## 4 Simulation Experiment and Result Analysis
### Analysis of Results  
Multi-flight combination simulation experiments were conducted for UAVs of category 1, and the minimum outer catch sphere radius was used as the radius of the UAV safety zone. The experimental results are shown in Figure 9.  
As demonstrated in Figure 9, for the stochastic heading model, the UAV operational sorties were kept constant, and the conflict rate of UAVs in the airspace exhibited a fluctuating pattern around a specific value. It is worth noting that the magnitude of this fluctuation decreased as the number of operational sorties increased, while at the same time, the conflict rate exhibited an irregular upward trend.  
For the two UAVs of category 1, the radius of the safety zone of their UAV combination sphere \(\lambda\in[1,50]\) as adjusted to be the independent variable, and the step size was set to 1. Simulation experiments were conducted, and the experimental results are shown in Figure 10.  
As illustrated in Figure 10, the probability of conflict among UAVs increased monotonically with a larger safety radius of the combined sphere. Notably, there was a significant acceleration in the growth rate when the radius reached 10 m. Conversely, as the safety radius of the combined sphere increased, the airspace utilization rate in relation to safety spacing demonstrated a monotonically decreasing trend. The decline in utilization rate  
Figure 9: Graph of experimental results of 10 UAVs of the same category.  
gradually slowed down, and beyond a radius of 9 m, the change became relatively insignificant. Therefore, we concluded that the optimal safety interval for type 1 UAVs is 10 m.  
Figure 11 further supports this conclusion. As the safety radius of the combined sphere gradually increased, the conflict probability between UAVs showed a consistent upward trend. Particularly at a radius of 10 m, the rate of increase in conflict probability was notably accelerated. At the same time, the airspace utilization rate corresponding to the safety interval exhibited a monotonically decreasing trend, with the rate of decline tapering off over time. Similarly to the earlier findings, when the safety radius exceeded 9 m, the difference in the rate of change became less pronounced.  
Based on the comprehensive analyses presented, we can conclude that the safety interval for type 1 UAVs should indeed be set at 10 m. In addition, similar experiments were conducted for the other categories of UAVs to calibrate their respective safety intervals, as illustrated in Figure 11.  
The specific results of the UAV safety interval calibration are shown in Table 3.  
Figure 11: Results of simulation experiments for each category: (**a**) plot of conflict probability versus safety zone radius; (**b**) plot of airspace utilization versus safety zone radius.  
Figure 10: Experimental results of single category UAV simulation.  
To further validate the rationale behind the calibration of UAV safety intervals, we designed an experimental scheme to analyze the fusion operations of the four categories of UAVs with equal proportions. The results of this experiment are presented in Figure 12, which clearly illustrates that the airspace conflict probability was significantly influenced by the category of UAV when the radius of the combined sphere safety zone was small. As the safety zone radius increased, the impact of UAV category on conflict probability gradually diminished. Our analysis indicates that at smaller safety zone radii, the size and speed of the UAVs have a notable effect on the probability of conflict. However, as the radius of the safety zone increased, the significance of these factors in determining conflict probability became less pronounced. Eventually, when the safety zone radius reached a specific threshold, the conflict probability curves for the different UAV types began to overlap. This experimental finding further confirmed the validity of the safety interval calibration conducted for the individual UAV categories.