# A Performance-Based Airspace Model for Unmanned Aircraft Systems Traffic Management
## 4 Verification Case Study
### UAM Air-Taxi Scenario  
An on-demand air-taxi scenario in the Melbourne Central Business District (CBD) is simulated for this case study. The operational sequence is as described in Section 2.1. The test platform utilised in this study is the Electric Vertical Takeoff and Landing (eVTOL) concept UAM vehicle developed in the Airbus Pop.Up One project [45]. An urban building height database is utilized in generating the scenario. The operational airspace in the vertical plane is assumed to extend from 330 m AGL upwards. This is to allow a minimum clearance of 30 m above the tallest building height (298 m as recorded in the height database). The urban airspace is assumed to originate at a specified point initialised at the corner of Flinders Street and Spencer Street (\(-\)37.821058, 144.955217, 330) since it is the southmost point of Melbourne CBD. In this case, a GNSS constellation of 30 satellites with orbital radii of 26561.750 km is assumed. The inclination angle was set at 55 degrees, and longitude and timing offsets are neglected. To obtain realistic and representative values of HDOP and VDOP, a ground-vehicle measurement campaign was conducted in an open sky area, a highway route proceeding towards a residential area. Although these values differ from the ones that will be observed in a UAM mission, the measurements obtained from this campaign are deemed to be more conservative since the satellite visibility is generally lower at ground level. The measured HDOP and VDOP values are therefore conservative. The time-series of these two parameters during the experiment are shown in Figure 10. The maximum recorded HDOP (0.703) and VDOP (1.103) are used to define the elementary cell dimensions according to Equations (12) and (13). The lengths of \(\mathrm{r}_{x,y}\) and \(\mathrm{r}_{z}\) for the grid above the skyline are computed to be 11.6 m and 18.2 m respectively. These inputs from Table 3 are fed into Equations (22)-(25). The values for the velocity are based on the specifications for the Airbus Pop.Up One [45]. Due to the dense population and small space in the urban area, the strict speed restriction is applied at the maximum of 10 m/s. The airspace sectorization results are presented in Figure 11. The inefficiency surface for the communication overhead (OH) and Computational Complexity (CP) are plotted. The optimum points lie on the intersection between these two surfaces: OH and CP (Figure 11a). The vertical sector dimension is derived to avoid overlap with the Terminal Area airspace (TMA) which begins from 457 m (1500 ft) and the base height of the over skyline starts at 330 m. Hence, the preferred k\({}_{z}\) is calculated from dividing the total heights of low-level airspace above skyline by the vertical dimension of the elementary cell (r\({}_{x}=18.2\) m), k\({}_{x}=\frac{(457-330)}{18.2}\approx 7\). The optimal point is marked in red. Based on that, the value for k\({}_{x}\) is 8. The result from Figure 11b is the number of elementary cells in one sector as calculated from Equation (26): 448 cells. \begin{table}
\begin{tabular}{c c c c} \hline \multicolumn{2}{c}{**Hardware**} & \multicolumn{2}{c}{**Software**} \\ \hline Velocity (m/s) & 10 & Time handshake (s) & 0.3 \\ \hline Vertical rate (m/s) & 4 & Time avg (s) & 112 \\ \hline Length (m) & 4.4 & Time moto (s) & 12e5 \\ \hline Height (m) & 0.85 & Computational power & 2.1e9 \\ \hline Width (m) & 5 & & \\ \hline \end{tabular}
\end{table} 
Table 3: Airspace sectorisation input parameters. Figure 10: Cell dimensions from collected open-sky data: (**a**) HDOP (**b**) VDOP (**c**) horizontal cell dimension (**d**) vertical cell dimension. The resulting sectorisation of the skyline above the city centre is illustrated in Figure 12.  
In the case of an intruder aircraft, the required inputs for CNS protection volume generation are shown in Table 4. The value of PDOP was set in a similar manner to the HDOP and VDOP from the measurement campaign. A maximum allowable delay of 2 s for autonomous conflict detection and resolution is assumed.