Birds actively modulate unsteady aerodynamic forces through complex chordwise deformations during flapping to achieve superior lift and propulsion. However, the physical mechanisms underlying the influence of nonuniform chordwise deformation on aerodynamic force generation remain unclear. In this study, we construct a two-dimensional flexible flapping wing model based on the mid-span (50%) cross section of a pigeon wing, integrating coupled plunging, and pitching motions. A novel modeling approach utilizing controlled camber-line displacement is employed to continuously vary deformation distributions from leading-edge-dominated to trailing-edge-dominated deformation. Numerical simulations systematically evaluate how different deformation gradients and deformation amplitudes affect aerodynamic performance metrics, including lift, thrust, propulsive efficiency, and lift-to-power efficiency. Results reveal that nonuniform deformation significantly reshapes the camber distribution, altering local midline angles relative to the effective angle of attack, which influences the formation, evolution, and shedding of the leading-edge vortex. Additionally, camber-induced fluid acceleration modifies surface pressure distributions, thereby impacting aerodynamic force magnitudes and directions. Consequently, deformation-induced camber deformation profoundly redistributes aerodynamic forces, affecting overall performance. Specifically, leading-edge-dominated deformation enhances thrust and propulsive efficiency at larger deformations, while trailing-edge-dominated deformation is advantageous for lift generation at smaller amplitudes. A critical deformation amplitude optimizing propulsive efficiency is identified, emphasizing the necessity to tailor deformation distributions according to distinct flight objectives, such as enhanced lift or thrust production. The findings of this study enhance our understanding of the mechanisms through which nonuniform deformation modulates aerodynamic forces, thereby providing theoretical support and practical insight for the design and optimization of high-performance bio-inspired flapping wing systems.
Zheng et al. (2026) studied this question.