# Preliminary Propulsion and Power System Design of a Tandem-Wing Long-Range eVTOL Aircraft
## 3 Results and Discussion of the Propulsion System Design
This number is based on the noise and manufacturing considerations previously mentioned, and on that fact that more blades result in higher efficiency, as seen in the sensitivity analysis presented in Section 3.2.1. Moreover, the non-dimensional hub radius, \(\xi_{0}\), is assumed to be 0.1. The last parameter needed is the rpm at the design condition. The maximum allowable rpm level is 4791 based on a limit tip Mach number of 0.75. Going beyond this Mach number may result in shock waves at the tips that would lead to additional losses due to wave drag and to high noise levels. The exact maximum allowable Mach number beyond which shock waves develop depends on the airfoil and loading conditions of the blade, and may be in excess of 0.75, but this number is chosen to simplify the analysis procedure presented herein while ensuring that the maximum value is below a safe threshold. With this maximum value in mind, it was chosen to design the propellers for 1350 rpm at the design condition. This rpm value, below 30% of the maximum allowable number, is needed to ensure that there is enough rotational speed margin to meet the maximum thrust requirements at maximum rotational speed. The pitch of the blades is also altered to achieve this difference in thrust, but the wide range of thrust conditions cannot solely be achieved by pitch variation. The resulting propeller has an efficiency of 81% at the design condition and a solidity of 0.36. The propeller solidity represents how much area of the propeller disk is occupied by the blades. The reference pitch setting at the design condition, defined as the pitch at 70% of the propeller radius, is 66 degrees. The next step to analyse the propellers is to see whether they can meet the maximum thrust requirement. For controllability in OEI conditions, the thrust-to-weight ratio needed is 1.5 (this requirement is obtained from a controllability analysis performed in the original project, as can be seen in [3] for reference). With an MTOM of 3025 kg and 12 propellers, this results in a required maximum thrust of 3708 N per propeller. This value includes contingencies: the systems of the Wigeon are sized for an operating empty mass (OEM) 10% higher than the predicted one, to ensure that the design would work in the event that the predicted mass is underestimated, as specified in the original project [3]. In order to achieve this, the propellers are accelerated up to the maximum rpm (4791), and the blades are pitched down by 45 degrees with respect to the design condition; this means reducing \(\beta\) in Figure 4. This results in a thrust of 3745 N per propeller. The efficiency of this condition is 39%, a low value which is expected due to the high disk loading, 317 kg/m\({}^{2}\), and the low advance ratio, J = 0.12 (at the assumed 10 m/s inflow velocity). These values are obtained at a height of 500 metres, with the corresponding air density, temperature, and dynamic viscosity being obtained from the International Standard Atmosphere. The reason why this height was chosen instead of sea level was to allow for a safety margin and for controllability in higher operations. It is worth noting that the inflow speed for this condition was chosen to be 10 m/s. This is because the analysis method does not work for inflow speeds of 0 m/s. However, with lower inflow speed, the thrust of the propeller increases [16] due to the increase in the angle of attack of the blades, which means that this is a conservative estimate. Having this conservative estimate for maximum thrust is also good for the design, since some of the effects are not modelled. The assumption of the thrust increasing under static conditions holds unless the propeller blades suffer significant separation under this condition. This cannot be analysed with the current tools, hence verifying the validity of this assumption for the obtained design remains a point of future work for further stages of the design--for example, by performing a numerical simulation at this condition with the obtained geometry from the design framework.