# Influence of Electric Wing Tip Propulsion on the Sizing of the Vertical Stabilizer and Rudder in Preliminary Aircraft Design

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## Abstract

**:**

## 1. Introduction

#### A Short Discussion of “Critical Loss of Thrust”

## 2. Methodology

^{®}-based tools.

#### 2.1. Overview of the Conceptual Aircraft Design Tool MICADO

#### 2.2. Reference and Concept Aircraft

#### 2.3. Considered Wiring Configurations

#### 2.4. Handbook Methods for Vertical Tail Plane Sizing According to Roskam

#### 2.5. Calculation of the Vertical Tail Plane Geometry

^{®}script that loops the whole process described in Section 2.4. The needed aircraft parameters are obtained from the aircraft designs calculated in MICADO. For atmospheric parameters, the ICAO standard atmosphere [26] at sea level is used. Depending on the wiring configuration selected (on-wing or cross wiring), the yawing moments resulting from the thrust of the remaining engines and the drag from the inoperative propellers are determined. Then, starting from a simplified original geometry of the VTP, the initial values for the coefficients and derivatives are calculated. In order to be able to utilize the aforementioned diagrams from Roskam Part VI [25], they were evaluated at discrete points and implemented as tables, splines or polynomial equations and interpolated between the given values. Using Roskam’s statement that the maximum rudder deflection must not be more than ${25}^{\circ}$, Equation (4) gives the maximum value for ${C}_{{n}_{{\delta}_{r}}}$ and via Equation (5) the maximum ${C}_{{y}_{{\delta}_{r}}}$. The resulting new surface of the vertical tail plane can be derived from Equation (6).

#### 2.6. Iteration Over the Whole Aircraft

#### 2.7. Assumptions and Restrictions

## 3. Results

#### 3.1. Sensitivity Study on the Vertical Tail’s Volume Coefficient

#### 3.2. Size of the Adjusted Vertical Tail

#### 3.3. Results of the Total Aircraft Iteration

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

CG | Centre of gravity |

CS | Certification specification |

CLT | Critical loss of thrust |

DEP | Distributed electric propulsion |

EASA | European Union Aviation Safety Agency |

ICAO | International Civil Aviation Organization |

MICADO | Multidisciplinary Integrated Conceptual Aircraft Design and Optimization |

MTOM | Maximum take-off mass |

NASA | National Aeronautics and Space Administration |

OEI | One engine inoperative |

OME | Operating mass empty |

TLAF | Top level aircraft functions |

TLAR | Top level aircraft requirements |

UNICADO | University Conceptual Aircraft Design and Optimization |

VTP | Vertical tailplane |

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**Figure 1.**PT2025 aircraft with on-wing (Configuration 1) and cross wiring option (Configuration 2), as well as the PT2025opt aircraft with on-wing (Configuration 3) and cross wiring option (Configuration 4), with the red and green lines symbolizing the independent wiring harnesses.

**Figure 3.**Redesign of a Beechcraft 1900D (

**left**), modified redesign (

**centre-left**), as well as non-optimized PT2025 (

**centre-right**) and optimized PT2025opt (

**right**) versions of the partial turboelectric concept aircraft.

**Figure 6.**Partial turboelectric aircraft with optimized propeller positions and a volume coefficient of the vertical tail of 0.04253 (

**left**) and 0.14253 (

**right**).

**Figure 7.**Influence of the vertical tail’s volume coefficient on the OME (blue) and the trip fuel (red) for the PT2025 (left) and PT2025opt (right) configurations.

**Figure 8.**Original (blue) and resized (amber) vertical tail for the PT2025opt aircraft with cross wiring (Configuration 4).

Component | Density (kg/m${}^{3}$) | Thickness/ Diameter (mm) | |
---|---|---|---|

Wire | 8920 | ${D}_{wire}=\sqrt{\frac{4\xb7\phantom{\rule{4pt}{0ex}}0.0144\xb7I{\left[A\right]}^{1.4642}}{\pi}}$ | |

Insulation | 930 | ${t}_{insulation}=0.2325\xb7U\left[kV\right]+1.73682$ | |

Sheath | 930 | ${t}_{sheath}=0.035\xb7{D}_{wire}\left[mm\right]+1$ |

PT2025 | PT2025opt | |||
---|---|---|---|---|

On-Wing | Cross-Wing | On-Wing | Cross-Wing | |

(Configuration 1) | (Configuration 2) | (Configuration 3) | (Configuration 4) | |

Wingspan | 17.3 m | 17.3 m | 17.2 m | 17.3 m |

OME | 4892 kg | 4931 kg | 4825 kg | 4927 kg |

MTOM | 7629 kg | 7671 kg | 7537 kg | 7653 kg |

Conductor mass | 31.4 kg | 56.6 kg | 14.2 kg | 71.8 kg |

Trip fuel | 606 kg | 609 kg | 591 kg | 600 kg |

**Table 3.**Surface area and volume coefficients of the original and resized vertical tail for the four considered aircraft and wiring configurations.

Original VTP | Resized VTP | Change | ||
---|---|---|---|---|

Configuration 1 | ${S}_{v}$ | 6.75 m${}^{2}$ | 27.72 m${}^{2}$ | +310.7% |

${\overline{V}}_{v}$ | 0.083 | 0.247 | +197.6% | |

Configuration 2 | ${S}_{v}$ | 6.77 m${}^{2}$ | 13.47 m${}^{2}$ | +99.0 % |

${\overline{V}}_{v}$ | 0.082 | 0.147 | +79.3% | |

Configuration 3 | ${S}_{v}$ | 6.68 m${}^{2}$ | 36.38 m${}^{2}$ | +444.6% |

${\overline{V}}_{v}$ | 0.083 | 0.288 | +347.0% | |

Configuration 4 | ${S}_{v}$ | 6.87 m${}^{2}$ | 4.14 m${}^{2}$ | −39.7% |

${\overline{V}}_{v}$ | 0.083 | 0.053 | −36.1% |

**Table 4.**Comparison of VTP, OME and mission fuel of the original and optimized PT2025opt aircraft with cross wiring (Configuration 4), taking into account the iteration of the whole aircraft.

Original Configuration 4 Aircraft | Configuration 4 Aircraft with Adjusted Fin | Change | ||
---|---|---|---|---|

VTP surface | 6.87 m${}^{2}$ | 3.18 m${}^{2}$ | −3.69 m${}^{2}$ | −53.7% |

Volume coeff | 0.083 | 0.045 | −0.038 | −45.8% |

VTP mass | 146.6 kg | 66.9 kg | −79.6 kg | −54.3% |

OME | 4926.6 kg | 4744.6 kg | −182.0 kg | −3.7% |

Trip fuel | 600.3 kg | 571.8 kg | −28.5 kg | −4.9% |

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## Share and Cite

**MDPI and ACS Style**

Albrecht, A.; Bender, A.; Strathoff, P.; Zumegen, C.; Stumpf, E.; Strohmayer, A.
Influence of Electric Wing Tip Propulsion on the Sizing of the Vertical Stabilizer and Rudder in Preliminary Aircraft Design. *Aerospace* **2023**, *10*, 395.
https://doi.org/10.3390/aerospace10050395

**AMA Style**

Albrecht A, Bender A, Strathoff P, Zumegen C, Stumpf E, Strohmayer A.
Influence of Electric Wing Tip Propulsion on the Sizing of the Vertical Stabilizer and Rudder in Preliminary Aircraft Design. *Aerospace*. 2023; 10(5):395.
https://doi.org/10.3390/aerospace10050395

**Chicago/Turabian Style**

Albrecht, Alexander, Andreas Bender, Philipp Strathoff, Clemens Zumegen, Eike Stumpf, and Andreas Strohmayer.
2023. "Influence of Electric Wing Tip Propulsion on the Sizing of the Vertical Stabilizer and Rudder in Preliminary Aircraft Design" *Aerospace* 10, no. 5: 395.
https://doi.org/10.3390/aerospace10050395