# A Novel Aerodynamic Modeling Method Based on Data for Tiltrotor evtol
## 4 Results and Discussion
### Network Effect Verification  
Based on the analysis of dimensionless aerodynamic coefficients and their influencing factors in Section 2, it can be concluded that the rotor wake is the most significant aerodynamic characteristic affecting the transition phase of the XV15. This, in turn, affects the aerodynamic forces on other parts of the fuselage. The mathematical model report and wind tunnel test data of the XV15 tiltrotor aircraft support this conclusion. The tilt angle is the explanatory variable that has the greatest impact on the rotor wake. Therefore, wind tunnel test data under different tilt angle conditions were selected as the validation set to verify the network's predictive effect. The validation results compare wind tunnel data, results from the mathematical model established in the literature [9], and predictions from neural network models. The purpose is to illustrate the difference between data-driven modeling methods and models established using traditional physical formulas. Figures 6-8 present the predicted results for the selected transition conditions. Comparisons are made between traditional models and neural networks under different flap/aileron angle mode selection, Mach numbers, and elevator deflection angles. Figure 6 shows that the flap/aileron angle mode selection has a significant impact on the aerodynamic coefficient during the transition phase under low Mach number conditions. Increasing the angle of the flaps/ailerons to 40/25\({}^{\circ}\) results in a nearly 50% increase in the aerodynamic coefficient compared with the original. Figure 7 demonstrates that the impact of the Mach number on the aerodynamic coefficient is relatively small when it is low. The available wind tunnel test data only include the relationship between Mach number and aerodynamic coefficient. Furthermore, the tiltrotor evtol typically operates at low speeds or Mach numbers. Therefore, this article compares the aforementioned relationships. Figure 8 illustrates the impact of the elevator deflection angle on the lift coefficient and aircraft stall angle of attack. The results indicate that a 20\({}^{\circ}\) increase in elevator deflection angle leads to a 40% decrease in lift coefficient and a corresponding increase in the aircraft stall angle of attack. Figure 6: Relationship between angle of attack and selected flap/aileron angle with aerodynamic coefficient at a tilt angle of 0\({}^{\circ}\). (**a**) Drag coefficient. (**b**) Lift coefficient. (**c**) Pitch moment coefficient. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **MLP** \\ \hline Relative error & 1.314\% \\ \hline Coefficient of Determination & 0.9972 \\ \hline Total training time & 395.43 s \\ \hline \hline \end{tabular}
\end{table} 
Table 3: _Cont._It is evident that there is a significant discrepancy between the predicted data from the mathematical model and the wind tunnel data. The data-driven approach more accurately reflects the nonlinear aerodynamic characteristics during the transition phase, as indicated in the literature [19], which states that the mathematical model does not provide an accurate description of these rotor wake and stall phenomena. Table 4 displays the coefficient of determination R\({}^{2}\) and the relative error of the predicted data from the MLP neural network. The results indicate that the aerodynamic coefficient predicted by the network closely matches the wind tunnel data, with an error of approximately 2%. Meanwhile, the coefficient of determination for network prediction is close to 1, indicating that the model explains most of the variation in the dependent variable. In contrast, the prediction of aerodynamic coefficients based on mathematical models has an error of about 10%, and the accuracy of determining coefficients is relatively low. This level of accuracy meets the requirements for aerodynamic models reported in the literature literature. Figure 8: Relationship between angle of attack and angle of elevator deflection with aerodynamic coefficient at a tilt angle of 60\({}^{\circ}\).