A numerical and theoretical study of the aerodynamic performance of a hovering rhinoceros beetle (Trypoxylus dichotomus)

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Abstract

The aerodynamic characteristics of a hovering rhinoceros beetle are numerically and theoretically investigated. Its wing kinematics is measured using high speed cameras and used for numerical simulations of flow around a flapping rhinoceros beetle in hovering flight. The numerical results show that the aerodynamic forces generated (especially for lift) and power required by the hind wing during a quasi-periodic state are quite different from those during the first stroke. This indicates that the wing–wake interaction significantly affects the aerodynamic performance of the hind wing during the quasi-periodic state. Also, twisting of the hind wing along the wing span direction does not contribute much to total force generation as compared to that of the flat wing, and the role of elytron and body on the aerodynamic performance is quite small, at least for the present hovering flight. Based on a previous model (Wang et al., J. Fluid Mech., vol. 800, 2016, pp. 688–719), we suggest an improved predictive aerodynamic model without any ad hoc model constants for a rigid and flat hind wing by considering the effect of the wing–wake interaction in hovering flight. In this model, we treat the wake as a steady or unsteady non-uniform downwash motion and obtain its magnitude by combining a quasi-steady blade element theory with an inviscid momentum theory. The lift and drag forces and aerodynamic power consumption predicted by this model are in excellent agreement with those obtained from numerical simulations.

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The aerodynamic effects of wing rotation and a revised quasi-steady model of flapping flight.

P Sane, Michael H. Dickinson (2002)

We used a dynamically scaled model insect to measure the rotational forces produced by a flapping insect wing. A steadily translating wing was rotated at a range of constant angular velocities, and the resulting aerodynamic forces were measured using a sensor attached to the base of the wing. These instantaneous forces were compared with quasi-steady estimates based on translational force coefficients. Because translational and rotational velocities were constant, the wing inertia was negligible, and any difference between measured forces and estimates based on translational force coefficients could be attributed to the aerodynamic effects of wing rotation. By factoring out the geometry and kinematics of the wings from the rotational forces, we determined rotational force coefficients for a range of angular velocities and different axes of rotation. The measured coefficients were compared with a mathematical model developed for two-dimensional motions in inviscid fluids, which we adapted to the three-dimensional case using blade element theory. As predicted by theory, the rotational coefficient varied linearly with the position of the rotational axis for all angular velocities measured. The coefficient also, however, varied with angular velocity, in contrast to theoretical predictions. Using the measured rotational coefficients, we modified a standard quasi-steady model of insect flight to include rotational forces, translational forces and the added mass inertia. The revised model predicts the time course of force generation for several different patterns of flapping kinematics more accurately than a model based solely on translational force coefficients. By subtracting the improved quasi-steady estimates from the measured forces, we isolated the aerodynamic forces due to wake capture.

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Biology and Physics of Locust Flight. III. The Aerodynamics of Locust Flight

M. Jensen (1956)

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The mechanics of flight in the hawkmoth Manduca sexta. I. Kinematics of hovering and forward flight.

Marriah C. G. Ellington, P. Willmott (1997)

High-speed videography was used to record sequences of individual hawkmoths in free flight over a range of speeds from hovering to 5 ms-1. At each speed, three successive wingbeats were subjected to a detailed analysis of the body and wingtip kinematics and of the associated time course of wing rotation. Results are presented for one male and two female moths. The clearest kinematic trends accompanying increases in forward speed were an increase in stroke plane angle and a decrease in body angle. The latter may have resulted from a slight dorsal shift in the area swept by the wings as the supination position became less ventral with increasing speed. These trends were most pronounced between hovering and 3 ms-1, and the changes were gradual; there was no distinct gait change of the kind observed in some vertebrate fliers. The wing rotated as two functional sections: the hindwing and the portion of the forewing with which it is in contact, and the distal half of the forewing. The latter displayed greater fluctuation in the angle of rotation, especially at the lower speeds. As forward speed increased, the discrepancy between the rotation angles of the two halfstrokes, and of the two wing sections, became smaller. The downstroke wing torsion was set early in the halfstroke and then held constant during the translational phase.