## 3 Holding Area Conceptual Design and Turning Performance Analysis
### Current Aircraft Turning Performance Analysis  
In order to validate the turning performance in these holding areas, calculations have been performed to satisfy a bank angle of 25\({}^{\circ}\) or turn rate of 3\({}^{\circ}\)/s according to current aircraft flight procedure standards. Considering stalling, the maximum bank angle has been limited to 45\({}^{\circ}\)[8; 9]. A Cessna 182T, a fixed-wing aircraft, and a Robinson R44, a rotary-wing aircraft, have been selected as the target aircraft for analysis. This is because these two aircraft are similar to the weight of UAM vehicles, so they are suitable for comparison when analyzing the turning performance of UAM vehicles. The bank angle, turning radius, and turn rate of the current aircraft at constant speed are as shown in Table 3 and the following equations. For banked level turns by fixed-wing aircraft,  
\[Lcos\phi-W=0 \tag{1}\]  
\[Lsin\phi=m\frac{U^{2}}{\chi} \tag{2}\]  
\[tan\phi=\frac{1}{g}\frac{U^{2}}{\chi} \tag{3}\]  
For the load factor,  
\[n=\frac{L}{W}=\frac{1}{cos\phi}=sec\phi \tag{4}\]  
For the turning radius of the banked level turn,  
\[R=\frac{U^{2}}{g}\frac{1}{tan\phi}=\frac{1}{g}\frac{U^{2}}{\sqrt{n^{2}-1}} \tag{5}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Concepts** & **Features** & **Pros** & **Cons** \\ \hline \multirow{6}{*}{Concept 3} & \multirow{6}{*}{This holding area can be established in an area} & \multirow{6}{*}{Since the UAM corridor is set in the longitudinal direction, when UAM vehicles are only cruising straight without holding procedures, the noise effect on the surrounding area can be reduced.} & \multirow{6}{*}{\(\bullet\)} & The structure of the holding area is is complicated, so situation awareness and sequencing are required for holding, climb and descent. \\  & & & \\ \cline{1-1}  & & & \\ \cline{1-1}  & & & \\ \cline{1-1}  & & & \\ \cline{1-1}  & & & \\ \cline{1-1}  & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._ \begin{table}
\begin{tabular}{c c c} \hline \hline
**Variables** & **Definition** & **Unit** \\ \hline \(L\) & Lift force & N \\ \hline \(W\) & Weight of aircraft & N \\ \hline \(m\) & Mass of aircraft & kg \\ \hline \(U\) & Airspeed & m/s \\ \hline \(\phi\) & Bank angle & degree \\ \hline \(n\) & Load factor & - \\ \hline \(R\) & Turning radius & m \\ \hline \(\dot{\psi}\) & Turn rate & degree/second \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Definition of variables. For the turn rate,  
\[\dot{\psi}=\frac{U}{\chi}=\frac{g}{U}\sqrt{n^{2}-1} \tag{6}\]  
For rotorcraft, the turn rate and turning radius calculation is the same as for fixed-wing aircraft at the banked level turn. First, the turning performance of the Cessna 182 aircraft was analyzed. The Cessna 182 is a four-seater, single-engine light aircraft with a maximum takeoff weight of 1406 kg and a cruising speed of 269 km/h [10]. The shape of Cessna 182 is shown in Figure 5, and its specifications are shown in Table 4.  
The result of the turning performance analysis of the Cessna 182T is shown in Figure 6. At a cruise speed of 74.7 m/s (about 269 km/h), the bank angle of 22\({}^{\circ}\) was calculated at a turn rate of 3\({}^{\circ}\)/s, and a turn rate of 3.5\({}^{\circ}\)/s was calculated at a bank angle of 25\({}^{\circ}\). As a result of the turning radius calculation, the turning radius was derived as 1400 m when turning at a turn rate of 3\({}^{\circ}\)/s at cruise speed. When turning at a bank angle of 25\({}^{\circ}\), the turning radius was calculated as 1220 m.  
To verify the validity of the calculation result, it has been compared with the result using the aircraft's general turning performance (GTP) chart. The GTP chart is a graph that confirms how much turning radius is obtained by comparing the bank angle, rate of turn, and speed when an aircraft turns [12].