## 4 Results
### Calibrated Drag Coefficients for System 002  
The results presented in Figure 19 are a consequence of the optimization of the OF axial drag coefficient (\(C^{*}_{D,\text{OF},a}\)) for different span lengths. Those coefficients, in turn, are a consequence of the mesh cross flow drag coefficients (\(C^{*^{\prime}}_{D,\text{mem}}\)), calculated with the AquaSim Equation (10) (2 nd validation cycle) and estimated by the CFD model (3 rd validation cycle). Therefore, it is important to tabulate and analyze these coefficients.  
Table 4 includes the mesh cross flow drag coefficients (\(C^{*^{\prime}}_{D,\text{mem}}\)) for the 2 nd and 3 rd cycles, for different angles of attack.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \(\theta\) (\({}^{\circ}\)) & **2 nd Cycle** & **3 rd Cycle** \\ \hline
90 & 1.5999 & 1.5967 \\
45 & 1.5999 & 1.5589 \\
30 & 1.5999 & 1.3822 \\
20 & 1.5589 & 1.2649 \\
10 & 0.5639 & 0.8492 \\
5 & 0.2005 & 0.6076 \\
3 & 0.0933 & 0.5253 \\
2 & 0.0508 & 0.4849 \\
1 & 0.0180 & 0.4732 \\
0 & 0.0 & 0.4614 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Mesh cross flow drag coefficients (\(C^{*^{\prime}}_{D,\text{mem}}\)) for the 2 nd and 3 rd validation cycles.  
It is clear that the drag coefficients of the second validation cycle exhibited a sharp reduction until 0.0 with decreasing \(\theta\). In contrast, the coefficients estimated by the CFD model followed a less-steep reduction, and in parallel flow, the value was larger than 0.0. This difference explains the deviation between the 2 nd and 3 rd validation cycle towline tension curves. As an example to quantify the difference, the 3 rd cycle drag coefficient was 9.5-times larger than the second cycle drag coefficient at an angle of attack of 2\({}^{\circ}\). In other words, the CFD model provided an estimate of the shielding effect that was very different from the estimate given by AquaSim Equation (10).  
Another relevant remark is that the \(C_{\mathrm{D,mem}}^{*}\) values at 90\({}^{\circ}\) were lower than the value of 1.9623 obtained from [PERSON] semi-empirical Formula (22). This is logical since, in both, the AquaSim formulation and CFD model, the twine is modeled as a cylinder. In [PERSON]'s case, the twine is a real one moving through water. The results presented in Figure 19 indicate that the Naumov value seems closer to the real-world data and keeping it as the OF normal drag coefficient (\(C_{\mathrm{D,OF,}n}^{*}\)) led to accurate results.  
Table 5 presents the OrcaFlex recommended axial drag coefficients for System 002's net and for \(u_{\mathrm{stw}}>0.5\) m/s.  
For a narrow span, the axial drag coefficient decreased from 0.208 in the first cycle to 0.01 in the second cycle and increased to 0.082 in the third cycle. This is consistent with the differences in the mesh cross flow drag coefficient (\(C_{\mathrm{D,mem}}^{*}\)) shown in Table 4. Taking the average of the second and third cycles yielded an axial drag coefficient of 0.046, which is a 78% decrease relative to the first cycle.  
For the nominal span, the axial drag coefficient increased from 0.208 in the first cycle to 0.332 in the second cycle and to 0.285 in the third cycle. This is consistent with the differences in the mesh cross flow drag coefficient (\(C_{\mathrm{D,mem}}^{*}\)) shown in Table 4 for an angle of attack of 30\({}^{\circ}\). The 0.285 coefficient represents a 37\({}^{\circ}\) increase relative to the first cycle.  
For the wide span, the axial drag coefficient increased from 0.208 in the first cycle to 0.301 in the second cycle and further increased to 0.324 in the third cycle, which is a 56% increase relative to the first cycle.