## 1 Introduction  
In recent years, there has been a growing interest in unmanned stratospheric platforms for long-duration Earth observation and telecommunications, commonly referred to as HAPSs. These platforms represent a valuable complement to satellites and RPAS. Most HAPSs operate at altitudes of approximately 18-20 km, which are well above commercial air traffic. At these altitudes, the atmospheric conditions are relatively stable, with minimal convective activity and nearly constant temperatures. Wind speeds are also generally lower compared to those observed in both lower and higher atmospheric layers, making this region of the stratosphere particularly attractive for persistent operations. This segment of the atmosphere is part of what is often referred to as Near Space, qualitatively defined as the region extending from around 20 km altitude up to the Karman line at 100 km. Earth observation from the stratosphere benefits from the proximity to the Earth's surface, enabling higher spatial resolution than satellite imagery, assuming equivalent optical payload characteristics. Furthermore, temporal resolution is significantly enhanced, as HAPSs can maintain a fixed position (station-keeping), thereby eliminating or substantially reducing revisit times. Until recently, HAPS technologies had received limited attention. However, several configurations have now been proposed and can generally be classified into two main categories, based on their method of lift generation: fixed-wing platforms and lighter-than-air systems. Among the fixed-wing solutions, the Airbus Zephyr platform [1] and the AE Prismatic PHASA-35 system [2] show considerable promise. In the category of lighter-than-air systems, Thales is developing the Stratobus airship [3], while the SCEYE airship [4] has already completed multiple missions in the stratosphere. These platforms differ in configuration and payload capacity, which can range from a few kilograms (5-20 kg) to several hundred kilograms, depending on the specific design. Hybrid configurations have also been explored in the literature. For example, the Italian Aerospace Research Centre (CIRA) is actively developing a hybrid solution that combines both aerostatic and aerodynamic lift, as detailed in [5; 6; 7]. One of the most critical subsystems in HAPSs is the propulsion system, due to its significant impact on both power consumption and overall system weight. Achieving the required endurance and payload capacity at stratospheric altitudes and relatively low flight speeds presents a substantial challenge. The most feasible approach to address this issue is the adoption of propulsion systems characterized by high efficiency and low specific energy consumption. The design of propulsion systems for HAPSs has undergone significant evolution in recent decades, primarily driven by technological advancements in renewable energy sources (e.g., photovoltaic systems) and energy storage technologies (e.g., batteries). In [8], a study is presented on a propulsion system for a subsonic, high-altitude unmanned aircraft capable of operating at an altitude of approximately 30 km, with a loiter time of about three hours. The propulsion system in that case consisted of a turboprop engine fueled by onboard fuel and oxidizer. At that time, the endurance record at 20 km was held by the Boeing Condor, which achieved 58 h of continuous flight using a liquid-cooled, two-stage turbocharged spark-ignition engine. A key challenge associated with air-breathing turbocharged piston engines at high altitudes is heat rejection, due to the low ambient air density. This necessitates the use of larger radiators. In addition, achieving effective combustion requires very high pressure ratios to compensate for the low atmospheric pressure. In [9], a comparative study is provided, analyzing various propulsion system types for a High-Altitude Long-Endurance (HALE) airship across two mission profiles at altitudes between 18 km and 21 km, each with a target endurance of one month.