**1. Introduction**

Aircraft design is a complex and interrelated field of research. Every modification of a specific component in the design process has an influence on other components or the aircraft/platform itself. This leads to an iterative design process, ideally resulting in one converged optimum design for the given top level aircraft requirements (TLARs). Small, evolutionary technology changes mostly result in designs close to already known configurations, emphasizing today's well-chosen concepts. This changes for revolutionary technology steps, such as the implementation of distributed (electric) propulsion (DEP). Several designs, differing radically from today's configurations, have already been investigated in order to use the full technological potential enabled through the use of DEP on aircraft. Globally, there have been many research attempts trying to make use of DEP's aerodynamic potential. The NASA X-57 design uses the velocity increase downstream

**Citation:** 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

Academic Editor: Dimitri Mavris

Received: 13 February 2023 Revised: 27 March 2023 Accepted: 18 April 2023 Published: 25 April 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

of a propeller to reduce the wing surface [1]. Wing tip propellers are also used by other configurations in order to reduce the wake-induced drag, such as the NASA Pegasus [1], the Airbus/TBM/Safran EcoPulse [2] and the European research project FUTPRINT50 [3]. All of these projects feature designs with unconventional propeller positions for their propulsion system integration. This raises the question of the suitability of a volume coefficient-based vertical tailplane (VTP) sizing which is based on statistics of existing conventional aircraft without DEP. This is also valid for the configurations investigated in this paper.

The study presented is part of the GNOSIS project, which aims for a holistic evaluation of the potential of propulsion system electrification for commercial passenger aircraft with seat capacities in the range of 9 to 50 seats. In the first project phase, the focus is on the conceptual design of a 19-seater aircraft. The following study therefore compares a volume coefficient-based sizing of the VTP during preliminary aircraft design with handbook methods. This is performed for a partial turboelectric 19-seater incorporating wing tip propulsion with regard to the impact of the inboard engine position and the interconnection of the propulsors and thereafter the impact of a reduction in the required VTP size on the aircraft.

According to [4], the VTP is usually sized by two major flight conditions. One being the operation with one engine inoperative and the other with maximum cross-wind capability. The focus of the study presented here is the investigation of the usability of the given VTP in case of engine failure-induced thrust asymmetry and the possible reduction in VTP size and its impact on the preliminary aircraft design. As investigated by Hoogreef and Soikkeli [5], as well as Vechtel and Buch [6] and proven by Schneider et al. [7] in a full-scale flight test, the directional stability may also be provided by the use of differential thrust. Therefore, the influence of the directional stability on the vertical tail size is neglected in this study.

For conventional configurations, the dimensioning contributor for a critical loss of thrust (CLT), or "one engine inoperative" (OEI) scenario has been the control authority of the VTP around the yaw axis. Particularly for DEP configurations, the limiting CLT condition might also be given by the maximum aileron authority in certain configurations. For the study presented in this paper, only the VTP's yaw control authority shall be assessed, as the considered positions of the propulsion system integration lead to an aircraft, for which the resulting yaw moments are significantly larger than the roll moments [6].

The contents of the paper are structured as follows. First the preliminary aircraft design tool used and the methodology for calculation of the aircraft and vertical tail parameters are explained. Then, a short overview of the considered aircraft configurations is given. Thereafter, the results of the optimization of the vertical stabilizer size for the different aircraft are given. It is shown how the fin size changes depending on the propeller positions and electrical interconnections. Moreover, certain architectures lead to uncontrollable aircraft designs in case of a critical loss of thrust, refraining from the additional implementation of components and hence additional weight. The calculated VTP size is then used to determine the impact on the aircraft using a mission data analysis of the individual configurations, hence accounting for the interrelated effects of a possible reduction in VTP size on the preliminary aircraft design.
