# Validation of a Wind Tunnel Propeller Dynamometer for Group 2 Unmanned Aircraft
## Appendix A Propeller Modelling
### Propeller Geometry  
The blade element model requires a geometric description of the propeller geometry to specify the twist distribution and airfoil profile along the length of the blade. Beta is the measured geometric pitch angle between the chord line and fixed plane of rotation. The tables below capture the inputs to the BEM code used to generate the theoretical data in Figures 11-14. As documented in the narrative, since the vast majority of the propeller blade was reported to feature the NACA 4412 cross-section, the BEM results for all radial stations used airfoil data from this profile at the appropriate Reynolds number. \begin{table}
\begin{tabular}{c c c} \hline \hline
**r/R** & **c/R** & **Beta** \\ \hline  
\hline \end{tabular}
\end{table} 
Table 2: APC 16 \(\times\) 12 propeller geometry. \begin{table}
\begin{tabular}{c c c} \hline
**r/R** & **c/R** & **Beta** \\ \hline
0.10 & 0.166 & 25.85 \\ \hline
0.15 & 0.160 & 31.05 \\ \hline
0.21 & 0.164 & 36.02 \\ \hline
0.26 & 0.168 & 41.86 \\ \hline
0.32 & 0.161 & 39.68 \\ \hline
0.37 & 0.154 & 36.01 \\ \hline
0.43 & 0.145 & 33.35 \\ \hline
0.49 & 0.137 & 31.61 \\ \hline
0.54 & 0.127 & 29.28 \\ \hline
0.60 & 0.117 & 27.61 \\ \hline
0.65 & 0.105 & 25.28 \\ \hline
0.71 & 0.094 & 23.91 \\ \hline
0.76 & 0.081 & 21.55 \\ \hline
0.82 & 0.071 & 19.34 \\ \hline
0.87 & 0.058 & 19.07 \\ \hline
0.93 & 0.045 & 16.94 \\ \hline \end{tabular}
\end{table} 
Table 4: APC 18 \(\times\) 12 propeller geometry. \begin{table}
\begin{tabular}{c c c c c} \hline
**Speed (ft/s)** & **RPM** & **Prop Power (ft-lb/s)** & **Thrust (lb)** & **Torque (ft-lb)** \\ \hline
25 & 1517 & 3.3576 & 0.0123 & 0.0211 \\ \hline
25 & 2536 & 32.8465 & 0.8271 & 0.1237 \\ \hline
25 & 3514 & 94.5394 & 2  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Speed (ft/s)** & **RPM** & **Prop Power (ft-lb/s)** & **Thrust (lb)** & **Torque (ft-lb)** \\ \hline
25 & 1493 & 1.7466 & \(-\)0.0729 & 0.0112 \\ \hline
25 & 2502 & 38.1768 & 0.7454 & 0.1457 \\ \hline
25 & 355 \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Speed (ft/s)** & **RPM** & **Prop Power (ft-lb/s)** & **Thrust (lb)** & **Torque (ft-lb)** \\ \hline
45 & 2540 & 7.0606 & \(-\)0.3134 & 0.0265 \\ \hline
45 & 3550 & 103.2212 & 1.4735 & 0.2777 \\ \hline
45 & 4531 & 282.4474 & 4.1983 & 0.5953 \\ \hline
45 & 5533 & 553.6882 & 7.4286 & 0.9556 \\ \hline
50 & 1958 & \(-\)11.9256 & \(-\)0.8949 & \(-\)0.0582 \\ \hline
50 & 2599 & \(-\)0.6172 & \(-\)0.5372 & \(-\)0.0023 \\ \hline
50 & 3614 & 97.6277 & 1.1733 & 0.2580 \\ \hline
50 & 4538 & 289.6495 & 4.0235 & 0.6095 \\ \hline
50 & 5491 & 547.6228 & 6.9882 & 0.9523 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: _Cont._  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Speed (ft/s)** & **RPM** & **Prop Power (ft-lb/s)** & **Thrust (lb)** & **Torque (ft-lb)** \\ \hline
25 & 1465 & 3.2814 & \(-\)0.0176 & 0.0214 \\ \hline
25 & \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**J** & **Cp** & **Cq** & **Ct** & **eta** \\ \hline
0.6378 & 0.0353 & 0.0056 & 0.0263 & 0.4745 \\ \hline
0.3992 & 0.0479 & 0.0076 & 0.0670 & 0.5577 \\ \hline
0.2865 & 0.0519 & 0.0083 & 0.0944 & 0.5210 \\ \hline
0.2208 & 0.0476 & 0.0076 & 0.0932 & 0.4323 \\ \hline
0.1788 & 0.0462 & 0.0074 & 0.0949 & 0.3673 \\ \hline
0.7752 & 0.0266 & 0.0042 & 0.0128 & 0.3715 \\ \hline
0.4704 & 0.0506 & 0.0081 & 0.0669 & 0.6213 \\ \hline
0.3344 & 0.0512 & 0.0081 & 0.0881 & 0.5756 \\ \hline
0.2617 & 0.0511 & 0.0081 & 0.0970 & 0.4966 \\ \hline
0.2135 & 0.0479 & 0.0076 & 0.0955 & 0.4256 \\ \hline
0.9284 & 0.0149 & 0.0024 & \(-\)0.0062 & \(-\)0.3863 \\ \hline
0.5567 & 0.0420 & 0.0067 & 0.0468 & 0.6202 \\ \hline
0.3890 & 0.0528 & 0.0084 & 0.0854 & 0.6296 \\ \hline
0.3095 & 0.0514 & 0.0082 & 0.0926 & 0.5572 \\ \hline \hline \end{tabular}
\end{table} 
Table 15: APC \(18\times 14\) propeller wind tunnel processed data.