## 4 Results and Discussion
### Sensitivity Tests
The results for the nine cases are presented in Figure 6; there were no significant differences in the execution times since all were performed with a 0.25 m buoy. As shown in Figure 6, an increase in the \(OD\) coefficient induces an increase in the average power and its standard deviation. Changes in the \(ID\) did not show significant changes in the mean power (at least in the evaluated values). On the other hand, changes in the AD had considerable effects on the mean power and its standard deviation, at least for the shorter-period waves (4T) where the mean values were 34% higher. If a default value of AD = 1 was set, it produced the minimum value of the output power. In order to avoid a power overestimation, this would be the preferred setting. To complement the results presented in Figure 6, a further analysis was conducted by using the time series of other available variables, such as the center of mass of the buoy (_CofM_Z_), its angular momentum (_Mom_Ang_), its angular velocity (_Vel_Ang_), and the torque. Since the output power depends on both the angular velocity and torque, values of power (_Pot_) were also included in the analysis. The statistical parameters, calculated for each of the time-series pairs (test numbers in Table 5), included (i) the root mean square error (_RMSE_), to denote the magnitude of the error in the same units of the variable (small  
Figure 6: Mean absorbed power and its standard deviation for the sensitivity tests of the cases presented in Table 4 (\(H\) = 1.0 m and \(R\) = 0.25 m), organized by wave period and the tested parameters. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Test Number** & **Sensitivity Test** & **Cases Compared** \\ \hline
1 & OD-4T & P1, P2 \\
2 & ID-4T & P3, P4 \\
3 & AD-4T & P1, P5 \\
4 & AD-8T & P6, P7 \\
5 & ID-8T & P8, P9 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Sensitivity tests to evaluate the effects of the parameters AD, ID, and OD in the simulations. values of this parameter indicate a greater similarity between the cases in Table 5); (ii) the scatter index (_SI_), which indicates the error percentage, calculated by dividing the RMSE by the average of the model; (iii) the Pearson's correlation coefficient, denoted as r and ranging from \(-1\) to \(+1\), which defines the linear relationship as negative or positive, or the absence of a correlation (r \(\sim\) 0); and, finally, (iv) _BIAS_, a measure of the tendency for underestimation (overestimation) when negative (positive) values are found. Figure 7 shows the results obtained from the statistical analysis. The center of mass (_CofM_Z_) seems to be the best-performing variable, with low _RMSE_ and _SI_ values and a fairly high linear correlation, and showing very little effect of changing _OD_, _ID_, or _AD_. On the other hand, the torque seemed to be the variable with the highest _RMSE_ values of all the tests performed, with the changes in _ID_ being those that affected the RMSE the most. Torque was also the variable that showed the lowest linear correlation r, especially for changes in _ID_ and _AD_. Changes in the latter coefficient also had the highest values of positive bias (see Figure 7d). The statistics for the angular velocity had fairly low _RMSE_ and _SI_ values, respectively, and its _BIAS_ was fairly close to zero. This is a great advantage since the calculations of power rely on both torque and angular velocity. As no physical experiments were available for validation, the criteria for choosing the combination of parameters to use were those providing lower values of power BIAS  
Figure 7: Statistical analysis for the center of mass (_CofM_Z_), angular momentum (_Mom_Ang_), angular velocity (_Vel_Ang_), torque, and output power (_Pot_) for the cases presented in Table 5. (**a**) Root Mean Square Error (RMSE); (**b**) Scatter Index (_SI_); (**c**) Pearson correlation coefficient (r); (**d**) underestimation or overestimation tendency (BIAS). and of power RMSE, and those avoiding high overestimations for the torque.