# Short Landing for Flying-Wing Unmanned Aircraft with Thrust Vector
## 3 Short-Landing Performance Analysis
### Attainable Linear and Pitch Angular Acceleration
In contrast, the throttle shows a positive correlation with tangential acceleration, which gradually weakens as the velocity decreases in Figure 10b. The nozzle pitch angle and throttle both exhibit a negative correlation with the normal acceleration in Figure 10c,d. The sink rate significantly affects the control efficiency for normal acceleration when using the nozzle pitch angle. The throttle shows better control for normal acceleration than the nozzle pitch angle. Overall, for better control effectiveness, it is preferable to use the throttle to control \(V_{gz}\) and the nozzle pitch angle to control \(V_{gx}\), despite the control coupling phenomenon between the two. Equation (13) allows the acceleration control matrix to be calculated from trimmed results at different velocities and angles of attack. The attainable acceleration set (AAS) area can be evaluated from this matrix. The AAS area decreases with increasing trimmed velocity and increases with decreasing absolute sink rate, as shown in Figure 11a. In Figure 11b, the AAS area and attainable pitch angular acceleration (APAA) are compared, and they move in opposite directions as velocity increases. The equilibrium point, where the normalized AAS and APAA curves intersect, is shown in Figure 11c for different sink rates. The equilibrium points are calculated at various angles of attack and sink rates in Figure 11d, Figure 12a shows the AAS area [32] for a single trimmed point, with the throttle ranging from \(-10\%\) to \(10\%\) and nozzle pitch angle from \(-10\) to \(10\) degrees at an angle of attack of \(6\) degrees, and their mean velocity is presented in Figure 12b with an error bar. The equilibrium curve between the velocity and angle of attack provides the appropriate control command value for flight safety. Therefore, landing at the angle of attack and speed in Figure 12b maximizes the maneuvering margin during landing. For flight safety during short landings, Figure 12b indicates an entering speed of \(45\) m/s in level flight condition with the nozzle pitch angle down approximately \(45\) degrees, as illustrated in Figure 13a. The lift fan should be set at \(20\%\), as shown in Figure 13b. For continuous approaches, the recommended command values are a velocity of \(35\) m/s and angle of attack of \(6\) degrees, accounting for aerodynamic control effectiveness requirements for disturbance rejection. Figure 10: Control input matrix for acceleration (angle of attack \(\alpha=4\) deg); the gray area is the continuous error bar for various sink rates (\(0\)–\(-4\)m/s): (a) \(G_{11}\), (b) \(G_{12}\), (c) \(G_{21}\), and (d) \(G_{22}\). Figure 11: AAS and AMS calculation for short landing (angle of attack = 6 deg): (**a**) AAS area results, (**b**) AAS area and AMS results, (**c**) normalized AAS area and AMS results, and (**d**) equilibrium points for different sink rates. Figure 12: AAS area and equilibrium points curve: (**a**) AAS area (angle of attack = 6 deg, sink rate = \(-1\) m/s, and velocity = 35 m/s) and (**b**) equilibrium points curve.