## 5 Discussion and Conclusions  
Section 4 was dedicated to present the results from the validation process. In this section, these results are seen from the perspective of the main assumptions and the previous studies, in order to generate conclusions and recommended future studies. Since the validation process consisted of three cycles, it is logical to organize this section making reference to these three cycles. Figure 21: Schematic representation of the boundaries for the application of the results. The main assumption for the first cycle was that the normal drag coefficient obtained from the study of [PERSON] et al. (2011), together with an axial drag coefficient approximation, should be sufficient to accurately model the drag force of the net for different system spans in OrcaFlex. The results in Section 4.1 show that, as the system's span increased, the net started to resemble the net in perpendicular flow of the experiment carried out by [PERSON] et al. (2011). That led to a towline tension curve that accurately followed the GPGP data trend for a wide span. In contrast, when the system's net was experiencing parallel flow almost all along its length (i.e., narrow span), the towline tension considerably deviated from reality. That was due to the fact that an axial drag coefficient magnitude of \(C_{D,\text{OF},\mu}^{*}=\frac{1}{3\pi}C_{D,\text{OF},\mu}^{*}\) applied all along the wings is too high, in comparison with the reduced drag coefficient as a consequence of the shielding effect when \(\theta<24^{\circ}\). The nominal span result, which slightly underestimated reality, can be explained by comparing Equations (26) and (28). The AS equation includes the term \(f_{\text{vert}}\cdot\hat{\mathbf{t}}\), which represents the tangential component of the drag on the vertical twines in cross flow. In the OF model, that term cannot be included in the calculation with the cross flow drag coefficient, but only with the parallel (axial) flow drag coefficient, which is lower in magnitude, leading to the underestimation. In summary, after the first cycle, it was found that the [PERSON] semi-empirical formula ([PERSON] et al., 2011) was sufficient to accurately estimate the drag force of the ocean system's net in wide span with a mean deviation of just 1%, which, from another perspective, might be considered as lacking the desired minimum overestimation. Besides this, the first two limitations of the OF model, listed in Section 3.2, explain the deviation from reality of the drag force estimation for nominal and narrow spans. Moving forward to the second cycle, there were three key assumptions. First, by using the AS calculation, defined by [PERSON] et al. (1966), the large deviation between the towline tension curve for a narrow span and the GPGP data should be reduced, because the shielding effect is taken into account. Second, by using the AS calculation, the underestimation of the towline tension for nominal span should be reduced, since the twine-by-twine drag calculation is included. Third, the AS calculation can be reproduced in the OF model by optimizing the OF axial drag coefficient for the \(\theta\) assumed by the system's wings in different spans. The second cycle's results (Section 4.2) demonstrated that the first assumption is valid. Actually, applying the AS formula for the reduced drag coefficient (Equation (8)) corrected the narrow span curve from 276% deviation from GPGP data to about \(-10\%\) deviation. The second assumption is also valid, and in fact, the towline tension curve for nominal span moved from a slightly underestimating position to a slightly overestimating position (from a \(-3\%\) deviation to a \(14\%\) deviation), which is preferable. The third assumption was proven to be true since it was demonstrated that the OF axial drag coefficient optimization method, presented in Section 3.1, improved the estimation of the DT, and it can be consistently repeated for different system spans.