Time-Varying Wing-Twist Improves Aerodynamic Efficiency of Forward Flight in Butterflies

Abstract

Insect wings can undergo significant chordwise (camber) as well as spanwise (twist) deformation during flapping flight but the effect of these deformations is not well understood. The shape and size of butterfly wings leads to particularly large wing deformations, making them an ideal test case for investigation of these effects. Here we use computational models derived from experiments on free-flying butterflies to understand the effect of time-varying twist and camber on the aerodynamic performance of these insects. High-speed videogrammetry is used to capture the wing kinematics, including deformation, of a Painted Lady butterfly (Vanessa cardui) in untethered, forward flight. These experimental results are then analyzed computationally using a high-fidelity, three-dimensional, unsteady Navier-Stokes flow solver. For comparison to this case, a set of non-deforming, flat-plate wing (FPW) models of wing motion are synthesized and subjected to the same analysis along with a wing model that matches the time-varying wing-twist observed for the butterfly, but has no deformation in camber. The simulations show that the observed butterfly wing (OBW) outperforms all the flat-plate wings in terms of usable force production as well as the ratio of lift to power by at least 29% and 46%, respectively. This increase in efficiency of lift production is at least three-fold greater than reported for other insects. Interestingly, we also find that the twist-only-wing (TOW) model recovers much of the performance of the OBW, demonstrating that wing-twist, and not camber is key to forward flight in these insects. The implications of this on the design of flapping wing micro-aerial vehicles are discussed.

Bio-Inspired Flexible Flapping Wings with Elastic Deformation

“…Taken together, the wings with the better camber performance presented the higher lift/power, which means less energy consumption, with neglecting the effects of AOA. It should be noted here that previous studies have reported an impressive improvement of efficiency for the flexible insect wings [6,10,31,44]. These results are consistent with the role of wing flexibility.…”

Fluid-structure interaction enhances the aerodynamic performance of flapping wings: a computational study

“…A numerical study (Young et al, 2009) with realistic wing shapes based on the high-speed photogrammetry suggested that the twist and camber can enhance the aerodynamic efficiency of the forward flight of locusts. Similar benefits of the wing deformation have been confirmed in the flight of butterflies or beetles in spite of the great differences in flight morphology (Le et al, 2013;Zheng et al, 2013).…”

“…In terms of the amplitude of the wing deformation, large part of the wing twist in air, which is suggested to enhance the aerodynamic performance of flapping wings (Zheng et al, 2013), is induced by the inertial forces of the flapping wings. The aerodynamic force, however, accounts for the second peak in the deformation that is observed from the middle to the late of each half-stroke ( figure 4ai,aii).…”

Bending rules for animal propulsion

“…The energy savings accrued through maximizing energetic efficiency during thrust production may strongly favour evolutionary convergence on designs that produce such thrust advantages. Vortex circulation, thrust production and efficiency vary with flexibility, suggesting that the flexibility of animal propulsors may be tuned to maximize thrust production and efficiency [30][31][32][33] by controlling vorticity associated with propulsor bending. For example, although some bending is favourable, extensive bending can lessen thrust production efficiency 18 by disrupting vortex organization along the span of a propulsor 10 .…”