# Airplane Vortices Evolution Near Ground
## 4 Results and Discussion
### Time Reduction Analysis
The increase in time for the cases with \(U_{\infty}=1\) m/s is due to the strength of the crosswind not being high enough to move away the port vortex from the runway in a quick manner. For this case, the vortex speed is contrary to the crosswind velocity and the difference in velocity between them is small. As a result, the vortex needs to cross the whole runway moving slowly. Figure 25: X position of the starboard vortex throughout time. Two models and three different crosswind velocities have been considered. The black lines represent the point at which the vortices will leave the runway. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Type of Airplane** & **Time (s)** & **Time/\(t_{0}\)** & **Program’s Execution Time (s)** & \(\Delta x=\Delta y\) (m)** \\ \hline A320 - 0 (\(U_{\infty}=0\) m/s) & 35 & 1.9 & 19 & 0.1 \\ A340 - 0 (\(U_{\infty}=0\) m/s) & 55 & 1.8 & 17 & 0.1 \\ A320 - 1 (\(U_{\infty}=1\) m/s) & 150 & 8.3 & 18 & 0.1 \\ A340 - 1 (\(U_{\infty}=1\) m/s) & - & - & 19 & 0.1 \\ A320 - 2 (\(U_{\infty}=2\) m/s) & 40 & 2.2 & 19 & 0.1 \\ A340 - 2 (\(U_{\infty}=2\) m/s) & 55 & 1.8 & 18 & 0.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Calculated time for the vortex to leave the runway. Additionally, this time is presented in nondimensional form, the time elapsed during the calculation and the \(\Delta x\) and \(\Delta y\) used to perform the domain’s discretization are included. In all cases a time step of 0.5 s was used. Finally, except for the case of \(U_{\infty}=1\) m/s, the results should be taken as valid in the practical field, because the time elapsed does not widely exceed \(t^{*}=2\), and thus this stays inside the domain at which the in-house program is accurate, meaning that this application could be taken as reliable. At this point it is interesting to highlight that when considering the methodology proposed by [3], consistent in reducing the effect of fluid viscosity via sucking the boundary layer, or via causing the main vortex to split in many other small ones by putting horizontal plates in the runway ([PERSON] et al. [4]), the potential flow tool presented in this paper would be particularly useful, especially after considering its precision during the initial time steps, just before the vortex rebound starts. The tool presented in this paper needs to be seen as fast, widely applicable and accurate enough to estimate instantaneously the minimum time needed between two consecutive airplanes. The vortex behavior could be modeled even better if the secondary vortices' evolution was also included in the in-house code. This would allow to estimate the rebound effect and greatly improve the temporary results of the in-house program. It has been stated that the in-house code generates good results provided that the experimental circulation temporal decay is known. To extensively use the in-house code, the circulation temporal decay measured from different airplanes in different airports and under different ambient conditions needs to be known. A possible methodology, among others, to avoid performing such a large amount of measurements, would be using an Artificial Neural Network (ANN), and then the circulation decay for conditions not measured could be extrapolated. If this information could be implemented in the presented in-house program, the minimum time between any two consecutive airplanes under any atmospheric conditions and for any airport could be determined.