# Preliminary Propulsion and Power System Design of a Tandem-Wing Long-Range eVTOL Aircraft

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## Abstract

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## 1. Introduction

#### 1.1. Proposed Configuration

#### 1.2. Background

#### 1.3. Overview of the Design Procedure

## 2. Propulsion System Design Methodology

#### 2.1. Design of the Propeller Blades

_{l}/C

_{d}of the blade is maximised for each station, while maintaining a reasonable value for C

_{l}that allows the propeller to generate sufficient thrust. For this, the lift coefficient is first chosen, and the corresponding drag coefficient and angle of attack are then retrieved from known airfoil data. 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($\mathrm{\Phi}$). The chord can then be calculated as c = wc/w.

#### Implementation of the Blade Design Procedure in the Design Framework

#### 2.2. Propeller Positioning and Sizing

#### 2.2.1. Number of Propellers

**Disk loading:**Bigger propellers allow for a larger total area and hence a lower disk loading which improve efficiency. This directly translates into a lower required peak power which can decrease the size (and thus weight) of the electric motors and the power system [2];**Ground clearance:**More propellers means smaller radii, which therefore allows for more ground clearance when the wings are in horizontal position;**Propeller–wing interaction:**Bigger propellers have a higher slipstream height which results in a higher increase in lift due to the propeller slipstream for the same slipstream velocity [12]. On the other hand, bigger propellers would reduce the slipstream velocity;**Propeller–propeller interaction:**For the same front and rear wing separation, smaller front propellers with lower slipstream heights allow one to more easily place them such that the propellers on the downstream wing are outside the slipstream of the propellers on the upstream wing. This slipstream ingestion can lead to big losses in thrust from the second row of propellers [7] and increase noise emissions;**Blade rotation mechanism:**The propellers need a mechanism to alter the pitch of the blades. With very small propellers, implementing such a mechanism becomes more difficult.**Safety in OEI conditions:**More propellers mean more redundancy, and with more and smaller propellers, a failure of one of them has a smaller effect on the controllability in hover and on total thrust.

#### 2.2.2. Positioning and Sizing

_{fus}/2. To prevent problems with wing positioning and rotation, it was decided to define the required fuselage–propeller clearance, c

_{fp}, with respect to the maximum width of the fuselage, and not the local width. This ensures that, even when the wings are in vertical position, there is sufficient clearance between the inner propellers and the fuselage, without the need for having a detailed design of the fuselage shape at the position of the propellers. The distance between propeller tips is defined by c

_{pp}, the propeller–propeller clearance. These two clearances are inputs to the method which may be obtained from sizing constraints or estimated based on reference aircraft. The remaining width is taken by the two inboard propellers and half of the tip propeller. This is generalised in Figure 5 for an arbitrary number of propellers, where N

_{prop}is the number of propellers per half wing:

#### 2.3. Analysis of the Blades in Off-Design Conditions

_{y}and C

_{x}, which are related to the lift and drag coefficients of the blade sections, as shown in Equations (9) and (10). A visual representation of the definition of these coefficients on the blade is shown in Figure 4:

#### 2.4. Noise Analysis

_{1}is the reference noise level; it is based on the motor power and it is obtained from Figure B.2 in [14]. The next two terms are corrections for the number of blades, B, and propeller diameter, D (in ft). The next term, C

_{Mach}, is a correction for the tip Mach number, obtained from Figure B-3 in [14]. ${C}_{\theta}$ is a correction which accounts for the direction in which the noise is being calculated and it is obtained from Figure B-8 in [14]. For this calculation, it was decided to use a correction of +4 dB, which is the maximum value of the average curve, to obtain the noise at the position in which it is at a maximum. Lastly, the last term, where r is the distance in ft at which the noise is to be calculated, accounts for the noise attenuation due to propagation from source to observer.

## 3. Results and Discussion of the Propulsion System Design

_{0}, is assumed to be 0.1.

#### 3.1. Noise Analysis Results

_{1}for the Wigeon was determined to be 107 dB. The tip Mach number for the Wigeon is slightly below 0.3, for which C

_{Mach}is −19 dB. Using Equation (12) with these values, the noise from one propeller during cruise at 100 m from the aircraft was determined to be 65.06 dB. The 100 m distance was chosen as a sample distance to evaluate the noise. Similarly, for 1000 m, the noise representing the cruise height is 45.03 dB. For the 12 propellers combined, the noise levels at 100 m and 1000 m are 75.85 dB and 55.83 dB, respectively. The semi-empirical method used was not developed for highly loaded propellers under hovering conditions, and as such, only cruise estimates were presented here. Since hovering is a critical part of the noise performance of eVTOLs, this remains an important point for future work, as mentioned in Section 3.3.

#### 3.2. Sensitivity Analysis

#### 3.2.1. Sensitivity of the Design Procedure

#### 3.2.2. Sensitivity of the Propeller Analysis

#### 3.3. Future Recommendations on the Propulsion Design

**Stall of blade sections:**The aerodynamic data for the airfoil was computed in XFOIL, which loses accuracy in the post stall region of the lift polar. Since parts of the blades might be stalled during operation due to the wide range of operating conditions, it is important to ensure that the post-stall aerodynamic data of the airfoil is available and accurate. This is one of the points where the procedure needs improvement, and next steps could for example include the CFD simulations of the airfoil to obtain more accurate post-stall data.

**Blade design method:**The method used to design the blade geometry is not robust when the propellers are too highly loaded, where the iterative blade design procedure given in Section 2.1 can fail to converge. The momentum theory approximation that assumes that the increase in flow velocity with respect to the freestream velocity at the disk plane is half the total increase at the wake is not always accurate and can result in convergence issues [5]. Propellers with the moderate-to-high disk loading adopted for the Wigeon (317 kg/m${}^{2}$) can still be designed with this method, but a different approach would be needed if the chosen architecture features very highly loaded propellers or fans.

**Effects of interactions:**Due to the complexity of their analysis, the effects of propeller–wing and propeller–propeller interaction were not modelled in the present study. Since these interactions can have an effect on propeller performance, quantifying them is important for a more accurate design. For the Wigeon, a propeller lateral separation of 0.3 m was chosen, which corresponds to 30% of the radius. A study by de Vries et al. shows that, in horizontal flight, a distributed propulsion system using open rotors sees a drop in propeller efficiency of 1.5% for a separation between propeller tips of 2% of the propeller diameter [8]. In a different study carried out by Zhou et al., it was shown that the thrust coefficient of two propellers with a tip separation of 5% of the propeller diameter is within 2% of that of a single propeller under static thrust conditions, although a significant increase in thrust fluctuation is seen [9]. Zhou et al. also showed that an increase in noise was observed with decreasing separation [9]. Based on the results from these studies, it is expected that the interaction effects will not cause significant deviation from the predicted performance with the chosen clearance; however, the sensitivity analysis on the effect of this clearance could not be performed with the available tools. In transition, these effects can be more significant [7]. Another effect of propeller–propeller interaction is slipstream ingestion in the second row of propellers, located in the aft wing, and not considered in the present study. Quantifying this interaction is important because it can lead to more significant losses in the calculated thrust [7], while yet negatively affecting noise. Finally, the effect of the propeller blockage due to the wing was not modelled, which can also affect propeller performance, while also affecting the positioning of the propellers with respect to the wing in terms of height and depth.

**Airfoil selection:**For the present study, a NACA4412 airfoil was assumed, but improved airfoil selection and optimisation were expected in further stages of the design. An early airfoil selection that is more tailored to the configuration and mission of the aircraft to be analysed could already be considered in the preliminary design.

**Aeroacoustic simulation:**The noise analysis presented herein was based on a semi-empirical method which might not be accurate for the Wigeon configuration, especially considering the propeller–wing, propeller–propeller, and wing–wing interactions. Hence, the next design phases should move towards more accurate aeroacoustic simulations of the aircraft based on the geometry obtained from the preliminary design.

## 4. Power System Design Methodology

#### 4.1. Mass and Weight Calculations

^{3}.

#### 4.2. Battery Configuration

## 5. Results and Discussion of the Power System Design

#### 5.1. Battery Characteristics

#### 5.2. Powertrain Sizing

^{3}.

#### 5.3. Battery Configuration

#### 5.4. Sensitivity Analysis of the Power Design Methodology

#### 5.5. Future Recommendations

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ADT | Actuator Disk Theory |

BEMT | Blade Element Momentum Theory |

CAD | Computer Aided Design |

CICD | Continuous Integration/Continuous Delivery |

DEP | Distributed Electric Propulsion |

DOD | Depth of Discharge |

EOLC | End-of-Life Capacity |

eVTOL | Electric Vertical Take-Off and Landing |

MTOM | Maximum Take-Off Mass |

OEI | One Engine Inoperative |

OEM | Operating Empty Mass |

UAM | Urban Air Mobility |

UAV | Unmanned Aerial Vehicle |

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**Figure 4.**Velocities acting on the blade station with their corresponding angles. Nomenclature following [5].

**Figure 5.**Definition of the fuselage–propeller and propeller–propeller clearances used in the lateral positioning of the propellers.

**Figure 10.**Sensitivity analysis of propeller efficiency in the design procedure to variations in freestream velocity and propeller radius.

**Figure 11.**Sensitivity analysis of propeller efficiency in the design procedure to variations in rpm and the number of blades.

**Figure 12.**Sensitivity of the efficiency to changes in rpm and pitch angle of the blade in the off-design analysis procedure.

**Figure 13.**Sensitivity of the thrust to changes in rpm and pitch angle of the blade in the off-design analysis procedure.

**Figure 14.**Relation between cell capacity and the increase in the number of cells with respect to the number before taking the configuration into account.

**Figure 15.**Relation between cell voltage and the increase in the number of cells with respect to the number before taking the configuration into account.

Parameter | Cruise | Hover | Full Thrust |
---|---|---|---|

Thrust (N) | 158 | 2502.42 | 3745.14 |

RPM | 1090 | 4000 | 4791 |

∆β (deg) | 0 | −44 | −45 |

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**MDPI and ACS Style**

Alba-Maestre, J.; Prud’homme van Reine, K.; Sinnige, T.; Castro, S.G.P. Preliminary Propulsion and Power System Design of a Tandem-Wing Long-Range eVTOL Aircraft. *Appl. Sci.* **2021**, *11*, 11083.
https://doi.org/10.3390/app112311083

**AMA Style**

Alba-Maestre J, Prud’homme van Reine K, Sinnige T, Castro SGP. Preliminary Propulsion and Power System Design of a Tandem-Wing Long-Range eVTOL Aircraft. *Applied Sciences*. 2021; 11(23):11083.
https://doi.org/10.3390/app112311083

**Chicago/Turabian Style**

Alba-Maestre, Javier, Koen Prud’homme van Reine, Tomas Sinnige, and Saullo G. P. Castro. 2021. "Preliminary Propulsion and Power System Design of a Tandem-Wing Long-Range eVTOL Aircraft" *Applied Sciences* 11, no. 23: 11083.
https://doi.org/10.3390/app112311083