基于叶素原理的回旋镖运动轨迹规律研究

RESEARCH ON THE MOTION TRAJECTORY LAW OF BOOMERANGS BASED ON BLADE ELEMENT THEORY

  • 摘要: 回旋镖的“飞去来”特性源于低雷诺数下非定常气动力与刚体姿态动力学的耦合。本文基于准定常叶素原理,融合欧拉角姿态描述与牛顿–欧拉运动方程,构建了回旋镖简化动力学模型。借助“z–x–z”欧拉角旋转约定,建立坐标系转换关系,系统推导了升力、滚转力矩等关键气动力公式,分析了旋转气流周期性反转对气动特性的影响。通过 MATLAB 仿真获得不同初始速度和转速下的飞行轨迹,并利用参数可调发射装置与双高速摄像测量进行实验验证。本研究为回旋镖的结构优化与运动预测提供了理论支撑,同时有助于理解低雷诺数下旋转刚体气动力与姿态运动的耦合机制,并可为相关飞行器的设计与控制提供一定参考。

     

    Abstract: The “return-to-origin" characteristic of a boomerang arises from the coupling between unsteady aerodynamic forces and rigid-body attitude dynamics at low Reynolds numbers. Based on the quasi-steady blade element theory, a simplified dynamic model of the boomerang is developed by integrating the Euler-angle attitude description with the Newton–Euler equations of motion. Using the z–x–z Euler-angle rotation convention, the coordinate transformation relationships are established, and key aerodynamic formulas, including those for lift and rolling moment, are systematically derived; the effect of periodic airflow reversal induced by rotation on the aerodynamic characteristics is then analyzed. Flight trajectories under different initial velocities and rotational speeds are obtained through MATLAB simulations, and experimental verification is conducted using an adjustable launcher and dual high-speed camera measurements. This study provides theoretical support for the structural optimization and motion prediction of boomerangs, contributes to the understanding of the coupling mechanism between aerodynamic forces and attitude motion of rotating rigid bodies at low Reynolds numbers, and offers a reference for the design and control of related aerial vehicles.

     

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