Butterflies achieve their flight through a coupling of wing motion and remarkable body pitching and they seldom hover in nature compared to other flying insects. This study elucidates the aerodynamic mechanisms of the hovering butterfly using numerical simulation and vortex dynamics analysis, utilizing the detailed wing and body kinematics measured by highspeed filming. The results reveal that during each stroke, the leading-edge vortex (LEV) on the forewings and the trailing-edge vortex (TEV) on the hindwings initially attach to the wing surfaces and grow rapidly. The TEV, then, sheds, while the LEV maintains its strength and attachment. Thus, the high lift is mainly generated through the rapid acceleration and delayed stall mechanisms. During hovering, the mean body pitch angle approaches 90°, balancing the forward forces generated in each stroke. The substantial amplitude of body pitching enables the butterfly to project sufficient vertical force to support its weight. Notably, butterflies generate approximately 50% of the total aerodynamic force vertically, indicating lower efficiency. The wing motions during the upstroke and downstroke are approximately symmetrical, resulting in almost equal contributions to vertical force. The vertical force on the hindwings contributes only about 10% of weight supporting, attributed to earlier TEV shedding and the absence of low-pressure regions. However, the aerodynamic centers of the hindwings are far from the center of mass, ensuring the balance of pitching moments. This work provides deeper insights into hovering butterfly aerodynamics and offers theoretical guidance for the development of bio-inspired flying robots.
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The roles of body and wing pitching angles in hovering butterflies
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May 2025
Research Article|
May 13 2025
The roles of body and wing pitching angles in hovering butterflies
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Jianghao Wu (吴江浩)
;
Jianghao Wu (吴江浩)
(Conceptualization, Project administration, Resources, Supervision, Writing – review & editing)
School of Transportation Science and Engineering, Beihang University
, Beijing 100191, People's Republic of China
Search for other works by this author on:
Songtao Chu (褚松涛)
;
Songtao Chu (褚松涛)
(Conceptualization, Investigation, Methodology, Writing – original draft)
School of Transportation Science and Engineering, Beihang University
, Beijing 100191, People's Republic of China
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Long Chen (陈隆)
;
Long Chen (陈隆)
(Investigation, Writing – review & editing)
School of Transportation Science and Engineering, Beihang University
, Beijing 100191, People's Republic of China
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Yanlai Zhang (张艳来)
Yanlai Zhang (张艳来)
a)
(Formal analysis, Methodology, Validation, Writing – review & editing)
School of Transportation Science and Engineering, Beihang University
, Beijing 100191, People's Republic of China
a)Author to whom correspondence should be addressed: [email protected]
Search for other works by this author on:
Jianghao Wu (<span class='lang' lang='zh'>吴江浩</span>)
Conceptualization, Project administration, Resources, Supervision, Writing – review & editing
School of Transportation Science and Engineering, Beihang University
, Beijing 100191, People's Republic of China
Songtao Chu (<span class='lang' lang='zh'>褚松涛</span>)
Conceptualization, Investigation, Methodology, Writing – original draft
School of Transportation Science and Engineering, Beihang University
, Beijing 100191, People's Republic of China
Long Chen (<span class='lang' lang='zh'>陈隆</span>)
Investigation, Writing – review & editing
School of Transportation Science and Engineering, Beihang University
, Beijing 100191, People's Republic of China
Yanlai Zhang (<span class='lang' lang='zh'>张艳来</span>)
Formal analysis, Methodology, Validation, Writing – review & editing
a)
School of Transportation Science and Engineering, Beihang University
, Beijing 100191, People's Republic of China
a)Author to whom correspondence should be addressed: [email protected]
Physics of Fluids 37, 051904 (2025)
Article history
Received:
February 15 2025
Accepted:
March 31 2025
Citation
Jianghao Wu, Songtao Chu, Long Chen, Yanlai Zhang; The roles of body and wing pitching angles in hovering butterflies. Physics of Fluids 1 May 2025; 37 (5): 051904. https://doi.org/10.1063/5.0265833
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