蝴蝶翼展尺寸效應及飛行動態策略

Abstract

本文透過生物實驗與數值模擬方式分析蝴蝶尺寸對於飛行表現及飛行動態之影響，並從中提出小型蝶類提升翅膀負重與速度調控之機制與策略。實驗首先透過高速攝影機拍攝翼展差異明顯之四種蝴蝶(介於136-44 mm)於實驗箱中進行自由飛行，並篩選蝴蝶於前飛模式下之動態，藉由影像處理軟體對其動作分析。然而，由於實驗中過多參數之影響，造成部分趨勢不明顯，因此本文進一步透過數值模擬方式控制變因，定量分析尺寸差異對於飛行之影響，並比較實驗與模擬所呈現之結果。 實驗量測結果顯示蝴蝶翼面負重與翼展尺寸有正相關的趨勢，相較於數值計算之結果，在飛行動態固定之情況下，蝴蝶平飛時計算之翼面負重會隨翼展迅速下降，數值模擬預測小型蝶類所能承受之翅膀負重相較於真實蝶類不理想；在飛行動態方面，真實小型蝶類之拍撲頻率和身體俯仰振幅有高於大型蝶類之趨勢，因此推測小型蝶類可能透過動態差異提升翼面負重達到更好之飛行表現，因此本文進一步探討提升拍撲頻率和身體俯仰振幅動態對小型蝶類空氣作用力與功率產生之影響。透過數值模擬之方式，分析提升頻率與身體俯仰動態對於蝴蝶飛行之影響，研究結果發現兩者皆能有效提升蝴蝶翼面負重使達成穩定飛行，而前者對於蝴蝶能達到較高之飛行速度，但需要較多之空氣動力功率；而後者所能達到之飛行速度較低，但相對較節能，透過此兩動態之調配可進行飛行速度與飛行功率之調整。 本研究提供蝴蝶尺寸與翼面負重、功率與飛行速度等之關係，其可做為未來仿蝴蝶飛行器在尺寸、重量與馬達設計及材料選擇上重要之參考準則；此外，透過實驗與數值模擬結果之差異，本文提出運用飛行動態達到微飛行器飛行速度與功率之調控策略。

The scale of butterflies largely variate among species, and might affect their flight performance intrinsically. In this work, we carry out experimental observations and numerical analysis to investigate how flight performances and flight motions of butterflies correlate with their sizes, and a flight strategy to enhance wing loading of small size butterflies is proposed accordingly. Four different species of Taiwan butterflies with significant differences on wingspan (variating from 44-136 mm) were selected to study experimentally. The motions of butterflies were recorded with high-speed cameras when they were freely flying in an experimental chamber. The images of flight that close to forward flight were selected and analyze with the image processing software (Image J). The experimental results indicate that the wing loading of butterflies positively correlate to their wingspan, and the irregularity of the flight trajectory is not as evident as the previous research (Dudley, 1990). In addition, the flapping frequency and body angle amplitude of the small butterflies are found to be higher than that of large butterflies in our experiments. Numerical models of butterflies in different scales are further created to analyze the size effect quantitatively since various parameters in experiments are combined and are unable to control separately. The butterfly in the simulation translate freely along the vertical and horizontal directions; the flight speeds determined by calculating the aerodynamic force and gravity force. The shape and flight motions of butterflies are considered as the same in each cases, and the mass is manually controlled to find the maximum wing loading of butterflies in specific size. The simulations results show that the wing loading decreases with the wingspan sharply while the shapes and the flight motions are considered as the same. The decreasing rate is more rapid than the trend recorded from experiments, which implies that small butterflies may adjust their flight motions, flapping frequency and body angle amplitude in our observation, to enhance their wing loading in nature. To clarify the effects of these two motions, we further adjust the flapping frequency and rotation amplitude in the simulation model. The results show that both ways effectively improve the wing loading of the butterflies as excepted; moreover, the butterflies are able to achieve higher forward speed with the former motion and are more energy-efficient with the latter motion. Butterflies may alter the flapping frequency or rotation amplitude. Our results provide relations between the size of butterflies and the flight parameters. In an engineering perspective, these relations are especially important for the designing of flight vehicles; for example, determining the total weight of vehicles and power required of the motor. In addition, by comparing the difference between the experimental and simulation results, we proposed a motion control strategy to adjust the flight speed and power consumption of micro aircraft vehicles.