Interest grows rapidly in electric and hybrid electric aircraft. To determine the optimal performance and energy management required with such novel powertrain configurations, a knowledge-based aircraft and powertrain performance model is developed. The model is then used to set up an optimal control problem, which is transcribed to a non-linear programming problem using global orthogonal Legendre-Gauss-Radau collocation for single phase problems, and Hermite-Simpson local collocation for multiphase problems. The solution to the control problem allows identification of the best control strategies and energy management strategies. A case study is performed on the HY4 hybrid fuel cell aircraft and the hybrid electric Pipistrel Panthera. Solutions show that for best fuel economy, flying at a minimum drag airspeed, and keeping a constant power setting, proved more important than the choice of altitude. This was more noticeable for the HY4, with its relatively low power available and good aerodynamic properties following from its glider-based airframe.
The Fuel-optimal energy management strategies proved identical for both aircraft investigated. Batteries are used to provide a power boost during takeoff, after which batteries are discharged gradually throughout the remainder of the flight to maximize discharge efficiency. The engine or fuel cell are kept at approximately constant cruise power settings throughout the flight. The Panthera showed
consistent flight profiles with increasing range. For the HY4, however, achieved airspeeds reduced with increasing range, and additional measures were required to force a climb to non-zero altitudes due to its under-powered nature. The fuel-optimal trajectories offered an average of 10-15% of possible fuel
savings, depending mostly on the size of the onboard batteries. Fuel savings increased significantly at low ranges300km, where the contributions of the batteries have more impact.
Comparing different transcription methods and problem setups, it was concluded that global orthogonal, or pseudo-spectral, methods like Legendre-gauss-Radau collocation are not only faster, but also more consistent compared to simpler direct collocation methods. However, if the problem complexity increases and the performance limits of the aircraft are pushed, switching to a simpler method like Hermite-Simpson collocation reduced the time required to find a solution, with negligible differences in the resulting trajectories. Opting for a multiphase problem set-up, essentially splitting the problem in a series of individual subproblems, appeared less advantageous. While offering more control over the trajectories, time required to find solutions increased drastically, and offered no additional insight into the best energy management strategies.