- 學位論文
蝴蝶翅膀形狀對飛行軌跡之影響─以前翅掃掠角為主軸
Influence of Butterfly’s Wing Planform on Flight Trajectory — Based on the Lead-lag Angle of Fore-wing
摘要
本文綜整三種蝴蝶之生物實驗、數值分析、翼型設計，期望歸納之法則可應用於仿生蝴蝶拍撲飛行器之翅膀設計。研究成果證實，僅改變翅膀前、後掠角度，飛行位移(飛行性能指標)會產生顯著差距，以玉帶鳳蝶來說，後掠的翅膀外型能提升飛行水平位移90%左右。 蝴蝶飛行時，翅膀前後掃掠會同時造成平均弦長、展長以及翅膀形狀改變，而此三因素皆會影響飛行時的空氣動力，並對於蝴蝶的飛行操控產生顯著影響。本文以翅膀掃掠角(lead-lag angle)為主要參數，探討大白斑蝶(Idea leuconoe)、玉帶鳳蝶(Papilio polytes)與枯葉蝶(Kallima inachus)的翅膀參數如何影響飛行表現，並提出翅膀形狀設計準則，以作為微飛行器翅膀設計之參考。 本研究利用正交高速攝影機追蹤蝴蝶身體與翅膀上的特徵點，藉此分析蝴蝶飛行動態，並以此根據建立三維數值模擬。研究結果顯示，蝴蝶自由飛行時，翅膀形狀對於飛行軌跡造成直接影響，在大白斑蝶的模型中，翅膀前掠10度的模型能夠飛得最高且最遠，而前掠25度以上的模型卻無法成功穩定飛行，在前掠角度增加的情況下，前、後翅的重疊區域減少，整體面積增加，卻對飛行產生不利影響，因此本文進一步探討此原因。 模擬結果顯示：較長的平均弦長有助於低壓區分布範圍擴大，增加展長則能使翼尖速度加快，造成更強烈的翼前緣渦漩與翼尖渦漩。對於翅膀形狀來說，翅膀前掠使得翼前緣渦漩能貼附的有效面積減少，翼前緣渦漩較快消散，導致其強度降低且分布範圍縮小；當翅膀後掠時，翼前緣渦漩則會由翼根處沿著翅膀前緣發展，有助於翼前緣渦漩穩定貼附於翅膀表面，進而持續提供上下表面壓力差。 本文透過研究不同種蝴蝶，在翅膀動作、外型皆不一樣的情況下，歸納出其共通性，並分別得到平均弦長、展長與掃掠角對於飛行位移的效果，僅稍微改變翅膀形狀便可以大幅影響空氣動力，未來在設計仿蝴蝶拍撲機構的翅膀時，可以參考此研究，進而提升微飛行器之氣動效率。
並列摘要
Biological experiments, numerical analysis and wing design of three different butterflies are integrated in this thesis. This can be utilized in the field of wing design for butterfly-like flapping mechanism. Results show that little alternation of the lead-lag angle could cause magnificent effect on flight trajectory. Take Papilio polytes for instance, backward-sweeping wing helps rise the horizontal trajectory about 90%. When butterflies fly, the lead-lag(sweeping) motion of the fore-wing changes average chord length, span and wing planform simultaneously. It affects the aerodynamic forces and hence exerts significant influence on flight maneuverability. From the perspective of lead-lag angle (η), this thesis aims to discuss how the wing parameters of Idea leuconoe and Papilio polytes affect flight performance, serving as important insight for the design of micro aerial vehicles (MAVs). Orthogonally-aligned high speed cameras are used to track feature points on butterflies. Flight dynamics is further analyzed and used to create a numerical simulation. The study indicates that, under the free flight condition, wing planform has great impact on flight trajectory. Among the models of Idea leuconoe, forward-sweeping wings of η = 10° flies highest and farthest, whereas the one for η = 25° cannot maintain a stable flight. Although a larger lead-lag angle decreases the overlapping area between forewing and hindwing and thus increases the total area of the wing, it negatively affects flight performance. Such unexpected phenomenon urges deeper exploration in this field. Simulation results show greater chord length helps low-pressure area to expand and larger span accelerates wing-tip velocity, generating stronger leading-edge vortex (LEV). The forward-sweeping wing of the wing planform has a smaller region for LEV to attach. Therefore, the LEV sheds more quickly, which attenuates the strength of the LEV. As for backward-sweeping wing, the LEV starts from the wing base and expands along the leading edge until it reaches the wing tip. The stable LEV remains attached throughout the stroke, which consistently contributes a large amount of pressure difference between the upper and lower surface of the wing. In this study, through investigating several kinds of butterflies with different flight motions and wing planforms, we reveal how mean chord length, span and lead-lag angle affect flight trajectory. Little changes of wing planform can induce tremendous effect on aerodynamic forces. This study provides valuable insight into designing wings of butterfly-like flapping machines to improve aerodynamic efficiency.