# A Performance-Based Airspace Model for Unmanned Aircraft Systems Traffic Management
## 4 Verification Case Study
### UAS Delivery Scenario  
This scenario investigates a SUAS delivery operation below the city skyline. To set the elementary cell dimensions for this low altitude region of airspace, the portion of the ground-vehicle measurement campaign within the city centre was extracted and the worst-case observed DOP parameters were utilized. The DOP time series and correspondingly computed cell dimensions are shown in Figure 14. As expected, the DOP is degraded (by nearly a factor of 2) from the open-sky scenario. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline PDOP & 1.3 & \(\sigma_{\text{UEEE}}\) & 5.5 m \\ \hline \(\
u\) & 10 m/s & \(t_{\text{SA}/\text{CA}}\) & 3 s \\ \hline \(\sigma_{\
u}\) & 0.058 m/s & \(\sigma_{\text{ISA}/\text{CA}}\) & 0.5 s \\ \hline \(\sigma_{\text{vd}}\) & 0.005 m & rPRV & 26.2 m \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Inputs for CNS protection volume generation. Figure 14: Cell dimensions for below skyline scenario: (**a**) HDOP (**b**) VDOP (**c**) horizontal cell dimension (**d**) vertical cell dimension. Figure 13: The intruder’s CNS protection volume and associated occupancy grid above skyline. The worst HDOP and VDOP for this scenario are 1.337 and 2.067 respectively. The fundamental cell dimension, therefore, equates to r\({}_{\text{x,y}}\)\(=\) 18.7 m and r\({}_{z}\)\(=\) 34.1 m. Since airspace within urban canyons is limited by buildings, the airspace generation procedure is different from the open-sky scenario. The algorithm pseudocode is presented in Table 5.  
If the urban canyon width can only fit a single row of cells, the width of the elementary cell is stretched to be equal to the canyon width. In this case study, the elementary cell width is 18.7 m, while the canon width is 25 m. Hence, the width of the cell is stretched to 25 m.  
For determining the optimal sector size, the same methodology presented in Section 3.4 is applied. The urban canyon airspace extends from 30m AGL to 330m AGL. It is desirable to have at least 2 altitude levels. Accordingly, the vertical size of the elemental cells is set at k\({}_{\text{z}}=\frac{300/341}{2}\approx 4\). The optimal value for k\({}_{\text{x,y}}\) is rounded down to 4 (Figure 15). The total number of elementary cells in one sector is 64 cells. The resulting optimal sectorisation below the skyline is depicted in Figure 16. Similar to the first case study, the required inputs for the generation of UAS protection volume are shown in Table 6. Currently, there is a lack of established standards for the s UAS speed limit in urban areas. The top speed of most s UAS ranges from 5 to 10 m/s [46]. However, a speed limit of 2 m/s is assumed, which is comparable to the top speed of several micro UAS [46], to allow sufficient time for the system to respond in case of emergencies. The PDOP in this case is 2.6. The rest of the parameters remains the same as in Table 4.  
The protection volume and occupancy grid are illustrated in Figure 17. The resulting spherical CNS protection volume of an intruder and host UAS exceeds the below-skyline sector width (urban canyon width W = 25 m). Consistently with our proposed two-way approach (Figure 4), this is a clear indication that the observed CNS performance is insufficient for safe navigation along the street and stricter CNS performance requirements are to be fulfilled to access such urban airspace portion. In future work, tailored directional inflations (in x, y, z) will be investigated, driven both by relative dynamics, weather, wake turbulence and other relevant factors.