Abstract
This paper is concerned with optimal flight trajectories in the presence of windshear. The abort landing problem is considered with reference to flight in a vertical plane. It is assumed that, upon sensing that the airplane is in a windshear, the pilot increases the power setting at a constant time rate until maximum power setting is reached; afterward, the power setting is held constant. Hence, the only control is the angle of attack. Inequality constraints are imposed on both the angle of attack and its time derivative.
The performance index being minimized is the peak value of the altitude drop. The resulting optimization problem is a minimax problem or Chebyshev problem of optimal control, which can be converted into a Bolza problem through suitable transformations. The Bolza problem is then solved employing the dual sequential gradient-restoration algorithm (DSGRA) for optimal control problems. Numerical results are obtained for several combinations of windshear intensities, initial altitudes, and power setting rates.
For strong-to-severe windshears, the following conclusions are reached: (i) the optimal trajectory includes three branches: a descending flight branch, followed by a nearly horizontal flight branch, followed by an ascending flight branch after the aircraft has passed through the shear region; (ii) along an optimal trajectory, the point of minimum velocity is reached at about the time when the shear ends; (iii) the peak altitude drop depends on the windshear intensity, the initial altitude, and the power setting rate; it increases as the windshear intensity increases and the initial altitude increases; and it decreases as the power setting rate increases; (iv) the peak altitude drop of the optimal abort landing trajectory is less than the peak altitude drop of comparison trajectories, for example, the constant pitch guidance trajectory and the maximum angle of attack guidance trajectory; (v) the survival capability of the optimal abort landing trajectory in a severe windshear is superior to that of comparison trajectories, for example, the constant pitch guidance trajectory and the maximum angle of attack guidance trajectory.
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Portions of this paper were presented at the IFAC 10th World Congress, Munich, Germany, July 27–31, 1987 (Paper No. IFAC-87-9221).
This research was supported by NASA Langley Research Center, Grant No. NAG-1-516, by Boeing Commercial Airplane Company (BCAC), and by Air Line Pilots Association (ALPA). Discussions with Dr. R. L. Bowles (NASA-LRC) and Mr. C. R. Higgins (BCAC) are acknowledged.
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Miele, A., Wang, T., Tzeng, C.Y. et al. Optimal abort landing trajectories in the presence of windshear. J Optim Theory Appl 55, 165–202 (1987). https://doi.org/10.1007/BF00939080
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DOI: https://doi.org/10.1007/BF00939080