## 5 Propeller Design for HAPS Operation
### Recent Development on Propeller Design Methodology
Regarding chord distribution, the results show low values at the root, peak values in the 60-80% span range, and low values at the tip. Additionally, it has been found that properly increasing the camber of the sectional airfoil can improve the aerodynamic efficiency of the propeller at low Reynolds numbers [40]. An innovative design aimed at further enhancing propeller efficiency is presented in [45], involving the addition of a Gurney flap to the propeller airfoil. A Gurney flap is a small, flat plate mounted vertically at the trailing edge of the airfoil, typically with a height between 0.5% and 5% of the chord. Its primary function is to increase lift by increasing pressure on the lower surface of the airfoil. The design process described by the authors is iterative and consists of several steps. Initially, design parameters such as free-stream velocity, propeller radius, blade number, required thrust, rotation speed, and initial airfoil data are established. The initial chord and pitch distributions are then determined using the Betz method. Subsequently, the cross-sectional airfoils with a Gurney flap are optimized using MIGA, where the airfoils are parameterized and iteratively optimized to maximize the lift-to-drag ratio. The chord and pitch distributions of the propeller are also optimized using MIGA, focusing on maximizing efficiency while meeting thrust requirements. The optimization considers Reynolds number effects through iterative updates based on CFD and BEMT results. CST parameterization is used to define the airfoil shape, and each design iteration is validated against aerodynamic constraints. After each iteration, convergence is assessed by comparing efficiencies between iterations. If convergence is not achieved, the airfoil constraints are updated based on CFD data using the BEMT method, and the  
Figure 15: Efficiency curves of the propeller obtained from the optimization process described in [141]. The dashed line refers to the design point (V = 55 m/s, h = 16 km, Available power: 11–30 kW, D = 3, \(N_{b}\) = 3). process repeats until a final optimal solution with maximum efficiency is obtained. The optimal Gurney flap height was found to be between 1% and 2% of the chord, depending on airfoil geometry and operating Reynolds number. The CFD model used in this study was validated against wind tunnel data, showing agreement within 4% for thrust and surface pressure distributions, confirming its accuracy for low-Reynolds-number applications.t  
Figures 17 and 18 show the blades obtained from the optimization process and the corresponding efficiency results, comparing the optimized blade without a Gurney flap and the blade equipped with a Gurney flap, at an average Reynolds number of \(4\times 10^{4}\), supporting the reliability of the proposed design approach. As shown in Figure 18, the optimized propeller equipped with a Gurney flap consistently outperforms the configuration without the flap across a range of advance ratios. The maximum efficiency increases from approximately 80.2% to 82.0%, with a simultaneous reduction in power consumption. At low Reynolds numbers (\(10^{4}\) or less), provided that the three-dimensional separation bubble can be accurately predicted, the Gurney flap significantly enhances the lift coefficient of the airfoil with minimal drag penalty by effectively increasing camber and limiting the growth of laminar separation bubbles. This improvement leads to a higher ratio of lift to drag for the airfoil and consequently increases the overall propeller efficiency. Furthermore, the aerodynamic performances of the two propellers under higher Reynolds numbers have been calculated in the study. However, as the Reynolds number increases, the efficiency gains from the Gurney flap diminish and become negligible at Reynolds numbers above approximately \(1.4\times 10^{5}\) (Figure 19). This behavior occurs because laminar separation bubbles, which the Gurney flap helps control, naturally decrease with increasing Reynolds numbers, reducing their adverse effects.