Experimental study on the aerodynamic optimization design of flexible wings for tailless flapping wing micro air vehicles

Flexible wings, serving as the key components of tailless flapping wing micro air vehicles (FWMAVs), simultaneously generate lift, thrust, and control torques. Due to the complex unsteady fluid-structure interactions involved in their flapping, accurately predicting their aerodynamic performance, such as mean lift and lift-to-power efficiency, becomes challenging. There is also a lack of widely accepted and rational design methods for flexible wings. To address these, we propose an experimental optimization design method based on response surfaces methodology and investigate the impact of four design parameters—aspect ratio ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>A</mml:mi> </mml:math> ), slack angle ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>θ</mml:mi> </mml:math> ), taper ratio ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>λ</mml:mi> </mml:math> ), and flapping frequency ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>f</mml:mi> </mml:math> )—on the aerodynamic performance of flexible wings. The results show that the models accurately predict the aerodynamic performance of flexible wings, with an error margin of less than 10% compared to experimental measurements. Utilizing these models, an optimal flexible wing for a tailless FWMAV with a mass of 15 g was designed and manufactured, which can generate 15.24 gf of lift while maintaining a lift-to-power efficiency of 6.07 gf/W. Additionally, the models indicate that the four parameters are nearly equally important for the aerodynamic performance of flexible wings, and the coupling between these parameters also significantly affects the aerodynamic performance. Specifically, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>A</mml:mi> <mml:mi mathvariant="normal">&amp;</mml:mi> <mml:mi>λ</mml:mi> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>A</mml:mi> <mml:mi mathvariant="normal">&amp;</mml:mi> <mml:mi>f</mml:mi> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>θ</mml:mi> <mml:mi mathvariant="normal">&amp;</mml:mi> <mml:mi>f</mml:mi> </mml:math> , and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>λ</mml:mi> <mml:mi mathvariant="normal">&amp;</mml:mi> <mml:mi>f</mml:mi> </mml:math> affect mean lift, while <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>A</mml:mi> <mml:mi mathvariant="normal">&amp;</mml:mi> <mml:mi>λ</mml:mi> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>θ</mml:mi> <mml:mi mathvariant="normal">&amp;</mml:mi> <mml:mi>λ</mml:mi> </mml:math> , and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>θ</mml:mi> <mml:mi mathvariant="normal">&amp;</mml:mi> <mml:mi>f</mml:mi> </mml:math> affect lift-to-power efficiency. These coupling effects help explain the contradictions found in previous studies regarding the influence of different parameters. Our research provides clear guidance and practical methods for designing flexible wings in tailless FWMAVs.