## 7 Experimental Data and Model Validation
### Residual Analysis of the Lift and Drag Forces  
The observed and predicted lift and drag quantities were very close, as shown in the residual errors in Table 10. As mentioned in the ASME validation guidelines, a simulated CFD model should be able to predict up to 85% of the experimental output, with less than 5% error [44]. This means that for this project with 29 simulation and wind tunnel tests (Table 9), the validation guidelines require (29 \(\times\) 85% = 24.6) that at least 24 simulations results have 5% or less difference (error) with the experimental data.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & \multicolumn{2}{c}{**Flow Conditions**} \\ \hline Velocity Flow (m/s) & & 30.1 \\ Density air (kg/m\({}^{3}\)) & & 1.225 \\ Temperature (\({}^{\circ}\)C) & & 22 \\ \hline \multicolumn{3}{c}{Wing structure} \\ \hline Wingspan (m) & & 0.495 \\ Wing chord (m) & & 0.455 \\ Wing surface (m\({}^{2}\)) & & 0.2252 \\ \hline \multicolumn{3}{c}{Experimental data} \\ \hline Lift force (N) = & 1.942 \\ Drag force (N) = & 0.644 \\ \(C_{l}=\) & & 0.022869 \\ \(C_{d}=\) & & 0.007584 \\ \(\overline{D}=\) & & 3.02 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Aerodynamic parameters of the S45 reference wing.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Adaptive Wing Surfaces**} & \multicolumn{2}{c}{**Experimental**} & \multicolumn{2}{c}{**Simulation**} \\ \cline{2-7}
**Test** & \begin{tabular}{c} **Leading Edge** \\ **(Degrees)** \\ \end{tabular} & \begin{tabular}{c} **Trailing Edge** \\ **(Degrees)** \\ \end{tabular} & \
\begin{tabular}{c} **Wind Tunnel** \\ **Lexp (N)** \\ \end{tabular} &
\begin{tabular}{c} **CFD Model** \\ **Lexp (N)** \\ \end{tabular} \\ \hline
1 & 0 & 0 & 1.942 & \(-\)0.644 & 1.5885 & \(-\)0.6457 \\
2 & \(-\)5 & 0 & 1.839 & \(-\)0.67 & 1.4504 & \(-\)0.6637 \\
3 & \(-\)10 & 0 & 1.676 & \(-\)0.736 & 1.3584 & \(-\)0.6817 \\
4 & \(-\)15 & 0 & 1.484 & \(-\)0.84 & 1.2723 & \(-\)0.7870 \\
5 & \(-\)20 & 0 & 1.359 & \(-\)0.865 & 1.1917 & \(-\)0.8960 \\
6 & 5 & 0 & 2.011 & \(-\)0.618 & 1.7083 & \(-\)0.5690 \\
7 & 10 & 0 & 2.197 & \(-\)0.678 & 1.8239 & \(-\)0.5510 \\
8 & 15 & 0 & 2.254 & \(-\)0.713 & 1.9474 & \(-\)0.7460 \\
9 & 20 & 0 & 2.26 & \(-\)0.729 & 2.0792 & \(-\)0.7750 \\
10 & 0 & \(-\)5 & 2.293 & \(-\)0.701 & 2.0833 & \(-\)0.4341 \\
11 & 0 & \(-\)10 & 2.769 & \(-\)0.759 & 2.5740 & \(-\)0.5186 \\
12 & 0 & \(-\)15 & 3.506 & \(-\)0.908 & 3.0948 & \(-\)0.6004 \\
13 & 0 & \(-\)20 & 4.199 & \(-\)1.046 & 3.6680 & \(-\)0.6780 \\
14 & 0 & \(-\)25 & 4.784 & \(-\)1.135 & 4.3163 &The residuals of the lift and drag forces are defined as the differences between the observed values during the wind tunnel tests and the estimated values by the CFD simulation. Mathematically, the residual r of a specific value is the difference between the observed response value y and the predicted response value y. The residuals should be scattered randomly and centered on zero throughout the range of the fitted values. The non-random pattern in the residuals indicates a calibration error or a bias during the experimental tests or an inadequate model. The Fluent simulation accurately captures the interaction of the adaptive wing model with the fluid, as shown in the values of the residuals in Table 10.  
The residuals for the lift and drag forces appear to be random and distributed above and below the 0 error values, respectively. The differences between the experimental and the predicted values are independent and normally distributed, following a normal law with a mean value equal to zero and a very low variance. The residual values were calculated from the values shown in Table 10. The sum of the residuals shows that they are symmetric around the \"zero\" value.