## 6 Experimental Methods for Evaluating HAPS Propeller Performance
The scaled mobile testing system was validated through wind tunnel experiments involving a 1.0 m standard propeller in the NF-3 low-speed facility at Northwestern Polytechnical University (12 m \(\times\) 3.5 m \(\times\) 2.5 m test section), operating at 1500-3500 rpm and wind speeds up to 10 m/s. Aerodynamic loads were measured using a six-component strain gauge balance. Results from the wind tunnel closely matched those from the scaled mobile tests, with thrust and torque errors below 6%, attributed to the controlled environment and reduced vibration levels. Following validation, the full-scale 6.8 m propeller was tested with the full-scale propeller testing system at altitudes of 0.5 km and 3.6 km to obtain its performances at low altitudes. To replicate its performance at 20 km altitude, a geometrically scaled model was tested at 4 km, under similitude conditions, with the scaled propeller testing system. Specifically, the scaled test was conducted using a propeller with a diameter of 0.78 m, at an airspeed of 22 m/s and a rotational speed of approximately 4900 rpm. These values were selected to match the advance ratio, Reynolds number, and Mach number of the full-scale propeller operating at high altitude. The obtained performance has been compared with those obtained by CFD simulations. The comparison shows that, although the measured thrust, power coefficient, and efficiency are slightly lower than the predicted values, the overall trends are consistent. At the design point, the measured efficiency was approximately 3% lower than that estimated by CFD (Figure 22). These findings confirm that, despite a moderate degree of accuracy, the proposed testing method is a cost-effective and sufficiently reliable alternative for the aerodynamic evaluation of high-altitude propellers. As described in the previous work, predictions of full-scale propeller performance commonly rely on model-scale experiments. While flow around full-scale propellers is generally assumed to be fully turbulent, different flow regimes--including laminar, transitional, and turbulent--may coexist at model scale [153]. Additionally, flow separation that does not occur at full scale can arise at model scale. Complementing experimental tests, advances in high-performance computing enable increasing use of RANS solvers for performance prediction and scale-effect quantification. Use of turbulence models capable of simulating laminar-to-turbulent transition is critical, with several such models having been proposed in the literature [154,155]. Given the scarcity of experimental and flight data and the complexity of modeling low Reynolds number flows, Ref. [104] employs the PCE to assess performance uncertainty of high-altitude propellers. This study quantifies overall uncertainty considering both epistemic and aleatoric sources, applying PCE to two propeller flow modeling approaches: BEMT and three-dimensional RANS with the \(\gamma\)-\(Re_{\theta}\) transition model. Multipoint uncertainty quantification (UQ) analyses were conducted on two benchmark propeller geometries across operating conditions with available experimental data. For BEMT, uncertainty bounds encompassed experimental data for two distinct propellers operating at medium to low Reynolds numbers over a broad range of advance ratios. However, at high altitudes, these uncertainty bounds widened excessively, limiting  
Figure 22: Comparison of \(\eta\) versus \(J\) from CFD and Wind Tunnel measurements, \(Re=3.5\times 10^{5}\). predictive accuracy particularly at the highest advance ratios. Conversely, 3D RANS-based UQ yielded well-defined uncertainty bounds consistently containing experimental values. Predictions at high altitudes showed low standard deviation. Sensitivity analysis identified freestream velocity and the structure parameter \(\alpha_{1}\) as the most influential factors. Consequently, future UQ efforts using 3D RANS may focus primarily on these variables, enabling substantial computational cost reductions.