## 4 Discussion and Validation  
The validation of the results obtained in this paper could not be performed with real flights, so we decided to validate them by comparison with research results published by reference organizations. In this sense, documents published by Airbus and NASA were found. Additionally, pilot and expert statements [56] were gathered, which also agree with the values achieved by the proposed methodology, as shown in the following figure. The figure shows that the maximum values of aircraft altitude loss due to turbulence can reach 30 m (100 feet), categorising this type of turbulence as severe. This value coincides with those obtained in the proposed method, whose results were shown in the graphs above according to the categories and angles of attack [Figures 3-6]. Depending on the angle of attack, the turbulence intensity experienced by the aircraft changes, so higher values of vertical displacement can be achieved as the angle of attack in-creases. For example, wind intensities associated with moderate turbulences (25-45 kt) result in maximum vertical displacements of 6 m (20 ft), following the values shown in Figure 9. However, for that same turbulence intensity, maximum vertical displacements of 26 m (87 ft) are achieved in the graph developed for category A [Figure 3] and around 18 m (60 ft) for the other categories operating at maximum angles of attack (6\({}^{\circ}\)) [Figures 4-6]. These values are properly shown in Appendix A [Tables A1-A3]. Meanwhile, for lower angles of attack (2\({}^{\circ}\)), the altitude loss for categories C and D under wind intensities of 25-45 kt ranges between 3 and 8 m (8-28 ft). It is important to note that the data shown in Figure 9 correspond to categories C and D.  
In any case, the results obtained and those found coincide in that the maximum value of the aircraft altitude loss is around 30 m (100 ft). Thus, assuming 6\({}^{\circ}\) as a high angle of attack, the maximum altitude loss for a category A aircraft is around 29 m (96 ft) according to the proposed methodology, while for categories B, C, and D, the maximum vertical displacement achieved could be up to 21 m (68 ft). \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline
**Wind Speed [kt]** & 10 & 15 & 20 & 25 & 30 & 35 & 40 & 45 & 50 & 55 & 60 & 65 & 70 & 75 & 80 \\ \hline
**Cat. A [ft]** & 20 & 79 & 124 & 154 & 190 & 234 & 284 & 342 & 405 & 474 & 548 & 628 & 715 & 808 & 908 \\
**Cat. B, C, and D [ft]** & 20 & 47 & 78 & 113 & 153 & 200 & 254 & 316 & 381 & 449 & 522 & 603 & 689 & 781 & 880 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Additional clearance for mountainous terrain for a 6\({}^{\circ}\) angle of attack. Figure 9: Turbulence intensity. Referring to the document provided by Airbus [57], a figure presents the vertical wind speed variations as a function of time during a turbulence event that they categorize as excessive, and whose data have been obtained using flight recorder data. Analysing the 30 kt downdrafts and identifying that their duration time is approximately 2 s, it is determined that the aircraft's altitude loss would correspond to about 30 m, which is in agreement with the maximum vertical displacement value determined in this paper. On the other hand, based on the data gathered in NASA Technical Note D-5573 [32], which consists of an analytical study about the effects of severe turbulence on a subsonic jet aircraft, the maximum normal accelerations experienced by the aircraft were found. The following table includes these accelerations, which were calculated by a high-speed digital computer during the flight after taking eighteen different samples of two hundred-second periods. Each of these samples are listed in Table 11. The second column of this table indicates the maximum normal acceleration reached due to turbulence in each of the samples, and the third column represents the root mean square of the normal acceleration, obtained from all the values recorded in each sample.