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  1. The long-range migration of monarch butterflies, extended over 4000 km, is not well understood. Monarchs experience varying density conditions during migration, ranging as high as 3000 m, where the air density is much lower than at sea level. In this study, we test the hypothesis that the aerodynamic performance of monarchs improves at reduced density conditions by considering the fluid–structure interaction of chordwise flexible wings. A well-validated, fully coupled Navier–Stokes/structural dynamics solver was used to illustrate the interplay between wing motion, aerodynamics, and structural flexibility in forward flight. The wing density and elastic modulus were measured from real monarch wings and prescribed as inputs to the aeroelastic framework. Our results show that sufficient lift is generated to offset the butterfly weight at higher altitudes, aided by the wake-capture mechanism, which is a nonlinear wing–wake interaction mechanism, commonly seen for hovering animals. The mean total power, defined as the sum of the aerodynamic and inertial power, decreased by 36% from the sea level to the condition at 3000 m. Decreasing power with altitude, while maintaining the same equilibrium lift, suggests that the butterflies generate lift more efficiently at higher altitudes. 
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    Free, publicly-accessible full text available August 1, 2024
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  5. The long-range migration of Monarch butterflies extends over 4000 km. Monarchs experience varying density conditions during migration. Monarchs have been spotted at 1200 m during migration and overwinter at 3000 m, where the air density is lower than at the sea-level. Furthermore, Monarch butterflies have large flexible wings which deform significantly during flight. In this study, we test the hypothesis that the aerodynamic performance of the Monarch wing improves at reduced density conditions at higher altitudes. A design space with air density and stroke plane angle as design variables is constructed to evaluate the effects of fluid-structure interaction at high altitudes in the Reynolds number regime of Re = O(10^3). The effects of chordwise wing flexibility and the aerodynamic and structural response at varying densities are investigated by solving the Navier-Stokes equations, fully coupled to a structural dynamics solver at the Monarch scale. The lift, thrust and power are calculated in the design space. Our results show that lift increases with the stroke plane angle and the air density, whereas the thrust remains close to zero. The mean power required reduces with the altitude, eventually becoming negative at 3000 m. These results suggest that at lower altitudes near sea level, Monarchs can leverage the relatively large magnitude of their lift and thrust forces. At higher altitudes butterflies can fly while minimizing the power. 
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  6. The annual migration of monarch butterflies, Danaus plexippus, from their summer breeding grounds in North America to their overwintering sites in Mexico can span over 4000 kilometers. Little is known about the aerodynamic mechanism behind this extended flight. This study is motivated by the hypothesis that their flapping wing flight is enhanced by fluid-structure interactions. The objective of this study to quantify the aeroelastic performance of monarch butterfly wings and apply those values in the creation of an artificial wing with an end goal of creating a biomimetic micro-air vehicle. A micro-CT scan, force-deflection measurements, and a finite element solver on real monarch butterfly wings were used to determine the density and elastic modulus. These structural parameters were then used to create a monarch butterfly inspired artificial wing. A solidification process was used to adhere 3D printed vein structures to a membrane. The performance of the artificial butterfly wing was tested by measuring the lift at flapping frequencies between 6.3 and 14 Hz. Our results show that the elastic modulus of a real wing is 1.8 GPa along the span and 0.20 GPa along the chord, suggesting that the butterfly wing material is highly anisotropic. Real right forewings performed optimally at approximately 10 Hz, the flapping frequency of a live monarch butterfly, with a peak force of 4 mN. The artificial wing performed optimally at approximately 8 Hz with a peak force of 5 mN. 
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