# Effects of Aft-Body Extension Design on the Fundamental Characteristics of HWB Civil Aircraft
## 4 Characteristics Evaluation
### Basic Takeoff and Landing Performance Analysis  
#### 4.2.1 Takeoff Performance Analysis  
The basic takeoff performance of these four aircraft configurations was evaluated based on two parameters: the rotary speed and the takeoff field length. The calculation of rotary speed and takeoff glide distance for HWB aircraft is based on the following three conditions: First, the HWB aircraft accelerates to the rotary speed in the ground state, and at this speed, the aircraft can generate the specified angular acceleration by deflecting the elevons within a limited angular range. Second, after the rotation, the pitch moment of the aircraft is balanced with a slight restoration of control surface, so that the aircraft can be stabilized in a suitable takeoff attitude. Third, based on the takeoff attitude calculated by the second condition and takeoff speed (takeoff speed is about 1.1 times of rotary speed), the lift generated by the aircraft can offset the gravity to achieve the off-ground action. When calculating the rotary speed and takeoff glide distance, care should be taken to keep the deflection angle of the elevons within a reasonable range to avoid excessive deflection. This is mainly due to two considerations. On the one hand, it is a common problem for every aircraft when lifting the nose; that is, too much deflection will increase the restoration of control surface after leaving the ground, which will cause drastic changes in attitude of aircraft and deteriorate the controller quality. Another aspect is the unique problem of HWB aircraft. Since the lift surface and control surface of the HWB are highly integrated, a large control surface deflection will lead to a serious loss of lift, which will make the takeoff attack angle too large and affect the normal takeoff of the aircraft. From the comprehensive view of the literature, the upper limit of elevon deflection angle is set here to \(\pm 15^{\circ}\) when rotating the HWB aircraft. The elevon deflection angle is deflected to the upper limit, and then the rotary speed is derived by the Equation (9), which requires that the pitch aerodynamic moment generated by the elevon deflection at this speed be sufficient to lift the nose of the aircraft and produce the specified instantaneous angular acceleration:  
\[I_{y}\ddot{\theta}=qS\big{[}cC_{m}(\alpha,\delta_{e})+C_{L}(\alpha,\delta_{e} )\big{(}x+fy_{g}\big{)}\big{]}-\big{(}G-Tsin\alpha\big{)}\big{(}x+fy_{g}\big{)} -Ty_{p} \tag{9}\]  
where \(\ddot{\theta}\) is the angular acceleration generated by the pitch moment of the whole aircraft at the instant of rotation; \(\ddot{\theta}\) is set to \(3^{\circ}/s^{2}\) according to the general rule of rotation for blended wing-body aircraft [28]. Moreover, \(x\) is the horizontal distance from the aircraft's center of gravity to the wheel axis of main landing gear. This value can be calculated by the weight ratio carried by the main landing gear and front landing gear (in this paper this \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Aircraft Configuration** & **OPT1** & **OPT2** & **OPT3** & **OPT4** \\ \hline MTOW, kg & 209,664 & 210,798 & 211,495 & 213,406 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: MTOWs of four HWB configurations. ratio is set to 9:1) and the position of the center of gravity. Furthermore, \(f\) is the rolling friction coefficient of the wheel of the main landing gear and \(y_{g}\) is the plumb distance from the center of gravity to the ground. Based on the already derived rotary speed, a rough estimate of the gliding distance required for the entire takeoff process can be obtained. The takeoff performance calculation results for the four configurations within the configuration family are shown in Figure 11, in addition to the takeoff data for the B777 in the same class of civil aircraft for comparison. The blue bars in the figure indicate the rotary speed, and the gray bars indicate the gliding distance.