## 4 Discussion and Validation
The data shown in Table 11 were obtained through a figure shown in the reference document [32], and each sample is represented in graphs as a function of time, from which these values of maximum accelerations are obtained. By analysing these plots, it is possible to obtain the duration time of each vertical gust and the normal acceleration variation given in that time, which is related to the load factor variation. Then, for a better understanding of how the following Table 12 data were obtained, the graph corresponding to \"Sample 1\" is represented in Figure 10, where the maximum normal acceleration values measured are \(-\)1 g and 4.75 g, with \"g\" being the Earth gravity (g \(\approx\) 9.81 m/s\({}^{2}\)). Therefore, knowing that the aircraft is operating with a load factor of 1.00 g units, the maximum normal acceleration variations in this case are \(-\)2 g and 3.75 g (a\({}_{\text{n}}-1\)g). On the other hand, the duration time is obtained approximately by analysing the abscissa axis of the graphs, where time is expressed in seconds and is measured from the time when the normal acceleration begins to increase or decrease until it reaches its maximum value. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Sample**} & **Maximum Normal Acceleration,** & **Root Mean Square,** \\  & **a\({}_{\text{n}}\) [g units]** & **a\({}_{\text{n}}\)** \\ \hline
1 & \(-\)1.00 to 4.75 & 0.891 \\
2 & 0.20 to 3.00 & 0.723 \\
3 & \(-\)0.50 to 1.60 & 0.310 \\
4 & 0.00 to 2.00 &  
Figure 10 shows that the maximum normal acceleration values reached in Sample 1 are 4.75 g and \(-1.00\) g, and that the time in which these values are achieved is barely one second. This procedure was repeated with each of the reference document figures, obtaining the normal acceleration variations and times shown in Table 12.  
The load factors given in Figure 10 and Table 11 usually range between \(-1\) and \(2.5\) (orange lines), which coincide with the maximum values for clean configuration specified by EASA for the flight manoeuvring envelope in the CS-25 certification document [58]. This range for the load factor of an aircraft corresponds to the theoretical limit within which there would be no structural damage that would prevent aircraft operation, although such damage should be reviewed after landing. If these limit values (\(-1\), \(2.5\)) are exceeded, as in \"Sample 1\", the structural integrity would be severely threatened, and it must be evaluated through an exhaustive inspection and its corresponding maintenance specified by the manufacturer. Moreover, Airbus specifies that, after the occurrence of severe loads and overload, they must be notified of the event and receive the event data for analysis; they also indicate the steps to follow when experiencing any type of load [57]. Once \"time\" and \"maximum acceleration variation\" are estimated, the maximum vertical displacements experienced by the aircraft are calculated following Expressions (24) and (27), with the difference that, in this case, the time and acceleration variation are known parameters, while the unknown is the variation in the aircraft's vertical speed. In this sense, based on the data provided by NASA for a turbulence event that is considered severe, the proposed methodology is applied in order to verify whether the aircraft altitude losses calculated for real values are consistent with those presented by Airbus, pilots, and experts, as well as those determined in this paper. \[\text{a}=\frac{\text{V}-\text{V}_{0}}{\text{t}-\text{t}_{0}}\boldsymbol{ \texttt  
Negative values in the table refer to a loss of altitude, while positive values refer to aircraft vertical displacements in the opposite direction to the force of gravity. As mentioned above, values higher than 2.5 g and lower than \(-\)1 g are not usual, being considered under extreme events, and thus, Samples \"1\" (4.75 g) and \"2\" (3 g) must be reported to the aircraft manufacturer for a structural integrity inspection.