# A Conceptual Design Methodology for e-VTOL Aircraft for Urban Air Mobility
## 4 Sensitivity Analyses for Design Space Exploration
### Current Powertrain Technology  
In this section, the results of the conceptual design of the _TiltOne_ with current powertrain technology are presented. The design has been carried out assuming the TLARs reported in Table 8, whereas values of the technological parameters are reported in Table 10. The main assumptions concerning the design mission are detailed in Table 11.  
Sensitivity analyses to wing loading (varying from 70 kg/m\({}^{2}\) to 100 kg/m\({}^{2}\)) and propellers' disk loading (varying from 40 kg/m\({}^{2}\) to 70 kg/m\({}^{2}\)) have been carried out, and the results are reported in the following wing loading-disk loading charts. In these charts, each point corresponds to a configuration with different wing loading and disk loading; moreover, each aircraft is designed according to the workflow depicted in Figure 2 and substantial information can be extracted, such as MTOW, wingspan and battery mass. A general picture is shown in in Figure 10, where several variables have been considered; namely, MTOW (Figure 10a), battery mass (Figure 10b), propeller clearance (Figure 10c), wingspan (Figure 10d) and propeller diameter (Figure 10e). \begin{table}
\begin{tabular}{c c} \hline Electric Motor Power Density [45, 68, 86, 87] & 5 kW/kg \\ \hline Battery Energy Density @ pack level [45] & 250 Wh/kg \\ \hline Battery Management System Power Density [68] & 20 kW/kg \\ \hline ESC Power Density [87] & 20 kW/kg \\ \hline Cable power density [78] & 10 g/(m kW) \\ \hline Wire efficiency [68] & 0.99 \\ \hline ESC efficiency [88] & 0.95 \\ \hline Battery efficiency [89] & 0.92 \\ \hline Motor efficiency [89, 90] & 0.92 \\ \hline \end{tabular}
\end{table} 
Table 10: Current technological parameters for electric machines and components, and batteries. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Phase (See Table 4)** & **Name** & **Assumption** \\ \hline
1–2 & Take-off & Maximum power for 30 s \\ \hline
2–3 & Hovering & Hovering for 30 s at 100 m AGL \\ \hline
3–4 & Transition & Uniform horizontal acceleration from 0 m/s to climb speed \\ \hline
4–5 & Climb & Constant CL (Equation (8)) and RoC = 500 ft/min \\ \hline
5–6 & Cruise & Constant speed (Table 8) @ 500 m AGL \\ \hline
6–7 & Descent & CL of maximum efficiency and RoD = –500 ft/min \\ \hline
7–8 & Transition & Uniform horizontal deceleration from descent speed to 0 m/s \\ \hline
8–9 & Hovering & Hovering for 30 s at 100 m AGL \\ \hline
15–16 & Landing & 80\% of requested power in hovering \\ \hline \end{tabular}
\end{table} 
Table 11: Main assumptions of the design mission of the _TiltOne_. Figure 10a shows how MTOW is affected by both disk loading and wing loading:  
* by keeping the disk loading constant and increasing the wing loading, aerodynamic performance in fixed-wing flight improves; since cruise is the most energy consuming phase (see Figure 11b),), the total energy for the mission decreases (Figure 11a) as well as the amount of battery mass embarked (Figure 10b), so MTOW decreases;
* vice versa, by keeping the wing loading constant and increasing the disk loading, the power required for take-off increases according to Equation (3), as well as motor weight and the energy demand for the phases accomplished in multi-rotor mode (i.e., take-off, hovering and landing). This results in the increase of battery mass (Figure 10b), hence MTOW increases as well. Figure 11: Energy demand to fly the design mission (range = 60 nm, speed = 50 m/s): (**a**) sensitivity analysis to wing loading and disk loading; (**b**) energy requirement phase by phase, for design point \(W\)/\(S\) = 90 kg/m\({}^{2}\) and \(T\)/\(A\) = 60 kg/m\({}^{2}\). Figure 10: Wing loading (\(W\)/\(S\)) vs disk loading (\(T\)/\(A\)) charts (current technology level, range = 60 nm, speed = 50 m/s): (**a**) MTOW; (**b**) battery mass; (**c**) propeller clearance; (**d**) wingspan; (**e**) propeller diameter. Wingspan (Figure 10c) is influenced more by wing loading than disk loading.