Scaling laws with hand-wing index and application to flapping-wing vehicle design

Bird-like flapping-wing aerial vehicles (BFAVs) emulate avian flight mechanisms and exhibit superior maneuverability, efficiency, and adaptability. Conventional scaling law models, typically based only on body mass or wing area, fail to capture the aerodynamic influence of the wing shape. This study integrates multi-source avian morphological datasets with additional wingbeat frequency samples to analyze the scaling relationship between wing morphology and flapping kinematics. The hand-wing index (HWI) is introduced as a morphological descriptor of wing shape. The results indicate that HWI could independently characterize wing shape. Distinct HWI distributions among the four wing types-elliptical, lift, soaring, and high-speed, demonstrate a strong link to flight strategy. An improved HWI-mass-area (HMA) model was developed for wingbeat frequency prediction, achieving higher accuracy and stronger biological interpretability than traditional allometric models. Based on this model, a 0.3 kg flapping-wing prototype with a lift-type wing (HWI = 32.4) was designed and fabricated, demonstrating the applicability of the model in bioinspired design. This study establishes a morphology-informed scaling framework bridging avian biomechanics and engineering, offering a quantitative foundation for parameterized BFAV design.