Optimal Trajectories for Tiltrotor Aircraft in Total Power Failure

This paper investigates optimal tiltrotor flight paths in the event of a total power failure. A longitudinal rigid body model is used which has as state variables; aircraft position, body components of aircraft velocity, pitch angle and rate, and rotor angular speed. The control variables are the thrust coefficient of one rotor and the pilot’s longitudinal stick displacement. Aerodynamic data of the XV-15 are interpolated with smooth functions and are used in trajectory optimization. Path constraints are imposed on the control variables and the rotor speed, and the forward speed is kept positive. Optimal control problems are formulated for flights after total power failure to minimize a combination of the horizontal and vertical speeds at touchdown. Numerical solutions are obtained. Optimal flight paths can achieve small vertical impact speeds at touchdown by properly managing and distributing aircraft potential, kinetic, and rotor rotational energies. Results indicate that with sufficient initial speeds, aircraft can make safe landings after total power failure. Effects of initial aircraft height, horizontal speed, and rotor speed, as well as aircraft weight and rotor inertia are examined. Higher initial energy, lower gross weight, and/or higher rotor inertia all result in smaller impact speeds at touchdown. In addition, optimal control problems are formulated to determine points on the boundaries of a Height-Velocity diagram. The H-V diagram determined in the paper resembles that for a conventional helicopter. Results and methods presented in this paper can be used to provide guidelines for flight tests and to aid the design of tiltrotor aircraft.