## 1 Introduction
When integrated with renewable energy sources such as solar panels, these systems offer not only high precision and reliability, but also enable the long-duration, continuous operations that are essential for sustained HAPS missions in the stratosphere. Some of the most representative HAPS configurations developed over the past 40 years, each of which has successfully completed at least one flight, are presented in Figures 1 and 2, along with their corresponding altitude and endurance performance data. The year indicated for each platform refers to the date when the performance was actually achieved or to the year in which such performance is expected to be reached on the basis of the design specifications. The data illustrated in these figures clearly demonstrate that, on average, HAPSs equipped with electric propulsion systems tend to achieve superior altitude and endurance capabilities compared to those powered by combustion-based propulsion. Figure 1: Altitude performance of some of the main HAPSs developed over the last 40 years, that have successfully flown at least once [2, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27]. The year corresponds to the year in which each altitude performance was achieved or was projected to be achievable. Figure 2: Endurance performance of some of the main HAPSs developed over the last 40 years, that have successfully flown at least once [2, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27]. The year corresponds to the year in which each endurance performance was achieved or was projected to be achievable. As a result, two main categories of HAPS can currently be identified: solar-powered airplanes and solar-powered airships [28]. Among the most notable solar airplane projects, both past and present, are Helios [29], AEV-3 [30], Aquila [31], and Zephyr [32]. Regarding solar airships, key projects include HiSentinel [33], the Stratospheric Platform (SPF) [34], the Korean Stratospheric Airship Program [28], the High-Altitude Airship (HAA) [35], and Stratobus [28]. To achieve high endurance capabilities at high altitudes, it is essential not only to improve engine efficiency but also to properly design propellers to enhance their performance. A key factor in propeller design and operation is the environment in which it functions. High-altitude conditions (ranging from 17 km up to 50 km) present unique challenges for propeller operation. At these altitudes, airfoils operate under low Reynolds number conditions, typically between \(10^{4}\) and \(10^{5}\)[36]. Within this range, the transition from laminar to turbulent flow plays a crucial role, with viscous forces becoming a significant factor influencing flow behavior. Compared to high Reynolds number operations, some of the most notable effects include a sharp decrease in the lift-to-drag ratio after its maximum, caused by the development of thicker boundary layers; possible nonlinear behavior of airfoils at low angles of attack; laminar flow separation along the blades leading to short or long laminar separation bubbles; increased sensitivity of the flow to free-stream turbulence; and a consequent rise in drag forces resulting in reduced efficiency [36; 37; 38]. The laminar separation bubble is a primary factor contributing to the decrease in propeller efficiency at very low Reynolds numbers [39]. The key to designing an effective propeller lies in mitigating the detrimental effects of laminar separation bubbles on the blades [40]. Furthermore, the interactions between three-dimensional effects, such as centrifugal [41; 42] and Coriolis forces, with the transition process and the development of laminar separation bubbles along the blade, are not yet fully understood. These three-dimensional effects, amplified by blade rotation, can induce cross-flow within the boundary layer and alter the transition location, thereby influencing both the extent and stability of laminar separation [43].