# Preliminary Propulsion and Power System Design of a Tandem-Wing Long-Range eVTOL Aircraft
## 2 Propulsion System Design Methodology
### Design of the Propeller Blades
The optimum angle is not the same for every station as it depends on the Reynolds number with respect to the blade chord and local effective velocity, which increases moving outboard on the blade. The procedure used to obtain the airfoil data in this paper is explained later. For the chord, if the product \(wc\) is calculated from Equation (3), and from the blade geometry shown in Figure 4, \(w\) can be defined as \(V(1+a)/\sin(\Phi)\). The chord can then be calculated as \(c=wc/w\). In both equations, the displacement velocity ratio \(\zeta\) is needed and it needs to be iteratively calculated, as it is not known beforehand. This procedure is not the focus of this paper, but rather a tool used in the design, and it has already been detailed by the original authors [5] and explained in greater detail in the original project report [3]. Thus, the calculation of the displacement velocity ratio is not further detailed in the present paper. Implementation of the Blade Design Procedure in the Design Framework  
The procedure takes as inputs the working conditions of the propeller at the design point and the predefined characteristics of the propeller geometry, and it optimises the blade shape to maximise the efficiency in the design condition. The working conditions are the flight speed, the air properties at the design point, the thrust that needs to be delivered by the propeller, and the rotational speed that the propeller operates at. The propeller  
Figure 4: Velocities acting on the blade station with their corresponding angles. Nomenclature following [5]. geometry that needs to be predefined comprises the number of blades, the propeller radius, the radius of the propeller hub, and the lift and drag coefficients of the airfoil used in the blades. The propeller radius comes from the method outlined in Section 2.2 and an initial guess for the radius of the propeller hub can be estimated from existing propellers with similar radii and working conditions. The number of blades is a parameter that needs to be optimised for the final design of the aircraft. However, a reasonable initial estimate can be found by taking into account the effects of the number of blades. More blades result in less noise, since the pressure increment per blade is smaller (for the same total thrust), and can also result in higher efficiency. However, having more blades implies that they will have lower chord values for the same span (higher aspect ratio), since, for a fixed set of inputs, modifying only the number of blades results in propellers with the same solidity [6]. If the aspect ratio becomes too high, this can lead to structural or manufacturing issues. Moreover, introducing a pitch control mechanism for more blades can increase its complexity. Finding a balance for these characteristics is necessary for a detailed, optimised design, but a reasonable estimate suffices for the procedure used, as the result is not highly sensible to the chosen number of blades (a sensitivity analysis is presented in Section 3.2.2). The flight speed and air properties at the design point and the thrust needed from the propeller may be obtained from the mission analysis of the desired configuration and a preliminary flight performance estimate. For this paper, a NACA4412 was selected as the airfoil for the blades [3] with its performance analysed using XFOIL [11] through which the airfoil is simulated at a wide range of Reynolds numbers and angles of attack in order to create a database for the airfoil performance. With this, during the design process, the lift and drag coefficients of the airfoil at a certain angle of attack and Reynolds number can be retrieved. To account for compressibility, the Mach number at each station is calculated from the known local effective flow velocity \(w\), and the Prandtl-Glauert correction factor is then applied. It is worth mentioning that the overall performance of the propeller will be hindered by the fact that only one airfoil is used for the entire blade.