蝴蝶展向撓曲變形相位差對飛行操控之影響

Abstract

本文旨在分析蝴蝶翅膀撓曲變形動態以及其對於飛行動態的影響，並聚焦於展向撓曲變形。首先簡化翅膀曲面變形函數，提出展向變形重要參數：傾角之斜率(SoA)，以利歸納。以三部高速攝影機拍攝七隻大白斑蝶共72次的前飛數據，取12組較無偏航且散布於慢平飛、慢爬升、快平飛、快爬升四個象限的飛行資料進行分析，以獲得不同飛行狀態下的翅膀動態。 實驗結果顯示翼旋轉角峰值領先0.1相位約可增加0.3 m/s的平均總速率，而SoA峰值領先0.1相位約可增加0.1的垂直速率比例。此外，大白斑蝶與過去文獻被動旋轉翅傾角數據的比對以及翼旋轉角峰值相位與展向變形峰值相位呈正相關的現象，皆支持蝴蝶得以使用根部肌肉間接以慣性延遲控制展向變形的論點。 數值模擬結果與生物實驗歸納的策略預測相符，翼旋轉角領先有較大的平均總速率，而SoA相位領先除了同實驗歸納有較大的垂直速率比例外，亦有較大的平均總速率。然而所需功率皆大幅上升，使升力效率降低15%至42%不等，此策略僅適合用於操控用途，穩定前飛時適合採用原始正常相位。爬升與加速最有效果的策略皆為翼旋轉角正常相位、SoA領先0.1相位的飛行，相較正常相位飛行，平均總速率增加30.9%、垂直速率比例增加29.9%，然而升力效率降低26.43%。 在SoA領先0.1相位的飛行中，上拍後期過小的傾角使翼面力導至垂直方向，產生負升力峰值。本文於數值模擬中以延遲身體俯仰角0.1相位使翼面方向改變，結果顯示最多可降低負升力28.08%。本文亦發現蝴蝶具自主俯仰角調節機制，同樣可使翼面力重新導向。 未來設計拍撲翼微飛行器時若有快速爬升或加速的需求，可採用蝴蝶構型並裝配較剛性的被動旋轉翅，使翅膀受到慣性後SoA相位較提前，並以正常相位之翼旋轉飛行。

This study analyzes the wing spanwise deformation of butterfly and its impact on flight dynamics. The wing’s surface function was simplified, and a crucial parameter for spanwise deformation, the slope of angle-of-incidnece (SoA), was introduced. Butterflies in forward flight were captured by three high-speed cameras, and twelve datasets covering various flight conditions were employed for the analysis. The biological experimental results indicated that a 0.1 phase lead in the peak of wing rotation angle could lead to an increase of approximately 0.3 m/s in mean total velocity. Also, a 0.1 phase lead in the peak of SoA exhibited an increase of approximately 0.1 in the vertical velocity ratio. The angle-of-incidence dynamics of Idea leuconoe were compared with those of a passively rotating wing from earlier literature. Furthermore, a positive correlation between the peak phase of wing rotation angle and the peak phase of spanwise deformation was noted. These observations both bolster the argument that butterflies can indirectly control wing spanwise deformation through root muscles. The numerical simulation results align well with the strategies inferred from biological experiments. Advancing the wing rotation angle phase leads to a higher mean total velocity. Whereas an advanced SoA phase not only yields a greater vertical velocity ratio, as observed in biological experiments, but also contributes to a higher mean total velocity. However, these strategies entail a significant increase in required power, resulting in a reduction in lift efficiency ranging from 15% to 42%. Consequently, the strategies involving advanced wing rotation angle phase or advanced SoA phase are primarily suitable for maneuvering purposes, whereas stable forward flight is best achieved by utilizing the original normal phase. Among these cases, employing normal phase of wing rotation angle coupled with a 0.1 phase-leading SoA phase proves to be the most effective strategy for climbing and acceleration. Compared to normal phase flight, this strategy leads to a 30.9% increase in mean total velocity and a 29.9% increase in vertical velocity ratio, but yields a corresponding reduction of 26.43% in lift efficiency. In flight where the SoA phase advanced, a deficiency in the angle-of-incidence during the latter stage of the upstroke results in a negative peak lift. In this study, a delay of the body pitch angle by 0.1 phase was introduced in the numerical simulation to address this issue. The results showed that this adjustment can reduce the negative lift by up to 28.08%. Additionally, this study revealed that butterflies possess an inherent mechanism for autonomously adjusting the body pitch angle, which similarly aids in reducing negative lift. In the prospective development of flapping-wing micro air vehicles, if a requirement for rapid ascension or acceleration arises, the design can adopt a butterfly-like configuration, combined with more rigid passively rotating wings. Such a wing design would result in an advanced SoA phase. Within this configuration, flight with normal-phase wing rotation facilitates effective climbing and acceleration.