# Effects of Aft-Body Extension Design on the Fundamental Characteristics of HWB Civil Aircraft
## 2 MDO Optimization Platform
### Weight Module  
The weight module is a key part of the multidisciplinary optimization design, which will be used to estimate the mass of the configuration and its distribution and, thus, determine important parameters such as center of mass and moment of inertia, the results of which will also affect the static stability margin. The total mass of the aircraft includes the mass of several major components, including the structural mass, propulsion system, fixed airborne equipment, landing gear, fuel, crew, and cargo. The location of the center of mass of the entire aircraft is derived by combining the masses of the above major components and their locations.  
The total mass of the aircraft is calculated by the following regression equation:  
\[M_{t}=M_{cabin}+M_{aft}+D_{o}+M_{V}+Mr+M_{cqui}+M_{prop}+M_{lg}+M_{load}+M_{ cargo}, \tag{1}\]  
The first five items on the right hand of the above equation are the structural masses of the whole aircraft, specifically the mass of the cabin part of the center body, the mass of the aft-body of the central fuselage, the mass of covers and webs, and the mass of ribs of the outer wing, which will change with the different parameters of the planform; the subsequent items are the items corresponding to the propulsion system, fixed airborne equipment, landing gear, fuel, crew, and cargo, which are set as constant values in the calculation. However, the positions of these parts have an influence on the calculation of the rotational inertia and the position of the center of mass of the entire aircraft.  
The structural mass corresponding to the central body is divided into two parts, namely the cabin part and rear part, for which the mass calculation method of these two parts is given in the literature [22].  
The two terms corresponding to the structural mass of the outer wing and transition part can be estimated by a method based on empirical equations, which is similar to the estimation methods of traditional wing [23]. Moreover, the masses of covers and webs in outer wing and transition part are as follows:  
\[D_{o}=0.85[\overline{N}M_{T}b^{3}r_{o}e_{o}\;\text{sec}\;\varphi_{o}\;\text{sec }\;\varphi_{o}\;\text{sec}\;\gamma_{o}y_{k}^{A}(1+0.375y_{k})]^{1/2}\times \left(\frac{S_{o}^{\prime}}{S_{o}}\right)\left(\frac{\rho_{o}\overline{T}}{A} \right)\left(\frac{c_{k}}{\tau_{k}}\right)_{o}^{0.25}\times 10^{-5}\text{kg}, \tag{2}\]  
Furthermore, \(\overline{f_{a}}\) is the ratio of allowable stress in the kink station between the transition part and center body to the allowable stress of the structural material:  
Figure 3: Internal layout of the HWB aircraft.  
\[\overline{f_{a}}=\frac{(f_{a})_{k}}{(f_{a})_{limit}}, \tag{3}\]  
\[(f_{a})_{k}=\overline{A}[0.727\overline{N}M_{T}A_{o}r_{o}(1+\lambda_{o})\mathbf{ s}\rho_{o}s\gamma_{o}y_{k}^{2}\times\frac{(1+0.375y_{k})}{e_{o}(c_{k}\tau_{k})_{o}^{1.5}}] ^{1/2}, \tag{4}\]  
The mass of the rib structure in the outer wing and transition part is calculated as follows:  
\[M_{r}=4.4S_{o}e_{o}(c_{k}\tau_{k})_{o}^{1/2}(1+0.35\lambda_{o})\rho_{o}\ \times 10^{-3} \text{kg}, \tag{5}\]  
As for the mass of the V-tail, the calculation can refer to the following equation:  
\[M_{V}=0.1V_{D}\mathbb{S}_{V}^{1,15}\text{kg} \tag{6}\]  
where \(V_{D}\) is the aircraft design speed and \(S_{V}\) is the wing area of the V-tail.  
The coordinates of the center of mass of each major mass part are varied with the value of the planform geometric parameters, and the distribution of the main mass part is shown in the Figure 4. Based on the mass of each main part and its position, the total mass and moment of inertia, as well as the position of the center of mass of the entire aircraft, can be derived.