# Improvement of Take-Off Performance for an Electric Commuter Aircraft Due to Distributed Electric Propulsion

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Aerodynamic Numerical Model

#### 2.2. Propeller Design

_{t}is the tangential velocity component, V

_{a}is the axial velocity component, and W is the resulting velocity.

_{T}= T/(ρn

^{2}D

^{4}), Thrust coefficient,

_{P}= P/(ρn

^{3}D

^{5}), Power coefficient,

_{T}/C

_{P}J, Propeller efficiency.

#### 2.3. Flap Settings Design

- gap, which is the vertical distance between the lip of the main wing and the flap;
- overlap, which is the longitudinal distance between the lip of the main wing and the foremost point of the flap.

- gap 3%, overlap 2%, flap deflection 35 deg;
- gap 2.5%, overlap 2.7%, flap deflection 30 deg.

## 3. Results

#### 3.1. Low-Speed Aerodynamic Analysis Results (Power-off)

_{H}defined as in Equation (5), where l

_{h}is the distance between aerodynamic center of the tailplane and the CG position, the negative lift coefficient of the tailplane was computed by means of Equation (6).

#### 3.2. Investigation of Propulsive Effects on the Aircarft Aerodynamics at Take-Off

_{Lmax TO}= 2.55 instead of 1.9). It was possible to define a new take-off forward speed (V

_{TO}= 44 m/s instead of 51 m/s) based on the high-fidelity power-off estimation of the maximum lift coefficient. Numerical results are reported in Figure 24 and Figure 25 and Table 17. With this assumption, the blowing effects were higher since the same propeller induced an axial velocity of about 6–7 m/s (see Figure 10) at a lower forward speed. Since the lift force increment depends on the ratio of induced axial velocity and the forward speed, the jump in the maximum lift coefficient value was higher than the previous calculations, and the coefficient achieved a value of 3.24 (untrimmed, instead of 2.95).

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

AC or A/C | Complete aircraft configuration |

AoA, α | Angle of attack |

AR | Aspect ratio |

C(·)α | Derivative of the aerodynamic coefficient with respect to α |

CG | Center of gravity |

CFD | Computational fluid dynamic |

C_{D}, C_{d} | Drag coefficient |

C_{L,} C_{l} | Lift coefficient |

C_{L max} | Maximum lift coefficient |

C_{L0} | Lift coefficient at an angle of attack of 0 deg |

C_{M} or C_{M CG} | Pitching moment coefficient with respect to the centre of gravity |

C_{P} | Power coefficient |

C_{T} | Thrust coefficient |

D, d | Diameter |

DAF | Design of aircraft and flight technologies |

DEP | Distributed electric propulsion |

J | Advance ratio |

JPAD | Java program for aircraft design |

l_{H} | Longitudinal distance between the tail aerodynamic center and CG |

LE | Leading edge |

LND | Landing |

M | Mach number |

MAC, mac | Mean aerodynamic chord |

MIL | Minimum induced loss |

MTOM | Maximum take-off mass |

P | Power |

Q | Torque |

Re | Reynolds number |

RPM orn | Round per minute |

RANS | Reynolds average Navier–Stokes |

S(.) | Component surface |

T | Thrust |

TO | Take-off |

TR | Taper ratio |

V, V_{0} | Forward speed |

V_{a} | Axial speed |

V_{H} | Horizontal tailplane volumetric coefficient |

V_{s} | Stall speed |

V_{t} | Tangential speed |

V_{TO} | Take-off forward speed |

β | Blade pitch angle |

η | Propeller efficiency |

ρ | Air density |

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**Figure 3.**Convergence plot for lift coefficient (

**a**) and drag coefficient (

**b**). Cruise condition, M = 0.32, Re = 9.2 Mil.

**Figure 6.**Two-dimensional mesh for flapped airfoil analysis: (

**a**) Global overview of C-shape domain; (

**b**) mesh details around the airfoil and flap.

**Figure 7.**Blade geometry definition and velocity of interest: α is AoA for the blade element, β is the geometric pitch angle, φ is the helix angle, V

_{t}is the tangential velocity component, V

_{a}is the axial velocity component, and W is the resultant velocity.

**Figure 8.**TIP propeller designed with MIL approach. (

**a**) Chord distribution. (

**b**) Pitch angle distribution.

**Figure 9.**DEP propeller designed with Patterson’s approach. (

**a**) Chord distribution. (

**b**) Pitch angle distribution.

**Figure 10.**Induced axial speed Va (m/s) for DEP propeller designed following Patterson approach and the equivalent one designed following the MIL approach.

**Figure 11.**Propellers efficiency map (different blade pitch angles). (

**a**) Tip propeller. (

**b**) DEP propeller.

**Figure 12.**Propellers thrust coefficient map (different blade pitch angles). (

**a**) Tip propeller. (

**b**) DEP propeller.

**Figure 13.**Propeller power coefficient map (different blade pitch angles). (

**a**) Tip propeller. (

**b**) DEP propeller.

**Figure 15.**Numerical results in terms of lift coefficient curves of 2D analysis at different flap positions, landing condition, M = 0.15, Re = 5.7 × 10

^{6}.

**Figure 17.**Effect of the wing–fuselage fillet on the flow separation (skin friction map), AoA equal to 14 deg. (

**a**) Geometry without fillet. (

**b**) Geometry with fillet.

**Figure 18.**Numerical results of 3D simulations in terms of global lift coefficient for different flap positions, landing condition, M = 0.15, Re = 5.7 × 10

^{6}.

**Figure 19.**Total lift coefficient curves for clean and flapped (take-off and landing setup) wing configurations, low-speed conditions, M = 0.15, Re = 5.7 × 10

^{6}.

**Figure 20.**Drag and pitching moment curves, take-off and landing condition, M = 0.15, Re = 5.7 × 10

^{6}. (

**a**) Drag polar (drag expressed in counts). (

**b**) Pitching moment coefficient w.r.t. CG pos. (31% mac).

**Figure 21.**Total lift coefficient curves for power-off and power-on take-off conditions, M = 0.15, Re = 5.7 × 10

^{6}, J

_{TIP}= 0.78, rpm

_{TIP}= 1600, J

_{DEP}= 0.89, rpm

_{DEP}= 2000.

**Figure 22.**Drag and pitching moment curves for power-off and power-on take-off conditions, M = 0.15, Re = 5.7 × 10

^{6}, J

_{TIP}= 0.78, rpm

_{TIP}= 1600, J

_{DEP}= 0.89, rpm

_{DEP}= 2000. (

**a**) Drag polar (drag expressed in counts). (

**b**) Pitching moment coefficient w.r.t. CG pos. (31% mac).

**Figure 23.**Vorticity scene with the body skin friction contour and plot of pressure coefficient for sections located behind the propeller, AoA = 10 deg, take-off power-on, M = 0.15, Re = 5.7 × 10

^{6}, J

_{TIP}= 0.78, rpm

_{TIP}= 1600, J

_{DEP}= 0.89, rpm

_{DEP}= 2000.

**Figure 24.**Total lift coefficient curves for power-off and power-on take-off conditions, V

_{TO}= 44 m/s and V

_{TO}= 51 m/s, Re = 5.7 × 10

^{6}, J

_{TIP}= 0.78, rpm

_{TIP}= 1600, J

_{DEP}= 0.89, rpm

_{DEP}= 2000.

**Figure 25.**Drag and pitching moment curves, take-off condition V

_{TO}= 44 m/s and V

_{TO}= 51 m/s, Re = 5.7 × 10

^{6}, J

_{TIP}= 0.78, rpm

_{TIP}= 1600, J

_{DEP}= 0.89, rpm

_{DEP}= 2000. (

**a**) Drag polar (drag expressed in counts). (

**b**) Pitching moment coefficient w.r.t. CG pos. (31% mac).

Wing | |

S_{w} | 33.94 m^{2} |

AR | 13 |

root chord | 1.851 |

Kink position | 2.88 m |

TR | 0.65 |

MAC | 1.645 m |

LE sweep angle | 0 deg |

TE sweep angle (kink-tip) | 4 deg |

wing incidence | 3 deg |

tip washout | −3 deg |

Airfoil (root, kink, tip)
| NACA 23018/18/15 |

Fuselage | |

Length | 18 m |

Cabin Diameter | 2.150 m |

Cabin Height | 2.262 m |

Horizontal tail | |

S_{h} | 10.6 m^{2} |

AR_{h} | 4.6 |

root chord | 1.76 |

TR | 0.72 |

LE sweep angle | 8 deg |

Airfoil | NACA 0012 |

Vertical tail | |

S_{v} | 10.6 m^{2} |

AR_{v} | 1.6 |

root chord | 3.345 m |

TR | 0.37 |

LE sweep angle | 45 deg |

Airfoil | NACA 0012 |

Weight and Balance | |

MTOM | 8139 kg |

CG (%mac) | [30–40%, 0.0, −25%] Wing reference frame |

Mesh Type | Unstructured (Polyhedral Cells) |
---|---|

Number of cells | ~8,500,000 |

Number of prism layer | 33 |

Wall distance of the first cell | 6 × 10^{−6} m |

Turbulence models | Spalart–Allmaras (SA) |

Flow model | Ideal gas |

Solver | Steady Coupled implicit |

Number of iterations per AoA | 1000 |

Boundary conditions | Inflow: Free Stream |

Outflow: Pressure Outlet |

Low Speed | Climb | Cruise | |
---|---|---|---|

Mach number | 0.15 | 0.26 | 0.317 |

Reynolds number | 5.7 × 10^{6} | 8.7 × 10^{6} | 9.2 × 10^{6} |

Reference altitude | S/L | 1500 m | 3048 m |

Reference density | 1.225 kg/m^{3} | 1.058 kg/m^{3} | 0.909 kg/m^{3} |

Speed of sound | 340.3 m/s | 334.5 m/s | 328.4 m/s |

Low-Speed Conditions | |
---|---|

Mesh type | 2D-Structured |

Number of cells | 86,179 |

Mach number | 0.15 |

Reynolds number | 5.7 × 10^{6} |

Speed of sound | 340.3 m/s |

Number of iterations per AoA | ~1000 |

Altitude | Speed | Shaft Power TIP | Shaft Power DEP | |
---|---|---|---|---|

Take-Off | 0 m | 51 m/s | 217 kW | 126 kW |

Climb | 1500 m | 94 m/s | 225 kW | 131 kW |

Cruise | 3000 m | 104 m/s | 221 kW | 129 kW |

Descent | 1500 m | 66 m/s | 32 kW | 49 kW |

Landing | 0 m | 54 m/s | 16 kW | 6 kW |

**Table 6.**DEP and TIP propeller geometries (r, blade station, R, blade radius, c, blade local chord).

DEP Propeller | TIP Propeller | ||||
---|---|---|---|---|---|

r/R | c/R | Blade Pitch Angle β (deg) | r/R | c/R | Blade Pitch Angle β (deg) |

0.101 | 0.04 | 80.70 | 0.106 | 0.031 | 82.63 |

0.103 | 0.042 | 80.36 | 0.129 | 0.037 | 77.97 |

0.111 | 0.049 | 79.35 | 0.165 | 0.048 | 70.79 |

0.124 | 0.061 | 77.73 | 0.207 | 0.059 | 63.49 |

0.142 | 0.079 | 75.59 | 0.253 | 0.068 | 56.96 |

0.165 | 0.105 | 73.04 | 0.3 | 0.072 | 51.36 |

0.192 | 0.12 | 69.1 | 0.347 | 0.074 | 47.25 |

0.224 | 0.129 | 64.58 | 0.394 | 0.074 | 43.78 |

0.259 | 0.126 | 59.52 | 0.44 | 0.073 | 40.85 |

0.298 | 0.113 | 54.38 | 0.485 | 0.071 | 38.37 |

0.34 | 0.103 | 49.81 | 0.529 | 0.068 | 36.26 |

0.384 | 0.094 | 45.76 | 0.572 | 0.066 | 34.44 |

0.43 | 0.086 | 42.21 | 0.614 | 0.063 | 32.87 |

0.478 | 0.079 | 39.1 | 0.654 | 0.061 | 31.51 |

0.526 | 0.073 | 36.4 | 0.692 | 0.058 | 30.33 |

0.575 | 0.068 | 34.07 | 0.728 | 0.056 | 29.28 |

0.623 | 0.063 | 32.06 | 0.763 | 0.053 | 28.37 |

0.671 | 0.059 | 30.34 | 0.795 | 0.051 | 27.56 |

0.717 | 0.056 | 28.86 | 0.826 | 0.048 | 26.85 |

0.761 | 0.053 | 27.61 | 0.854 | 0.045 | 26.23 |

0.803 | 0.05 | 26.56 | 0.88 | 0.042 | 25.68 |

0.841 | 0.047 | 25.7 | 0.903 | 0.038 | 25.21 |

0.877 | 0.045 | 25 | 0.924 | 0.035 | 24.81 |

0.908 | 0.042 | 24.47 | 0.943 | 0.031 | 24.47 |

0.936 | 0.039 | 24.1 | 0.959 | 0.026 | 24.2 |

0.958 | 0.035 | 23.89 | 0.972 | 0.022 | 23.99 |

0.976 | 0.03 | 23.83 | 0.983 | 0.018 | 23.83 |

0.989 | 0.023 | 23.9 | 0.991 | 0.013 | 23.73 |

0.997 | 0.013 | 24.02 | 0.997 | 0.008 | 23.68 |

0.999 | 0.006 | 24.09 | 0.999 | 0.005 | 23.65 |

M114 Airfoil | SDA1075 Airfoil | ||||
---|---|---|---|---|---|

AoA | cl | cd | AoA | cl | cd |

−6 | 0.257 | 0.00818 | −6 | −0.467 | 0.0073 |

−5 | 0.382 | 0.00697 | −5 | −0.362 | 0.0068 |

−4 | 0.51 | 0.00641 | −4 | −0.256 | 0.0064 |

−3 | 0.636 | 0.00628 | −3 | −0.151 | 0.0059 |

−2 | 0.762 | 0.00604 | −2 | −0.045 | 0.0056 |

−1 | 0.88 | 0.00617 | −1 | 0.061 | 0.0053 |

0 | 1.001 | 0.0063 | 0 | 0.167 | 0.0051 |

1 | 1.12 | 0.00656 | 1 | 0.273 | 0.005 |

2 | 1.239 | 0.00668 | 2 | 0.378 | 0.005 |

3 | 1.358 | 0.00699 | 3 | 0.478 | 0.0048 |

4 | 1.475 | 0.00732 | 4 | 0.591 | 0.0048 |

5 | 1.59 | 0.00779 | 5 | 0.714 | 0.0054 |

6 | 1.704 | 0.00825 | 6 | 0.842 | 0.0061 |

7 | 1.815 | 0.00867 | 7 | 0.959 | 0.0071 |

8 | 1.921 | 0.00959 | 8 | 1.082 | 0.0085 |

9 | 2.019 | 0.01055 | 9 | 1.21 | 0.01 |

10 | 2.083 | 0.0118 | 10 | 1.317 | 0.0113 |

11 | 2.101 | 0.0232 | 11 | 1.389 | 0.0127 |

12 | 2.084 | 0.02084 | 12 | 1.458 | 0.0141 |

13 | 2.03 | 0.02262 | 13 | 1.494 | 0.0158 |

14 | 1.951 | 0.03242 | 14 | 1.535 | 0.0179 |

15 | 1.844 | 0.03692 | 15 | 1.57 | 0.0211 |

16 | 1.711 | 0.04214 | 16 | 1.597 | 0.0261 |

17 | 1.562 | 0.04865 | 17 | 1.605 | 0.0341 |

18 | 1.408 | 0.05684 | 18 | 1.598 | 0.0452 |

19 | 1.257 | 0.06743 | 19 | 1.569 | 0.0605 |

20 | 1.112 | 0.08102 | 20 | 1.509 | 0.0816 |

**Table 8.**Propellers take-off operating points. Both DEP and TIP propellers have a right-handed rotation.

D (m) | J | C_{T} | n (rpm) | Pitch Angle @.75 r/R (deg) | Efficiency | Power (kW) | |
---|---|---|---|---|---|---|---|

DEP | 1.89 | 0.89 | 0.138 | 2000 | 28.4 | 0.82 | 126 |

TIP | 2.54 | 0.78 | 0.1015 | 1600 | 23.8 | 0.86 | 217 |

Type | Fowler |

Flap/Wing chord ratio | 0.3 |

Inner station | 12% wingspan |

Outer station | 80% wingspan |

Airfoil (root, kink, tip) | NACA 23018/18/15 |

**Table 10.**Numerical results of 2D analysis at different flap positions, landing condition, M = 0.15, Re = 5.7 × 10

^{6}.

Gap | Overlap | Deflection | C_{l max} | C_{l} α | C_{l0} |
---|---|---|---|---|---|

3% | 0% | 35 deg | 2.88 | 0.108 | 1.53 |

3% | −2% | 35 deg | 2.51 | 0.105 | 1.22 |

3% | 2% | 35 deg | 3.56 | 0.107 | 1.68 |

3% | 3% | 35 deg | 3.52 | 0.108 | 1.69 |

2% | 0% | 35 deg | 3.11 | 0.108 | 1.46 |

4% | 2% | 35 deg | 2.99 | 0.106 | 1.50 |

2.5% | 2.7% | 35 deg | 2.98 | 0.097 | 1.64 |

2.5% | 2.7% | 30 deg | 3.45 | 0.108 | 1.94 |

Take-Off | |
---|---|

Gap | 3% chord |

Overlap | 0% chord |

Deflection | 15 deg |

Landing | |
---|---|

Gap | 2.5% chord |

Overlap | 2.7% chord |

Deflection | 30 deg |

**Table 13.**Numerical results for low-speed conditions, untrimmed maximum lift coefficient, moment coefficient calculated w.r.t. CG pos. (31% mac), M = 0.15, Re = 5.7 × 10

^{6}.

C_{Lmax} | C_{Lα} | C_{L0} | C_{Mα} | C_{M0} | |
---|---|---|---|---|---|

Clean | 1.57 | 0.110 | 0.27 | −0.053 | 0.118 |

Take Off | 2.65 | 0.118 | 1.05 | −0.045 | 0.100 |

Landing | 2.95 | 0.108 | 1.41 | −0.039 | 0.130 |

**Table 14.**Numerical results for low-speed conditions, trimmed maximum lift coefficient, moment coefficient calculated w.r.t. CG pos. (31% mac), M = 0.15, Re = 5.7 × 10

^{6}.

C_{Lmax} | C_{M cg} (@AoA = 14 Deg) | V_{H} | ΔC_{LH} | C_{Lmax trimmed} | |
---|---|---|---|---|---|

Take-Off | 2.65 | −0.593 | 1.5 | −0.12 | 2.53 |

Landing | 2.95 | −0.491 | 1.5 | −0.10 | 2.85 |

**Table 15.**Numerical results for take-off power-on condition, untrimmed maximum lift coefficient, moment coefficient calculated w.r.t. CG pos. (31% mac), M = 0.15, Re = 5.7 × 10

^{6}, J

_{TIP}= 0.78, rpm

_{TIP}= 1600, J

_{DEP}= 0.89, rpm

_{DEP}= 2000.

Take Off | C_{Lmax} | C_{Lα} | C_{L0} | C_{Mα} | C_{M0} |
---|---|---|---|---|---|

power-off | 2.65 | 0.118 | 1.05 | −0.045 | 0.100 |

power-on | 2.95 | 0.123 | 1.43 | −0.098 | 0.139 |

**Table 16.**Numerical results for take-off, trimmed maximum lift coefficient, moment coefficient calculated w.r.t. CG pos. (31% mac), power-on conditions: J

_{TIP}= 0.78, rpm

_{TIP}= 1600, J

_{DEP}= 0.89, rpm

_{DEP}= 2000. M = 0.15, Re = 5.7 × 10

^{6}.

Take Off | C_{Lmax} | C_{M cg} (@AoA = 14 Deg) | V_{H} | ΔC_{LH} | C_{Lmax trimmed} |
---|---|---|---|---|---|

power off | 2.657 | −0.593 | 1.5 | −0.12 | 2.53 |

power on | 2.95 | −1.210 | 1.5 | −0.25 | 2.70 |

**Table 17.**Numerical results for take-off power-on condition, untrimmed maximum lift coefficient, moment coefficient calculated w.r.t. CG pos. (31% mac), V

_{TO}= 44 m/s and V

_{TO}= 51 m/s, Re = 5.7 × 10

^{6}, J

_{TIP}= 0.78, rpm

_{TIP}= 1600, J

_{DEP}= 0.89, rpm

_{DEP}= 2000.

Take Off | C_{Lmax} | C_{Lα} | C_{L0} | C_{Mα} | C_{M0} |
---|---|---|---|---|---|

power-off | 2.65 | 0.118 | 1.05 | −0.045 | 0.100 |

power-on | 2.95 | 0.123 | 1.43 | −0.098 | 0.139 |

power-on(reduced V_{TO}) | 3.24 | 0.129 | 1.52 | −0.098 | 0.138 |

**Table 18.**Numerical results for take-off power-on condition, trimmed maximum lift coefficient, moment coefficient calculated w.r.t. CG pos. (31% mac), V

_{TO}= 44 m/s and V

_{TO}= 51 m/s, Re = 5.7 × 10

^{6}, J

_{TIP}= 0.78, rpm

_{TIP}= 1600, J

_{DEP}= 0.89, rpm

_{DEP}= 2000.

Take Off | C_{Lmax} | C_{M cg} (@AoA = 14 Deg) | V_{H} | ΔC_{LH} | C_{Lmax trimmed} |
---|---|---|---|---|---|

power off | 2.67 | −0.593 | 1.5 | −0.12 | 2.53 |

power on | 2.95 | −1.210 | 1.5 | −0.25 | 2.70 |

power-on(reduced V_{TO}) | 3.24 | −1.268 | 1.5 | −0.26 | 2.98 |

Take Off | C_{Lmax trimmed} | Take-Off Stall Speed (m/s) | Take-Off Distance (m) | Δ% |
---|---|---|---|---|

Reference | 2.0 | 40.37 | 507 | |

Power-off | 2.53 | 38.96 | 435 | −14% |

Power-on | 2.70 | 37.72 | 407 | −19% |

Power-on(reduced V_{TO}) | 2.98 | 35.90 | 365 | −27% |

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## Share and Cite

**MDPI and ACS Style**

Cusati, V.; Corcione, S.; Nicolosi, F.; Zhang, Q. Improvement of Take-Off Performance for an Electric Commuter Aircraft Due to Distributed Electric Propulsion. *Aerospace* **2023**, *10*, 276.
https://doi.org/10.3390/aerospace10030276

**AMA Style**

Cusati V, Corcione S, Nicolosi F, Zhang Q. Improvement of Take-Off Performance for an Electric Commuter Aircraft Due to Distributed Electric Propulsion. *Aerospace*. 2023; 10(3):276.
https://doi.org/10.3390/aerospace10030276

**Chicago/Turabian Style**

Cusati, Vincenzo, Salvatore Corcione, Fabrizio Nicolosi, and Qinyin Zhang. 2023. "Improvement of Take-Off Performance for an Electric Commuter Aircraft Due to Distributed Electric Propulsion" *Aerospace* 10, no. 3: 276.
https://doi.org/10.3390/aerospace10030276