# Helicopter Safe Landing Trajectory after Main Rotor Actuator Failures
## 5 Results and Discussion
Given the target landing longitudinal velocity of 15 m/s, if the collective pitch before the actuator failure falls in the range of the lower red line and the blue line, there will be a descending rate within 3 m/s at the specific forward speed. Figure 2: Safe landing trajectories at the initial speed of 20 m/s. The terminal time of each case is 48.0 s, 56.8 s, and 17.0 s, respectively. Meanwhile, in order to decelerate, given the same longitudinal cyclic pitch, the collective pitch is decreased for case 1, increased for case 2, and kept constant for case 3. Therefore, the steady forward landing speed of case 1 is highest among the three cases, followed by a lower landing forward speed of case 2, and the lowest landing forward speed of case 3. The above analysis agrees with the trajectory results shown in Figure 2.  
Three typical landing trajectories with different initial forward velocities and altitudes of all actuator failure cases are demonstrated in Figure 4, which are namely 15 m/s for the forward actuator failure in case 1, 44 m/s for the aft actuator failure in case 2 and 60 m/s for the lateral actuator failure in case 3. In case 1, the helicopter encounters the actuator failure at a very low altitude of 20 m. It is then accelerated to gain enough height before deceleration and descent. This shows a significant difference from the autorotation procedure, where the initial altitude is a key factor that determines whether the helicopter can be landed successfully. As for situations of actuator failures, the altitude can be adjusted by a slight adjustment of the longitudinal cyclic pitch. In case 3, the longitudinal cyclic pitch is carefully handled, and the helicopter goes through a procedure consisting of both ascending and descending. The helicopter eventually decreases to a safe velocity when it touches down. The maximum safe initial forward speed, which the algorithm can obtain after the aft actuator failure (case 2), is also demonstrated in Figure 4, represented by the red line. Figure 3: The characteristic “bucket profile” of the collective pitch of UH-60 during forward flight. Other safe boundaries of all the actuator failure cases are obtained by sweeps of speed from 5 m/s to 70 m/s. The results can be described as:  
The safe zones are reasonably different for different actuator failure cases. For the lateral actuator failure (case 3), the collective pitch is not affected by longitudinal manipulations. Thus, within the speed range of 25 m/s to 56 m/s, the position of the collective pitch is too low to sustain a low-speed flight. For the forward actuator failure (case 1), the deceleration from high speed leads to a considerable reduction in the collective pitch. Thus the safe zone is smaller compared to case 1. It is similar for the aft actuator failure (case 2); however, with an increase in collective pitch when decelerating, the safe zone has a wider low-speed boundary compared with case 1. Note that the boundaries of the safe forward speed closely depend on the safe landing requirements. Moreover, if the helicopter cannot touch down with wheel gears, which means a much smaller limitation of forward landing speed is required, there will be a significant reduction in the range of the above safe zones. Another difference lies in the specific control geometry of the helicopter. As shown in Section 2, the radius ratio and the  
Figure 4: Safe landing trajectories of various initial conditions. The terminal time of each case is 27.6 s, 11.9 s, and 55.4 s, respectively. distribution angle \(\gamma\) determine the influence on the collective pitch by the other two cyclic controls. Although due to the requirements of compactness of modern helicopters, the radius of the rotating ring and the non-rotating ring are similar, the above parameters should be determined accordingly.