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Kinematics and Inertial Effects in Locust Flapping Wings

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Abstract

In the present study, inertial forces and kinematics of wings of locusts, Schistocerca americana, were investigated experimentally. The developed experimental setup includes freshly extracted hindwings and forewings, a mechanical transmission producing pitching and flapping, a vacuum chamber, and a high-speed video system. Flapping angle amplitudes determined at the middle section are practically the same in air and in vacuum in both forewings and hindwings. Pitching amplitudes in the root and in the middle section of hindwing differ by up to 50 % due to torsional deformation or twist. In air, the average twist angles are 3° and 17° in forewings and hindwings, respectively. Amplitudes of twist angle are higher in vacuum, especially at relatively high flapping frequencies. Inertial forces are calculated based on a rigid-body model of a wing with prescribed displacements. The 5-segment mesh for hindwings and 2-segment mesh for forewings provide accurate determination of inertial forces. Amplitudes of the fifth harmonic in accelerations in air are substantially smaller than in vacuum and, therefore, inertial forces in air are about 30 % smaller than those in vacuum. Thus, aerodynamic loads suppressed high-frequency component in wing oscillations resulting in substantially smaller inertial forces in air.

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Abbreviations

A ik , B ik :

Coefficients in Fourier series approximations

c :

Wing chord

F x , F z :

Components of aerodynamic force

f :

Flapping frequency

f c :

Cutoff frequency

K :

Number of terms retained in Fourier series approximation

i, j, k :

Indices

l :

Wing length

m :

Wing mass

N :

Number of segments in rigid-body model of wing

T :

Time period of one flapping cycle

t :

Time

R x , R z :

Components of instantaneous reaction force

Q x , Q z :

Components of instantaneous inertia force

Δw :

Out-of-plane deformations in forewings

xyz :

Ground-fixed coordinate system

x ϕ y ϕ z ϕ :

Wing-fixed coordinate system

\( {\overline{x}}_{CM},{\overline{y}}_{CM} \) :

Nondimensional coordinates of wing center of mass

β :

Pitching angle

Δβ :

Peak-to-peak pitching amplitude

ϕ :

Flapping angle

Δϕ :

Peak-to-peak flapping amplitude

η :

Point on leading edge of wing

Δω :

Twist angle

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Acknowledgments

This project was sponsored by a grant from the Air Force Office of Scientific Research, FA9550-10-1-0452 (Dr. D. Smith, Program Manager). We would also like to thank Frank Oliver and Michael Fishburn for their contributions to the construction of the vacuum chamber facility. The authors would also like to thank Erlong Su for his assistance with video tracking.

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Authors and Affiliations

  1. Department of Aerospace and Mechanical Engineering, University of Arizona, 1130 N. Mountain Ave., Tucson, AZ, 85721, USA

    S. Shkarayev & R. Kumar

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  1. S. Shkarayev
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  2. R. Kumar
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Correspondence to S. Shkarayev.

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Shkarayev, S., Kumar, R. Kinematics and Inertial Effects in Locust Flapping Wings. Exp Mech 56, 245–258 (2016). https://doi.org/10.1007/s11340-015-0093-2

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  • DOI: https://doi.org/10.1007/s11340-015-0093-2

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