## 2 Materials and Methods
### Turbulence Clearance
#### 2.2.2 Methods
Following the same method as for the calculation of the vertical gust velocity, the values shown in Table 3 were analysed, and a trend line with its corresponding equation was found to obtain an approximation of the effective gust velocity as a function of the load factor variation. The data used are shown again in Table 7.  
Nevertheless, a sufficiently accurate approximation was not obtained, so it was also decided to divide the function according to the turbulence intensities (light, moderate, or severe) for a more accurate approximation. In this way, the effective gust velocity (\(\mathrm{U_{e}}\)) was obtained for each type of turbulence intensity, as shown below:  
Turbulence experienced by the aircraft as light:  
\[\mathrm{U_{e}=60~{}\Delta n+5\cdot 10^{-15}} \tag{21}\]  
Turbulence experienced by the aircraft as moderate:  
\[\mathrm{U_{e}=30~{}\Delta n+6} \tag{22}\]  
Turbulence experienced by the aircraft as severe:  
\[\mathrm{U_{e}=9~{}\Delta n+16.5} \tag{23}\]  
The effective gust velocity should be adjusted to obtain the vertical speed variation of the aircraft, resulting in the derived gust velocity (\(\mathrm{U_{de}}\)), which is 60% higher than the effective gust velocity [39]. The next step is to calculate the time during which the aircraft is exposed to turbulence. For this, the equation of linear motion is applied [55]:  
\[\mathrm{a=\frac{V-V_{0}}{t-t_{0}}} \tag{24}\] \begin{table}
\begin{tabular}{l c c c} \hline  & **Light** & **Moderate** & **Severe** \\ \hline Load factor variation, \(\Delta n\) & 0.05–0.2 g & 0.2–0.5 g & 0.5–1.5 g \\ Effective gust velocity, \(\mathrm{U_{e}}\) & 3–12 kt & 12–21 kt & 21–30 kt \\ \hline \end{tabular}
\end{table} 
Table 7: Load factor variation vs. effective gust velocity. This equation establishes the following:  
* t as the final time, i.e., the instant when a vertical gust ends;
* t\({}_{0}\) as the initial time, i.e., the instant at which a vertical gust begins;
* \((\text{t}-\text{t}_{0})\) as the duration time of the vertical gust affecting the aircraft;
* \((\text{V}-\text{V}_{0})\) as the vertical speed variation experienced by the aircraft due to the turbulence intensity, which corresponds to the derived gust velocity (U\({}_{\text{de}}\));
* \(a\) as the vertical acceleration experienced by the aircraft, being the sum of gravity and the vertical acceleration caused by the turbulence, which results from multiplying the gravity (g) and load factor variation (\(\Delta\)n) [43]: \[\text{a}=-(\text{g}+\Delta\text{n}\,\text{g})=-\text{g}\;(1+\Delta\text{n})\] (25)  
Substituting all these values in the previous equation and solving with time (t) as the unknown, the period of time in which the aircraft is affected by vertical air currents can be obtained:  
\[-\text{g}\;(1+\Delta\text{n})=\frac{-\text{U}_{\text{de}}}{\text{t}}\to\; \text{t}=\frac{\text{U}_{\text{de}}}{\text{g}\;(1+\Delta\text{n})} \tag{26}\]  
Finally, once the turbulence duration time and derived gust velocity have been obtained, the aircraft's vertical displacement caused by turbulence, \(\Delta\text{h}\), can be calculated:  
\[\Delta\text{h}=\text{U}_{\text{de}}\;(\text{t}-\text{t}_{0}) \tag{27}\]  
The turbulence clearance to be applied in mountainous terrains is proposed to correspond to that loss of altitude that the aircraft may experience when flying through mountain waves originated by the wind that is perpendicular to the mountain range. For its application, the vertical displacement values due to turbulence may be determined by two methods, analytical or graphical. The analytical method would be the application of the previous expressions, and the graphical one would be taking the values shown below. These graphs are based on altitude losses associated with a defined wind speed and flight altitude, which is required to determine the true airspeed (TAS), among other parameters. Thus, from a 53 kt wind speed or higher, the expression of the \"ICAO standard wind\" (12) is applied to obtain the flight altitude (h\([\text{ft}]=(\text{WindSpeed}[\text{kt}]-47)\cdot 1000/2\)).