## 4 Actuation System
### Finite Element Modeling of the Actuation System
5, the MLE is morphed to position S4, whereas the air speed and the AoA remain constant (Case S4 I in Table 3). The results shown in Table 3 show that the pressure load on the MLE is even higher for S4 than for S5 in that flight condition. Even though it is not intended to use aerofoil S4 at high AoA, this flight condition is included into the load cycle, because it is the most critical one. Not dimensioning for \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**No.** & **0** & **1** & **2** & **3** & **4** & **5** & **6** \\ \hline Geometry & Manu. & BL & S4 & S5 & S5 & S4 & S4 \\ Angle of Attack/\({}^{\circ}\) & 0 & 0 & 0 & 0 & 14.41 & 14.41 & 1 \\ True Air speed/(m/s) & 0 & 0 & 0 & 0 & 130.6 & 130.6 & 184.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Load conditions (steps) analysed in FE model. it would mean adding constraints to the acceptable flight envelope depending on the MLE position. * Case S5 IV (aerofoil S5 with low AoA and high true air speed) in Table 3 is not considered as a critical load case. The computed suction peak value is the highest one, but it occurs at the bottom, whereas the highest suction for all other cases occurs on the upper surface of the MLE. Section at the bottom for aerofoil S5 reduces forces on the actuation system because the aerodynamic pressure loads act in the same direction as the deformation enforced by the actuation system. * In step no. 6, aerofoil S4 is maintained, but the pressure loads are modified in order to correspond to cruise condition with reduced AoA and increased air speed. * A load cycle corresponding to one flight consists of steps no. 1 to 6 and then repeating the load conditions 5, 4, and 3 in reversed order. For each of the last three steps, a pressure distribution was derived by CFD analyses presented in Section 2.4. In between the load cases, pressure loads have been interpolated linearly over time. Between each load case, the linear actuator moves with constant piston velocity from one position to the next one. Hence, its stroke has also been interpolated linearly over time. The approximation of the target shapes is achieved with the proposed actuation system as computed with the FE model shown in Figure 16. While the actuation system positions the stringers exactly at the desired positions, the desired curvature of the aerofoil contour in between the stringers can only be met approximately by tailoring the local stiffness properties of the skin. The effect of the remaining deviation on aerodynamic performance is assessed using 2D CFD analysis. The results are depicted in Figure 17.  
For aerofoil S5 in high lift configuration, the lift coefficient of the achieved approximation is 0.2-0.8% higher than the lift coefficient of the target aerofoil, whereas the difference in drag is in the range between \(-1\%\) and +0.4%. For aerofoil S4, the comparison is made for the clean wing configuration (flaps retracted), because it is intended for flight in cruise condition. Here, larger relative deviations occur. For angles of attack between \(0^{\circ}\) and \(6^{\circ}\), which is typically the case for cruise condition, the drag coefficient is up to 1.3% lower than the drag coefficient of the target aerofoil, whereas the deviation in lift is in between \(-0.3\%\) and +1.1% in this interval. At other angles of attack, the relative deviation is higher, but regarding typical flight cycles, these conditions are of minor relevance. Figure 16: Achieved approximation of target shapes computed by FE model for load cases 4 and 5. The main purpose of the described FE model is the computation of the loads acting on the components of the actuation system.