Optimization and Guidance of Penetration Landing Trajectories in a Windshear

This paper is concerned with the optimization and guidance of penetration landing trajectories in a windshear. It is assumed that the aircraft is controlled by means of the angle of attack and the power setting. For the optimal trajectory, the performance index being minimized measures the deviation of the flight trajectory from the nominal trajectory. In turn, the nominal trajectory includes two parts: the approach part (nominal glide slope constant) and the flare part (nominal glide slope varying linearly with the horizontal distance). The final conditions are these: (i) the touchdown path inclination is specified; (ii) the touchdown velocity is to be in a specified range; and (iii) the touchdown distance is to be in a specified range. The numerical results show that the optimal trajectory deviates somewhat from the nominial trajectory in the shear region; the deviation increases as the windshear intensity increases; however, the optimal trajectory recovers gradually the nominal trajectory in the aftershear region. In addition, the point of minimum velocity occurs at the end of the shear. A guidance scheme is developed so as to approximate the optimal trajectory. In the guidance scheme, the angle of attack is determined by the windshear intensity, the absolute path inclination, and the glide slope angle, while the power setting is determined by the windshear intensity and the velocity. Numerical results indicate that the guidance trajectory is close to the optimal trajectory.