# Safety Evaluation Method and Management Strategy for Aviation Flight Plans
## 5 Case Analysis  
To demonstrate the safety index calculation method proposed in this study, this section abstracts the actual airspace and route structure in eastern China based on a 1000 km \(\times\) 700 km airspace. The flight plans of five aircrafts in this airspace are extracted based on the actual operational flight information. This airspace contains 16 waypoints (Figure 8), and their location information is listed in Table 1. The weather-influenced airspace W is represented by a circle. The center of airspace W is located at W1 (865, 345), and it will move to W2 (920, 565) from 12:12:24 to 17:52:24. The special airspace is represented by an irregular figure whose center is R1 (195, 605); the impact time lasts from 10:00:00 to 18:00:00 (Table 1). The flight plans of each aircraft are shown in Table 2, e.g., aircraft A is scheduled to move from waypoint 9 at 14:14:10 to waypoint 7 at 14:24:10 and from waypoint 2 at 14:51:50 to waypoint 1 at 14:39:00. Aircraft C is scheduled to pass waypoint 5 at 14:19:00, and it will be affected by the weather-influenced airspace W along the way. The results show that aircraft C and the airspace W initially have a high safety index, and there is a risk of conflict between 14:19:00 and 14:22:43, reaching the maximum instantaneous probability of conflict at about 14:20:51. At this point, the conflict probability is 0.3675, and the safety index is 2.721 \(\times\) 10\({}^{-3}\). \begin{table}
\begin{tabular}{c c c c c c c c c} \hline Waypoint & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ Coordinate & (400, 575) & (400, 425) & (675, 400) & (750, 400) & (840, 400) & (550, 332) & (400, 250) & (300, 220) \\ \hline Waypoint & 9 & 10 & 11 & 12 & 13 & 14 & 15 & 16 \\ Coordinate & (375, 145) & (615, 440) & (512, 505) & (230, 620) & (710, 460) & (640, 340) & (300, 375) & (470, 440) \\ \hline Centre & R\({}_{1}\) & W\({}_{1}\) & W\({}_{2}\) & & & & & \\ Coordinate & (195, 605) & (865, 345) & (920, 565) & & & & & \\ Time & 10:00:00–18:00:00 & 12:12:24–17:52:24 & & & & & \\ \hline \end{tabular}
\end{table} 
Table 1: Airspace configuration parameters. Figure 8: Airspace waypoint configuration and flight plan (The numbers represent the waypoints of the individual routes). \begin{table}
\begin{tabular}{c c c} \hline
**Aircraft** & **Waypoints along the Way** & **Waypoint Time** \\ \hline A & 9–7–2–1 & 14:14:10–14:24:10–14:39:00–14:51:50 \\ B & 8–7–6–3–4–5 & 14:09:40–14:18:20–14:31:20–14:43:00–14:49:50–14:57:00 \\ C & 5–4–3–10–11–12–12 & 14:19:00–14:27:20–14:33:10–14:40–14:49:30–14:58:20–15:12:50 \\ D & 13–14 & 14:32:00–14:44:00 \\ E & 15–16 & 14:14:10–14:29:00 \\ \hline \end{tabular}
\end{table} 
Table 2: The flight plans of each of the five aircraft. Aircraft C is scheduled to pass waypoint 1 at 14:58:20 and waypoint 12 at 15:12:50. On the way, it will be affected by the special airspace R. The results show that there is a risk of conflict between aircraft C and the special airspace R from 15:09:56 to 15:12:50, reaching the maximum instantaneous probability of conflict at about 15:11:30. At this time, the conflict probability is 0.5534, and the safety index is 3.614 \(\times\) 10\({}^{-4}\). Moreover, our results show a risk of conflict between aircraft C on route 3-10 and aircraft B on route 6-3. According to their accessible area and the potential conflict area (Figure 9), there is a risk of conflict between aircrafts B and C from 14:36:50 to 14:40:00. For aircrafts B and C, the potential conflict probabilities are 1.75 \(\times\) 10\({}^{-4}\) and 4.31 \(\times\) 10\({}^{-3}\), respectively, and the safety indices are 7.017543 and 5.948839, respectively. Aircraft C has a higher risk of conflict than aircraft B does. According to their accessible area and conflict area (Figure 10), potential three-aircraft conflicts also exist among aircrafts B, C, and D.  
A conflict risk exists for aircraft B at 14:38:15-14:40:43, for aircraft C at 14:37:20-14:40:06, and for aircraft D at 14:37:20-14:40:43.