## 3 Propulsion Systems for HAPSs
### Electric Propulsion
However, drawbacks include increased complexity--due to the presence of brushes, commutators, and controllers that wear out relatively quickly, especially in low-pressure and low-density environments--higher maintenance requirements, susceptibility to malfunctions compared to AC motors, greater cost, and lower energy efficiency. AC motors are electric motors that operate with alternating current. They can be classified into two main categories: synchronous and asynchronous. The primary advantages of AC motors include their simplicity, reliability (requiring less maintenance), efficiency (consuming less power), and wide availability. The main disadvantage is the necessity of an inverter in the system to supply power to the motor. Permanent magnet synchronous motors (PMSMs) and brushless DC motors (BLDCs) are, respectively, the most common AC and DC electric motors used in industrial applications. Due to their advantages, AC motors are generally preferred for HAPS propulsion systems. However, some studies in the literature have analyzed propulsion systems for HAPSs employing DC electric motors, demonstrating their feasibility for high-altitude applications [56]. In the literature, several curve fits have been developed using data from electric motors reported in open sources, which can be used to estimate the mass and efficiency of an electric motor based on the required power, \(P\)[57]. The mathematical expression for the mass curve is presented in Equation (4). \[m_{em}=0.2669+9.845\cdot 10^{-4}P_{\max}-1.120\cdot 10^{-10}P_{\max}^{2} \tag{4}\]  
The motor efficiency, in general, is a function of angular speed and power. A motor has a design rpm in which the efficiency is higher and working at a different rpm means working inefficiently. Often, a gearbox is necessary, and its use comes from a compromise between efficiency and weight. In [57], there is a simplified relationship to make a preliminary estimate of the efficiency, knowing the power \(P\), of a four-pole AC motor; this formula is shown in Equation (5). \[\eta_{em}=75.844+8.6059\log\left(\frac{P}{1000}\right) \tag{5}\]  
Extensive research has been conducted to improve electric motor efficiency, such as the work by [PERSON] [58] on PMSMs. [PERSON] proposes an integrated optimization control method that combines loss-model-based efficiency optimization control methods (which rely on loss models of PMSMs [59]) with search-based optimization control methods (which continuously regulate the stator current to drive system efficiency toward the optimum). This approach involves first determining the optimal value of the d-axis current using the loss-model-based efficiency optimization method and then, utilizing this value, applying the search-based optimization control method with a narrowed search interval. This strategy improves convergence time and efficiency, overcoming the limitations of applying the two methods separately. Motor efficiency affects not only power consumption but also heat generation. A less efficient motor dissipates more energy as heat, resulting in higher temperatures and potential performance issues, particularly in low-density environments. Electric motors designed for high-altitude applications must therefore achieve both high efficiency and effective cooling to dissipate heat. Some passive cooling solutions proposed by manufacturers include introducing cuts along the motor casing or open-frame designs (e.g., holes or fissures designed to promote airflow through the motor body) to enhance cooling performance. Several studies in the literature address the thermal response of motors operating in low-density environments. For instance, ref. [60] reports testing of a commercial off-the-shelf motor inside a large vacuum chamber capable of reaching high vacuum levels (\(10^{-10}\) atm). Results indicate that motor temperature increases with decreasing pressure and increasing angular velocity (power output), as expected. However, the motor remains adequately cooled throughout the simulations as long as the propeller continues spinning.