## 3 Design of Experiment
### Design of Experiment Steps
#### 3.1.4 Select Experimental Designs  
In order to evaluate the effects of the concepts chosen from the tradeoff study matrix, modeling and simulation are necessary. This requires a clear understanding of the performance of the baseline case. In this study, as a tool for modeling and simulation, the software programs of MS Excel, JMP developed by SAS [19], and the aforementioned PAV sizing tool developed for this study were employed. * PAV sizing program  
The PAV sizing program developed by the research team was programmed with Excel and Visual Basic for Application (VBA), and the initial sizing was performed by selecting the subsystems and mission profile. The PAV's subsystems include the fuselage material, the configuration of the main wing and winglet, the propulsion method, the number of propeller blades, and the configuration of the landing gear. After selecting the design parameters, the subsystem, and mission profile of the eVTOL PAV, the optimized eVTOL PAV sizing result can be obtained according to the options (1. Minimizing the required power/2. Minimizing the wing area). The program is composed of the mission sheet, concepts sheet, technology sheet, constraint analysis sheet, aerodynamics sheet, propulsion sheet, and weight sheet. The sizing results that can be obtained are the weight of the aircraft, MTOW, empty weight, and pay load, and the wing area, root chord length, and tip chord length of the main and tail wings. The PAV sizing program flow chart is shown in Figure 10.  
Screening tests can be carried out based on the modeling and simulation to find independent design parameters that have a significant impact on design target parameters. These design independent parameters can be quantitatively informed of their relationship to the design target parameters, and can identify which design target parameters are sensitive to which design independent parameters by selecting highly sensitive design independent parameters from many design independent parameters. This enables them to be used for modeling the eVTOL PAVs. In addition, Monte Carlo simulations can be applied after modeling to find possible design ranges for target design parameters. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Design Parameter** & **Min. Value** & **Max. Value** & **Standard Value** & **Unit** \\ \hline Range & 40 & 50 & 45 & mile \\ Max speed & 110 & 130 & 120 & kt \\ Cruise speed & 100 & 120 & 110 & kt \\ Cruise altitude & 5000 & 10,000 & 7500 & ft \\ Passengers & 1 & 3 & 2 & PAX \\ Baggage & 40 & 120 & 80 & lb \\ Rate of climb & 500 & 1000 & 750 & ft/min \\ Stall speed & 36 & 40 & 38 & kt \\ Service ceiling & 10,000 & 15,000 & 12,500 & ft \\ Turn speed & 60 & 90 & 75 & kt \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Design space of design parameters. * Screening test Screening testing is one of the methods used to find highly sensitive design independent parameters for design target parameters before using the response surface method. During the design of experiment, fractional factorial design was used to reduce the number of experiments. Assuming that there are 10 factors with two levels in the full factorial design, the total number of experiments is \(2^{10}=1024\). The number of experiments increases exponentially depending on the level and number of factors. The experiment was carried out efficiently by reducing the number of experiments, by using the partial factorial design method, which obtains the necessary data during experiments. * Response surface method Modeling uses the response surface method to estimate the regression equation for each design target parameter. The response surface method was performed using the central composite design method. In a factorial design with three or more factors, the number of experiments increases exponentially, which is expensive and inefficient. However, the central composite design method can be efficiently modeled because a secondary model can be designed by adding additional axial points and central points [20].