# A Conceptual Design Methodology for e-VTOL Aircraft for Urban Air Mobility
## 2 Design Methodology
### Mission Performance  
The _Mission performance_ module evaluates the aircraft performance in each phase of the design mission. All the assumptions about the design mission are reported in Table 4.  
In the phases from (1) to (3), the _TiltOne_ flies in multi-rotor mode, hence sustained by the thrust generated by the propellers. As Figure 6 shows, these phases are the most power demanding, and the power requested has been computed by using Equation (3) setting k\({}_{\rm T}\) to 1.2 in take-off phase and 1.0 in hovering phase. During the transition phase (3-4), the _TiltOne_ changes the wings layout, going from multi-rotor to fixed-wing mode, and at the same time the aircraft exhibits a constant longitudinal acceleration. This phase ends when the _TiltOne_ reaches the climb speed, which is calculated according with the assumptions on rate of climb (RoC) and lift coefficient introduced in the following. Because of the unsteady motions of the tilting wings as well as of the whole aircraft, the mathematical models of this phase can be complex, and it needs substantial information, which is not available in the early phase of the design process. To cope and reduce the complexity of the mathematical formulation, two assumptions have been considered:  
* the aircraft has a constant longitudinal acceleration of 2 m/s\({}^{2}\), as assumed in [30];
* the aircraft total thrust decreases linearly, from the thrust generated in multi-rotor mode to the thrust generated in fixed-wing mode at the beginning of the climb phase (Figure 7); \begin{table}
\begin{tabular}{c c c} \hline \hline
**Phase** & **Name** & **Assumptions** \\ \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 lift coefficient and RoC \\ \hline
5–6 & Cruise & Constant speed and height AGL \\ \hline
6–7 & Descent & Constant lift coefficient and RoD \\ \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
9–10 & Transition & Uniform horizontal acceleration from 0 m/s \\  & & to climb speed \\ \hline
10–11 & ClimbD\({}_{\rm DV}\) & Constant lift coefficient and RoD \\ \hline
11–12 & CruiseD\({}_{\rm DV}\) & Constant speed and height AGL \\ \hline
12–13 & DescentD\({}_{\rm DV}\) & Constant lift coefficient and RoD \\ \hline
13–14 & TransitionD\({}_{\rm DV}\) & Uniform horizontal deceleration from \\  & & descent speed to 0 m/s \\ \hline
14–15 & HoveringD\({}_{\rm DV}\) & Hovering for 30 s at 100 m AGL \\ \hline
15–16 & Landing & 80\% of requested power in hovering \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Assumption for the design mission of the _TiltOne_. * the power requested to accomplish the phase is given by the time integral of the total provided thrust and the aircraft speed, maintaining a constant value for the propeller efficiency (\(\eta prop=0.8\)) and assuming no losses in the mechanical transmission. During climb, cruise and descent phases, the aircraft performance is computed by using the flight mechanic equations developed for fixed-wing airplanes; for more details, the reader can refer to [73]. During climb, the aircraft lift coefficient is constant, and it is provided by the Equation (8), where \(CL_{Pmin}\) is the lift coefficient which minimizes the requested power in horizontal flight. This value is evaluated according to the following procedure:  
* definition of a set of aircraft speed values;
* evaluation of the lift coefficient which trims the aircraft in vertical direction for each value of the aircraft speed;
* estimation of the drag coefficient by means from the polar curve calculated in the _Aerodynamic_ module;
* estimation of the requested power for each drag coefficient-aircraft speed combination;
* evaluation of the lift coefficient which minimizes the requested power (\(CL_{Pmin}\)).