## 2 Materials and Methods
### Turbulence Clearance
#### 2.2.2 Methods
the weights for each aircraft category had been collected, a probability density function was obtaining, so that a low landing weight was identified. Since, as mentioned above, the largest vertical displacements occur when the aircraft is operating at low weights (keeping all other variables constant), the weights used for categories C and D were taken as the value from which 90% of the landing weights are found following the probability density function. This means that the weight taken is a value so that the probability of not being lower than it is less than or equal to 0.1 (10%), being a reliable reference as the lowest weight at which the aircraft model may operate. Figure 2 shows the histogram and probability density function obtained from analysing the landing weights of more than one hundred A320 flights. From the available sample, the histogram was fitted to a Weibull distribution. And from the probability density function, it can be said that with a probability of 0.1 (10%), the weight of the aircraft is 56,400 kg or less. This same methodology was followed for the A340-600 (Category D), giving a weight of 226,100 kg. It follows that the wind that is perpendicular to the mountain range at 700 hPa (Vnorm) identifies the intensity of the mountain wave and, therefore, the updrafts and downdrafts that will affect the aircraft. For this reason, it is necessary to convert the wind speed at a given flight altitude to its equivalent at the altitude corresponding to 700 hPa, as mentioned above. To determine the vertical gust velocity according to a mountain wave, an expression was developed for each mountain wave intensity (light, moderate, severe) in order to relate the wind speed at 700 hPa (Vnorm) to the vertical gust (Vgust), as the values indicated in Table 3, which are shown again in Table 6.  
The values from the table were used to obtain equations relating to these data. First, an attempt was made to find a common equation for all the intensities. However, the trend line did not fit accurately in some parts of the function. Therefore, the functions were divided by the turbulence intensity, resulting in the following three linear equations: \begin{table}
\begin{tabular}{l c c c}  & **Light** & **Moderate** & **Severe** \\ Wind perpendicular to the mountain range at 700 hPa, Vnorm & 15–25 kt & 25–45 kt & \textgreater{}45 kt \\ Vertical gust of mountain waves, Vgust & 9–27 kt & 27–53 kt & 53–107 kt \\ \hline \end{tabular}
\end{table} 
Table 6: Wind speed perpendicular to the mountain range vs. vertical gust velocity. Figure 2: Weibull distribution for A320 landing weights (category C). Vertical gust velocity for light-intensity mountain waves:  
\[\mathrm{V_{gust}=1.8~{}V_{norm}-18} \tag{18}\]  
Vertical gust velocity for moderate-intensity mountain waves:  
\[\mathrm{V_{gust}=1.3~{}V_{norm}-5.5} \tag{19}\]  
Vertical gust velocity for severe-intensity mountain waves:  
\[\mathrm{V_{gust}=2.16~{}V_{norm}-44.2} \tag{20}\]  
After obtaining the vertical gust (\(\mathrm{V_{gust}}\)), as well as the true airspeed (\(\mathrm{TAS=V_{\infty}}\)), lift coefficient (\(\mathrm{C_{L}}\)), air density (\(\rho\)), and aircraft characteristics such as the weight (W) and wing area (S), the load factor variation may be calculated (7). The load factor variation indicates the turbulence intensity experienced by the aircraft, since depending on the weight (W), wing area (S), and lift coefficient (\(\mathrm{C_{L}}\)), it will be more or less affected at the same wind speed and altitude. The lift coefficient depends directly on the angle of attack, and hence, it is defined at the beginning. In order to correlate the load factor variation with the buffeting experienced by the aircraft according to the type of turbulence perceived, the load factor variation and the effective gust velocity (\(\mathrm{U_{e}}\)) were related.