# A Conceptual Design Methodology for e-VTOL Aircraft for Urban Air Mobility
## 2 Design Methodology
### Weight Estimation  
The _Weight estimation_ module evaluates the aircraft mass breakdown. The _MTOW_ is computed by using the Equation (10). \[MTOW=M_{batt}+M_{puy}+OEW \tag{10}\]  
The battery mass (\(M_{batt}\)) is computed considering the energy necessary to accomplish the mission, provided by Equation (9), assuming an additional 5% for the energy consumption due to avionics and flight instruments. This value can be better evaluated once physic-based models are developed, as done in [74] for example. For safety reasons, the minimum state of charge at the end of the design mission (\(SoC_{fin}\)) is set to 20%, whereas the initial state of charge (\(SoC_{in}\)) is 100%. Battery mass evaluation is reported in Equation (11), by dividing the total required energy by the battery energy density (\(BED\)), which depends on the technology assumptions and, as the paper shows, has a significant impact on aircraft performance. \[M_{batt}=\frac{1.05\ E_{batt,miss}}{\left(SoC_{in}-SoC_{fin}\right)\ BED} \tag{11}\]  
Payload mass (\(M_{puy}\)) is evaluated by using Equation (12), where \(N_{max}\) is the maximum number of passengers carried by the _TiltOne_, as specified in the TLARs. \(M_{pux}\) is the mass of single passenger, set equal to 100 kg [38,70]. \[M_{puy}=N_{max}\cdot M_{pux} \tag{12}\]  
Operative empty weight (\(OEW\)) has been calculated according to the Equation (13). \[OEW=M_{struct}+M_{sys}+M_{TS}+M_{TMS}+M_{el} \tag{13}\]  
\(M_{struct}\) and \(M_{sys}\) are the structural and system weight, respectively. \(M_{TS}\), \(M_{TMS}\) and \(M_{el}\) are transition system, thermal management system and electric components weight, respectively. To compute structural and system weight, the tool FLOPS developed by NASA has been used [60]: According to [60], structural weight includes wings, tails, fuselage, nacelle and paint; system weight considers control surfaces actuators, instruments, avionics, anti-icing and furnishing. It is worth noting that the classical model for cantilever wings overestimates the structural mass of the box-wing architecture [75, 76, 77, 78], so the results reported in this paper (e.g., estimation of MTOW) are conservative. This tool is versatile since it can be used for aircraft ranging from general aviation to transport aircraft categories; in this paper, the general aviation category has been selected, since the weight formulation, adopted in this paper and described in FLOPS, have been specifically derived for general aviation aircraft category. The NASA's tool does not take electric components of the powertrain (i.e., electric motor, ESC, BMS, motors, cables and propeller) into account, thus ad hoc models have been used and reported in Equations (15)-(18). \[P_{batt\ max}=\underset{t_{start}\ \leq\ t\leq\ t_{end}}{max}(P_{batt}(t))\cdot 10^{-3} \tag{14}\]  
\[M_{BMS}=\underset{t_{start}\ \leq\ t\leq\ t_{end}}{max}\left(\frac{P_{ batt}(t)}{BMSPD}\right) \tag{15}\]  
\[M_{emot}=\underset{t_{start}\ \leq\ t\leq\ t_{end}}{max}\left(\frac{P_{ emot}(t)}{EMPD}\right) \tag{16}\]  
\[M_{cable}= CPD\cdot P_{batt\ max}\cdot L_{cable}\cdot 10^{-3} \tag{17}\]  
\[M_{TMS}=0.521\frac{1-\eta_{batt}}{\eta_{batt}}P_{batt\ max}+1.863 \tag{18}\]Equations (15) and (16) estimate the mass of the battery management system (\(M_{BMS}\)) and electric motors (\(M_{emot}\)), respectively; \(P_{batt\ max}\) is the maximum power supplied by the battery pack (measured in kW); \(BMSPD\) is the battery management system power density, \(P_{emot}\) is the power absorbed by the electric motor, and \(EMPD\) is the electric motor power density. Equation (17) has been introduced to evaluate mass of power and sensor cables \(M_{cable}\), according to the results of the VAHANA project [78]; in particular, \(CPD\) is the cable power density, and \(L_{cable}\) is the cable length.