At specified Reynolds numbers Re=ρvc/μ=5×105, this study investigates the power-extraction regime of a flapping-foil turbine executing a figure-eight trajectory. This study thoroughly explored the impacts of trajectory shape, heave and pitch amplitudes, phase difference, and pitch axis location on the power-extraction regime of a flapping turbine. A figure-eight trajectory substantially bolsters the energy harvesting capacity, achieving a peak efficiency of up to 50%. This trajectory capitalizes on the energy generated from the drag encountered by the flapping foil, thereby marking a significant efficiency breakthrough. This could denote a considerable progression for flapping foils tailored for heave and pitch motions since the free stream can be optimally harnessed by the trajectory we have established. In scenarios where the flapping foil undergoes the same maximum effective angle of attack, a wake diffusion spectrum aligns with the Betz limit threshold. Crucially, the closeness to this efficiency frontier suggests a universal maximum effective angle of attack—a consistent law that remains valid for the conventional flapping turbine design. It implies that selections for stroke and pitch amplitudes should be methodical rather than arbitrary. In addition, the positioning of the pitch axis ought to be modified in tandem with phase difference adjustments to bolster the synchronization between heaving motions and resultant lift. The ideal phase difference is variable, contingent on pitch amplitude and pitch axis position. Even with low pitch amplitudes, fine-tuning the phase difference guarantees that the energy harvesting efficiency does not fall below 30%. Such an enhancement would significantly broaden the operational envelope and the parameter space for flapping turbines.

Large-slenderness-ratio (LSR) aircraft exhibit more severe lateral–directional coupling compared with other aircraft, which poses a significant challenge to their flight safety, especially during high-speed maneuvers. Reliable attitude decoupling control is, therefore, essential for LSR aircraft. In this study, a novel control framework that combines incremental nonlinear dynamic inversion (INDI) and extended state observer (ESO) is proposed for supersonic roll maneuver control of LSR aircraft. The ESO is used to estimate the angular acceleration on the basis of an onboard mathematical model. The acceleration estimator based on ESO achieves superior noise reduction compared with the complementary filter (CF) and reduces the onboard model requirement without significantly sacrificing estimation accuracy. Monte Carlo (MC) simulations and frequency–domain analysis demonstrate the effectiveness and robustness of the proposed controller. The sensitivity of parameter uncertainties is also investigated, revealing that the natural frequency of the actuator is the most critical parameter affecting robustness. Finally, flight tests validate the effectiveness of the proposed control structure.