# Effects of Aft-Body Extension Design on the Fundamental Characteristics of HWB Civil Aircraft
## 3 Optimization Results  
As mentioned in Section 2, this paper intends to set different static stability margin constraints in the optimization calculation to obtain different degrees of aft-body extension  
\begin{table}
\begin{tabular}{c c c c c} \hline  & **Parameter** & **Ref.** & **Calculation** & \(\mathbf{\Delta}\)(\%) \\ \hline Weight Module & MTOW, kg & 150,846 & 155,510 & 3.1 \\ Aerodynamic & \(C_{L}\) & 0.2064 & 0.2083 & 0.9 \\ Module & \(C_{D}\) & 0.0082 & 0.0092 & 12.2 \\ Trim Module & AOA, degree & 2.7 & 2.99 & 10.7 \\ \hline \end{tabular}
\end{table}
Table 2: Weight, aerodynamics, and trim validation with SAX-40 [21].  
design of HWB planform based on the significant influence of static stability margin on the planform of HWB aircraft. Specifically, the static stability margins in the range of \(-\)0.1-0.2 are divided into four intervals, namely \(-\)0.1-0, 0-0.05, 0.05-0.1, and 0.1-0.2, and then these four intervals are applied as constraints to four optimization tasks. The results of the optimization calculation are shown in Figure 8. Moreover, Figure 8 includes the scatter plots of the four sets of optimization results; each set of results corresponds to a specific static stability margin constraint range, where the blue points form the pareto frontier of each set of optimization calculations, the red points indicate that the sample point does not satisfy the optimization constraints, and the black points indicate that the sample point satisfies all the optimization constraints.  
The pareto frontiers of the four sets of optimization results are extracted and placed in the same coordinate system, and the points corresponding to these four pareto frontiers at k = 23.5 (the red line shown in Figure 9 are chosen to form the configuration family, which is used as the basis for the subsequent analysis. The four configurations of configuration family were named OPT1-4 according to the ascending order of static margin, and the planform of the configuration family is shown in Figure 10. We selected configurations according to a fixed lift-drag ratio, rather than the aft-body length, based on the following consideration: A single value of aft-body length on the pareto frontier may correspond  
Figure 8: The optimization results under different static margin constraint.  
to multiple combinations of lift-drag ratio and weight and one combination may pareto dominate the other one, which made it difficult to choose a proper configuration from these combinations. So, we must determine the value of lift-drag ratio or weight before the choice of configuration for analysis. Considering that the lift-drag ratio is a more general parameter than weight, the data from other HWB designs can be used as a reference. At present, the cruise lift-drag ratio of HWB is generally between 22 and 24. [26; 27] Combined with the calculation results in this paper, the design lift-drag ratio is determined to be 23.5.  
Figure 10 shows that, for the HWB configuration, the smaller the longitudinal static stability margin, the more forward the outer wing moves, and the longer the aft-body length is. The fundamental reason for this phenomenon is that the aft-body extension design causes a larger shift of the center of mass backward compared to the aerodynamic center. This difference in offset distance results in lower static stability margins for con  
Figure 10: Planform of the configuration family.  
Figure 9: The pareto frontiers of the four optimization results.  
figurations with aft-body extensions and higher static stability margins for short fuselage configurations.