# Airplane Vortices Evolution Near Ground
## 4 Results and Discussion
### Time Reduction Analysis  
In the actual regulations, the time between two consecutive airplanes is established by the ICAO. Both at take-off (Table 7) and landing (Table 8), see reference [19], this time is a bit conservative, because it is based on a norm that has to be followed independently of the conditions under which the procedures are being designed. The aim of this section is to evaluate how much time could be saved if instead of generalizing and including all of the different conditions in the same rule, each case is studied independently with the conditions of each airport. In order to determine when the vortices leave the runway domain, Figure 25 was created, which for the different cases evaluated, shows the central core position along the abscissa axis over time. The equations characterizing the measured circulation decay were employed to generate this figure. The meaning of the legend presented in this figure is explained in Table 9. In this figure the runway width is presented as two horizontal lines. The times extracted from this graphic will be compared with the ones of reference [19], with the aim to see how much time can be reduced. The first thing to be observed is that the consideration of crosswind does not mean that the vortices will leave the runway earlier. Without crosswind, the vortices get away from the domain within a similar time to that when a crosswind velocity of 2 m/s is considered. On the other hand, the worst case is when the crosswind velocity is of 1 m/s; then for the A320 airplane (whose categorization is medium airplane), the vortices will leave the runway nearly 140 s after their formation. In the other case, for the heavy airplane (A340-300), the vortices leave the runway long after 180 s. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Following Airplane** & **Preceding Airplane** & **Departing Separation Minima** \\ \hline Light & Medium & 2 min \\ Medium & Heavy & 2 min \\ Light & Heavy & 2 min \\ Medium & A380 & 3 min \\ Light & A380 & 3 min \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Time between departing airplanes, information extracted from reference [19]. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Following Airplane** & **Preceding Airplane** & **Arriving Separation Minima** \\ \hline Light & Medium & 3 min \\ Medium & Heavy & 2 min \\ Light & Heavy & 3 min \\ Medium & A380 & 3 min \\ Light & A380 & 4 min \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Time between arriving airplanes, information extracted from reference [19]. Continuing with Figure 25, the next step is to extract the values from it. To round up the times, thus maintaining a small margin of error, an additional 15 s are added to the values retrieved from the graphic. As the widest runway is 60 m, it will be considered that the vortices leave it when the curve crosses the black line situated at 30 m. The results are presented in Table 9, in which it is seen that as the crosswind speed increases, the vortices of the medium airplane will leave the runway before those of the heavy one. The temporal variation of \(\Gamma\) in the case of the heavy airplane is the one stated in Equation (33). For the medium airplane, the temporal variation corresponds to the one shown in Equation (36). In both cases, as experimental data show (Reference [11]), the temporal variation of \(\Gamma\) is not being affected by the crosswind. These temporal variations are the ones during the landing procedure. In order to see which changes are produced by the introduction of the in-house program, the estimated time gain in percentage was calculated using Equation (38), which compares the times obtained by the in-house program with the ones defined in reference [19]. The results are presented in Table 10, and show how much time could be saved if the present in-house program is implemented at the airports. In most of the cases studied the time reduction oscillates between 50% and 80%.