## 5 Propeller Design for HAPS Operation
### Recent Development on Propeller Design Methodology
Once these bubbles nearly vanish, the Gurney flap no longer provides benefits in terms of camber increase or separation prevention. Instead, the additional drag introduced by the flap slightly reduces the ratio of lift to drag for the airfoil, leading to a decrease in propeller efficiency at higher Reynolds numbers. In order to further improve the design methodologies described previously, it is crucial to consider wind speed and its effects on the Reynolds number during the design phase. One possible approach, proposed in [84], involves performing a statistical study of wind conditions at the mission location to obtain a probabilistic wind distribution. This distribution can be discretized, and a cost function, defined as a weighted sum based on the probability of each wind value, can be maximized. In Ref. [148], an algorithm based on generalized polynomial chaos expansion theory, which utilizes wind intensity probability  
Figure 18: Comparison of the efficiency curves of the optimized propellers with and without the Gurney flap, \(Re_{average}=4\times 10^{4}\)[45]. density functions (PDFs), is proposed to convert the stochastic design problem into a deterministic one. This approach demonstrated, in the authors' case study, that stochastic design improves mean net propulsion efficiency by approximately 5% compared to a classical deterministic design. Finally, a fundamental aspect to consider is the implementation of a mechanism that allows in-flight adjustment of propeller pitch. During the design phase of a propeller for a stratospheric aircraft, assessing the need for a variable-pitch propeller is important to enhance the overall propulsion system performance. When a propeller optimized for high-altitude operation is used at lower altitudes,where air density is significantly higher, the maximum rotational speed is limited by the maximum torque constraint. This leads to reduced shaft power and thrust. A widely used solution to enhance the compatibility between the propeller and electric motor across varying altitudes is the implementation of a variable-pitch propeller. A study detailed in [149] compares the aerodynamic performance of a fixed-pitch propeller--optimized through surrogate-based methods for operation at 25 km altitude, 40 m/s wind speed, and 1200 rpm rotational speed--with variable-pitch propellers analyzed via RANS solvers. Table 3 provides a comparison between fixed-pitch and variable-pitch propellers in terms of thrust and efficiency at different altitudes and wind speed, under a constrained rated torque. Figure 19: Comparison of the efficiency curves of the optimized propellers with and without the Gurney flap, \(Re~{}=~{}1.8\times 10^{5}\). The contrast points indicate the same advance ratios as the design points, evaluated under higher Reynolds number conditions [45]. The results show that, although the efficiency of a variable-pitch propeller is lower than that of a fixed-pitch propeller, the rotational speed achieved and subsequently its maximum thrust is significantly higher, especially at low altitude and low wind speed, because the shaft power of the variable-pitch propeller is much greater than that of the fixed-pitch propeller. The maximum relative increase in thrust can exceed 80%, expanding the flight envelope of the aircraft. However, while this improves performance in off-design conditions, it also increases the weight and complexity of the platform due to the need for actuation systems. A thorough analysis should therefore be carried out to assess whether the performance benefits of a variable pitch propeller outweigh the additional weight and resulting increase in energy consumption. Finally, a summary of the methodologies, optimization techniques, and aerodynamic models adopted for the design of propellers in HAPS propulsion systems is provided in Table 4. Reported values include maximum propeller efficiency, reference diameter, and operating conditions, to allow for a more meaningful comparison across different works.