 10.4 (2.7) & 9.8 (2.2) & 9.6 (2.4) & 10.6 (2.9) & 9.5 (2.4) & 7.7 (2.4) \\ Heartwood, reference trees & 9.8 (2.5) & 10.0 (2.1) & – & 8.3 (2.6) & 7.9 (2.1) & 6.7 (1.6) \\ \hline \end{tabular}
\end{table}
Table 6: Modulus of elasticity (MOE) by species, damage class, radial position, and log type (GPa). Values are presented as the means, with the standard deviation in parentheses.  
\begin{table}
\begin{tabular}{l c c c c c c} \hline  & & **Norway Spruce** & & **Scots Pine** & \\ \hline
**Wood Material** & **Butt Log** & **Middle Log** & **Top Log** & **Butt Log** & **Middle Log** & **Top Log** \\ \hline Sapwood, heavily burned side & 446.5 (42.6) & 448.7 (32.5) & 442.0 (18.4) & 581.3 (71.8) & 489.9 (41.3) & 489.2 (33.4) \\ Sapwood, slightly burned side & 448.9 (44.1) & 455.5 (32.5) & 446.1 (34.4) & 585.4 (67.4) & 476.2 (31.3) & 489.0 (38.8) \\ Heartwood, burned trees & 388.3 (32.3) & 402.0 (25.1) & – & 544.2 (95.5) & 478.3 (28.4) & – \\ Sapwood, reference trees & 474.8 (40.7) & 448.9 (55.5) & 448.0 (47.3) & 527.7 (78.1) & 476.3 (63.5) & 446.2 (45.9) \\ Heartwood, reference trees & 467.5 (38.8) & 446.6 (33.4) & – & 468.6 (62.2) & 447.1 (22.4) & 450.0 (60.6) \\ \hline \end{tabular}
\end{table}
Table 5: Air-dry density by species, damage class, radial position, and log type (kg/m\({}^{3}\)). Values are presented as the means, with the standard deviation in parentheses.