蝴蝶轉彎飛行模式與操控

Abstract

本文結合實驗與數值模擬方法，將實驗觀測之真實飛行動態，利用週期性傅立葉級數擬合身體與翅膀旋轉角度函數，建立三維數值流場模型，旨在探討三種蝴蝶轉彎模式間，翅身動態與流場結構渦漩、作用力等機制。 隨著攝影技術的進步，得以將蝴蝶飛行瞬間運動的連續變化過程，以每秒幀率一千的高速攝影技術同步捕捉，解析運動軌跡紀錄。本研究選用台灣南部產大白斑蝶(學名Idea leuconoe)成蟲作為實驗對象，此種蝶類拍翅頻率較低且體型大、飛行速度較慢為其特色，然而該蝴蝶依然可以靈活地操縱身體，快速地達成轉彎避敵與穿梭。為量化一個拍翅週期內蝴蝶的轉彎程度，本研究將三維空間中所記錄的自由轉彎飛行移動軌跡，經改良過往投影方法至回歸平面，並將位於回歸平面上各時刻之軌跡點群擬合出轉彎半徑，以此劃分轉彎模式。 根據空氣動力與動態分析結果，發現蝴蝶翅膀初期主動進行不對稱的拍翅運動，可影響身體之滾轉角與偏航角，分別提供轉彎初始的傾斜及偏轉條件，在下拍中期至上拍初期，飛行姿態快速轉換影響作用力方向，而時間平均下的俯仰角變化在20度以內，對於三種轉彎模式的半徑幅度具有建設性影響。內外翅動態方面，比較時間平均下的拍撲振幅量值相近，但是有著外翅下拍振幅大於內翅、上拍振幅小於內翅的特色，並且隨著轉彎模式的半徑減小，平均前翅偏移的增量差異為1.3倍。若是從流場結構觀察渦漩分布特性，與翼表面受力位置和程度息息相關。最後，本研究嘗試組合大轉彎半徑的翅膀動態與小轉彎半徑的身體動態，由數值模擬果顯示，該動態搭配方式無法提供飛行充足的升力與轉彎穩定性，代表翅身動態於時序存在耦合效應。 本研究貢獻為歸納轉彎方面，真實蝴蝶於不同轉彎模式下的飛行動態，可將蝴蝶飛行轉彎方法，應用於未來仿生撲翼及微飛行器操控性設計，提供轉彎飛行多角化的觀點與更全面的知識架構，從而最佳化飛行任務。

To investigate the butterfly flight among three turning modes with wing and body motion, interaction forces, vortex structures and other mechanisms in air flow. Combing experimental and numerical simulation method, this research collected abundant of real flight motion data and modeled the three-dimensional numerical flow filed with periodic functions fitting body and wing angles by Fourier series. As the advance in photography technologies, the high-speed cameras with 1000fps resolution could synchronous capture of the instant locomotion of butterfly flight and record for later analyze. The subject is native species Idea leuconoe, taken from southern Taiwan, been used in the biological experiment. It has low flapping frequency and large size compare to other species. However it can still maneuver its agile body making sharp turn quickly to avoid predators. To quantify the degree of turning in one stroke, the feature point set of free turning flight trajectory in three-dimension space are projected to the regression plane by improved method. Fitting these in-plane points to the circle and categorize turning mode by the radius. According to the result analysis of aerodynamic and flight motion, in the early stage, an asymmetry flapping motion active by butterfly wings could affect yaw and roll angle of the body, respectively providing the initial tilt and deflection conditions for turning. During mid-downstroke to early upstroke stage, flight attitude rapid changes and affect the direction of response forces. While the pitch angle changes within 20 degrees under time averaging, this angle has a constructive influence to the radius length of the three turning modes. The flapping amplitude of inner and outer wing under mean time are similar, but the flap-down amplitude of the outer wing is larger than that of the inner wing, and the flap-up amplitude is in contrast, smaller than the other. As the radius of the turning mode decrease, the average forewing deviate angle increase 1.3 times. Observing the vortex distribution characteristics from the flow field, it is closely related to the position and degree of stress on the wing surface. Final section attempts to combine wing dynamics of large turning mode and body motion of small turning mode. Result shows this combination case cannot provide sufficient lift for flight and turning stability, indicating the coupling effect of motion timing. This work summarizes the flight dynamics of real butterfly in three turning modes. The turning flight method with a diversified perspective could be applied to future biomimicry design and micro-aircraft control design, providing a more comprehensive knowledge frame work to optimize flight missions.