利用翅膀掃掠動態控制蝴蝶拍撲飛行之研究

Abstract

蝴蝶飛行時，身體會有明顯的俯仰動作，而此動作在先前的研究中被證實可控制空氣作用力的方向而使蝴蝶操控飛行，利用不同的俯仰動作達到不同的飛行模式。然而目前對蝴蝶是如何達成穩定且週期性的俯仰動作，以及控制此動作的方法仍不完整。觀察蝴蝶拍撲飛行時，翅膀除了上下拍撲以外還會有明顯的前後掃掠動作。此動作可偏移拍翅平面，並影響空氣作用力矩的產生，因此被認為是造成身體俯仰以及蝴蝶得以操控飛行的因素之一。 本研究參考青斑蝶的幾何外形與動作參數建構出數值模型，並透過數值方式探討翅膀掃掠動態對蝴蝶身體俯仰動作以及飛行軌跡之影響。在模擬中，模型可達到自由飛行並具有三個自由度，分別為前後、上下移動以及俯仰轉動。研究發現翅膀掃掠動作會改變翅膀上壓力中心(COP)與身體旋轉中心之間的距離，進而影響俯仰力矩之大小與方向。首先模擬翅膀固定在不同掃掠角度的情況。當壓中心固定於旋轉中心前時，可產生與真實蝴蝶相位相同的俯仰動作，達成穩定且週期性的飛行。在此情況下，加大掃掠角度使壓力中心往前移，產生較大之俯仰力矩與俯仰振幅，使垂直方向的位移增加，飛行模式由斜飛轉為趨近於上飛。當壓中心固定於旋轉中心附近或之後時，俯仰動作之相位與真實蝴蝶相反，產生不足之空氣作用力，而無法達成穩定的飛行，最終墜落。接著加入翅膀掃掠動態，並以正弦函數描述，使翼尖移動軌跡呈橢圓形，壓力中心之位置隨著上、下拍不斷改變。加入此動作可大幅降低平均俯仰角度，微幅降低俯仰振幅，使垂直方向位移大幅降低，而達到前飛。加大掃掠振幅可進一步降低平均俯仰角，使蝴蝶呈下降飛行。本研究證實蝴蝶可利用翅膀掃掠動作操控飛行，達到不同的飛行模式，期望研究結果可用於未來微飛行器的設計，提供嶄新的操控方式。

Butterflies uniquely use the body postures to maneuver their flight directions and speeds, but the method how butterflies utilize to control their body pitching in the air is unclear. Experiment recording the real flight of butterflies indicate that butterflies fly with significant wing lead-lag motion, the wing motion that deviate from the stroke plane. In this research, we create a simulation of butterflies in free flight to investigate how butterflies utilize this motion to achieve different flight modes by controlling their body pitching. The wing lead-lag motion change the distance between the center of pressure (COP) of wing and the center of rotation (COR) of butterflies, and largely affect the direction and magnitude of aerodynamic torque. When the position of COP is fixed ahead of COR, the variations of pitching angle is similar to that of real butterflies in free flight, and the butterfly is able to perform a stable flight in the simulation. Increasing the lead-lag angle further increases the pitching moment and rotational amplitude, and the butterfly performs the flight motion close to vertical take-off. When the position of COP is fixed behind of COR, the variations of pitching angle is completely different from the real butterflies in free flight, and the flight is unstable and the butterfly falls down .When the lead-lag angle is considered as a function, and the trajectory of the wing-tip is an oval similar to that of a real butterfly. The distance between COP and COR is continually changing throughout the downs and upstroke. The average pitching angle decreases while slightly decreasing the pitching amplitude, and butterflies perform the forward flight. The lead-lag motion affects the generation of aerodynamic torque and force and plays an important role in the flight control of a butterfly. Our results might provide a new flight control method for designing high maneuverability aerial vehicle in the future.