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<p>Biologists have calculated the allometric growth patterns of birds in terms of morphological and motion parameters, expressing the five parameters of wingspan, wing area, cruising speed, flapping frequency, and flight power as power functions of weight. Aviation designers utilize this formula to derive the initial values of the morphological and motion parameters of Flapping Wing Air Vehicles (FWAV), a process we refer to as the traditional scaling method. Traditional avian scaling laws establish power-exponential relationships between body weight and key flight parameters, guiding bionic aircraft design. However, limitations persist in their direct application to FWAVs. This study proposes an enhanced scaling law methodology addressing four critical aspects: (1) Introducing a weight correction coefficient to map avian flight functionality specifically to FWAVs design requirements, isolating flight-related mass from total avian mass associated with broader biological activities. (2) Rectifying the frequency formula by incorporating wing length-frequency statistics and integrating flapping amplitude via the Strouhal number definition, comprehensively representing motion parameters through periodic average angular velocity. (3) Refitting scaling law parameters using morphological data from specific bionic objects (e.g., pigeons, eagles) to reduce parameter scatter inherent in traditional laws derived from birds spanning grams to kilograms with divergent morphologies. (4) Validating the method through the design and testing of a pigeon-inspired FWAV prototype. Experimental results demonstrate that parameters estimated via the improved method align closely with the optimized aircraft’s performance, achieving an endurance of 185&#xa0;min on a single charge. This approach significantly reduces intermediate optimization needs, enhances design rationality, and provides a novel pathway for efficient FWAV development.</p>

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Improved Scaling Law for Bio-inspired Flapping Wing Air Vehicles

  • 期刊论文

  • 发表日期：

    2026年2月26日

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  • Liu Liu,
  • Bifeng Song,
  • Xiaru Liu,
  • Dong Xue,
  • Jianlin Xuan,
  • Yugang Zhang

摘要

Biologists have calculated the allometric growth patterns of birds in terms of morphological and motion parameters, expressing the five parameters of wingspan, wing area, cruising speed, flapping frequency, and flight power as power functions of weight. Aviation designers utilize this formula to derive the initial values of the morphological and motion parameters of Flapping Wing Air Vehicles (FWAV), a process we refer to as the traditional scaling method. Traditional avian scaling laws establish power-exponential relationships between body weight and key flight parameters, guiding bionic aircraft design. However, limitations persist in their direct application to FWAVs. This study proposes an enhanced scaling law methodology addressing four critical aspects: (1) Introducing a weight correction coefficient to map avian flight functionality specifically to FWAVs design requirements, isolating flight-related mass from total avian mass associated with broader biological activities. (2) Rectifying the frequency formula by incorporating wing length-frequency statistics and integrating flapping amplitude via the Strouhal number definition, comprehensively representing motion parameters through periodic average angular velocity. (3) Refitting scaling law parameters using morphological data from specific bionic objects (e.g., pigeons, eagles) to reduce parameter scatter inherent in traditional laws derived from birds spanning grams to kilograms with divergent morphologies. (4) Validating the method through the design and testing of a pigeon-inspired FWAV prototype. Experimental results demonstrate that parameters estimated via the improved method align closely with the optimized aircraft’s performance, achieving an endurance of 185 min on a single charge. This approach significantly reduces intermediate optimization needs, enhances design rationality, and provides a novel pathway for efficient FWAV development.