## 3 Results
### Correlation Between fx and fy  
With a calculated strength (CS) of 100 kN, the fx and fy values according to Equations (11) and (12) were calculated independently, observing a strong relationship between both values, as can be observed in Figure 10a, where an R-square of 0.9585 reveals a high precision for a 2-degree polynomial regression. When other CS values in the range from 100 kN to 400 kN were simulated, other polynomial regressions were obtained, but with the same R-square, as can be noted from Figure 10b, corresponding to a CS = 400 kN. What is more, the distribution shape of the plots in the maps was identical, with a difference in the axis values, as is evident. This is considered a visually relevant result because a person in charge of the lashing arrangement can detect how to reach the condition of the lashing layout to fulfill both requirements of longitudinal (fx) and transverse (fy) force through the corresponding angles (\(\alpha\) and \(\beta\)). For instance, in the cases where the obtained fx is negative, it means that no lashing lines are needed to counteract the longitudinal force, so the lashing lines can adopt a more transverse direction. Furthermore, in both Figures, two groups of points are clearly observed, and the reason for this separation is the vertical stowage position. What is more, when the cargo \begin{table}
\begin{tabular}{c c} \hline \hline
**CS** & **No. of Lashing Lines** \\ \hline
100 & 2 \\ \hline
150 & 3 \\ \hline
200 & 4 \\ \hline
250 & 5 \\ \hline
300 & 6 \\ \hline
350 & 7 \\ \hline
400 & 8 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Number of lashing lines according to a supposed CS of 50 kN each. Figure 9: Example of the lashing line arrangement, where the red dotted lines are the projections of the lashing lines CS\({}_{1}\) in the vertical and transverse planes. item is stowed below the main deck (tween deck or cargo hold), the lower values of fx and fy are demanded (group of points plotted in the left side) due to non-influence of the external forces. Contrastingly, when CS values from 100 to 400 kN were simulated together and the fx and fy results were plotted in a map, as can be seen in Figure 11, a weak correlation between both values was observed, with a polynomial regression with an obtained R-square of 0.86 in the studied case of the present research. If other conditions, such as the ship's length or service speed, were simulated, the behavior of data on the map and polynomial regression would be different. These results show that unlike the results commented in Figure 10, when the requirements to reach a minimum CS were higher, the combination of angles \(\alpha\) and \(\beta\) have to be different between them in order to satisfactorily fulfill the balance of longitudinal and transverse forces. In any case, for the studied case, although the precision was not good enough, the visual distribution on the map of fx and fy values can be a good approach for the people in charge of the lashing arrangement. That is, this information can be useful for new decisions about the point of securing of the lashing lines for reaching a higher force in the longitudinal (fx) or the transversal (fy) direction in order to fulfill the balance of supported forces by the cargo item. Figure 11: The values of fx and fy (purple squares) for 100 kN \(<\) CS \(<\) 400 kN for the studied case. Figure 10: The values of fx and fy (purple squares) for (**a**) CS = 100 kN and (**b**) CS = 400 kN. However, keeping constant all variables of the studied case when the simulations were performed for a range of ship speeds between 6 knots and 20 knots, the highest precision of the polynomial regression was obtained for the highest ship speed, reaching an R-square of 0.87 for 20 knots, as is shown in Figure 12a. The lower the ship's speed, the lower the precision of the polynomial regression obtained, as is depicted in Figure 12b for a ship speed of 6 knots.