## 3 Propulsion Systems for HAPSs  
The capability of aircraft and airships to operate at high altitudes for extended durations is strongly dependent on the performance of the propulsion system. For many years, propulsion has been the primary limiting factor for stratospheric applications, mainly due to its power consumption--it is the largest power-consuming system onboard--and its weight. Significant research on propulsion systems for HAPSs has been conducted over the past fifty years to overcome these power and weight constraints and enhance aircraft performance in terms of altitude, flight endurance, and payload capacity. This section provides an estimation of the propulsion system power requirements and presents an overview of the main propulsion concepts proposed in the literature. A propulsion system for HAPSs must satisfy multiple requirements, primarily related to power, mass, and operating conditions. Regarding operational requirements, the propulsion system must function efficiently across a wide range of environmental conditions. A HAPS may need to autonomously take off from the ground and reach the stratosphere; therefore, the propulsion system should perform efficiently throughout the entire altitude range, characterized by varying temperatures and pressures. The propulsion power requirement is mainly driven by the thrust necessary to overcome drag and by the efficiencies of the system components. The drag forces for aircraft and airships are defined, respectively, by Equations (1) and (2).  
\[D=\frac{1}{2}\rho V_{\infty}^{2}SC_{D} \tag{1}\]  
\[D=\frac{1}{2}\rho V_{\infty}^{2}V_{a}^{\frac{3}{3}}SC_{D,\varphi} \tag{2}\]  
In Equation (2), the drag \(D\) is expressed as a function of the volumetric drag coefficient, \(C_{D,\varphi}\), and the volume of the airship, \(V_{a}\). The volumetric drag coefficient, \(C_{D,\varphi}\), can be related to the fineness ratio \(f\) (defined as the ratio of the length to the diameter or width of the airship). An equation proposed in the literature [52], valid for a maximum fineness ratio of 10 and for a cylindrical body with hemispherical ends, is presented in Equation (3).  
\[C_{D,\varphi}=0.23175-0.15757f+0.04744f^{2}-7.0412\cdot 10^{-3}f^{3}+5.1534 \cdot 10^{-4}f^{4}-1.4835\cdot 10^{-5}f^{5} \tag{3}\]  
The velocity \(V_{\infty}\) in the preceding equations depends on the specific application. For an airship aiming to maintain a stationary position, \(V_{\infty}\) corresponds to the ambient wind speed. Wind speeds represent a major design consideration for HAPSs, as they vary with time, location, and altitude. Many stratospheric platform concepts proposed in the literature operate at approximately 20 km altitude, where wind speeds generally reach a minimum. For high-altitude aircraft and airships, the typical thrust requirement ranges from 100 N to 100 kN. Once the drag is determined, the power required by propulsion systems employing propellers to generate thrust can be readily calculated. Numerous types of propulsion systems have been proposed and many have undergone testing. The following paragraphs provide an overview of the main propulsion systems discussed in the literature. These systems are categorized into four groups in this section: combustion propulsion, electrical propulsion, hybrid propulsion, and future propulsion concepts for high-altitude applications.