Flight efficiency is a key to diverse wing morphologies in small insects

Abstract

Insect wings are hybrid structures that are typically composed of veins and solid membranes. In some of the smallest flying insects, however, the wing membrane is replaced by hair-like bristles attached to a solid root. Bristles and membranous wing surfaces coexist in small but not in large insect species. There is no satisfying explanation for this finding as aerodynamic force production is always smaller in bristled than solid wings. This computational study suggests that the diversity of wing structure in small insects results from aerodynamic efficiency rather than from the requirements to produce elevated forces for flight. The tested wings vary from fully membranous to sparsely bristled and were flapped around a wing root with lift- and drag-based wing kinematic patterns and at different Reynolds numbers ( Re ). The results show that the decrease in aerodynamic efficiency with decreasing surface solidity is significantly smaller at Re = 4 than Re = 57. A replacement of wing membrane by bristles thus causes less change in energetic costs for flight in small compared to large insects. As a consequence, small insects may fly with bristled and solid wing surfaces at similar efficacy, while larger insects must use membranous wings for an efficient production of flight forces. The above findings are significant for the biological fitness and dispersal of insects that fly at elevated energy expenditures.

Efficiency and Aerodynamic Performance of Bristled Insect Wings Depending on Reynolds Number in Flapping Flight

“…Bristle diameter was ~1.1 mm or ~8.8 × 10 −3 wing length and the bristle angle α b relative to the wing's longitudinal axis was ~29 • (Figures 1h and 2e). The model wing was comparatively rigid as direct measurements have recently shown that real wing bristles are remarkably stiff [30] and we also numerically showed that bristle bending is likely to be negligible during wing flapping in tiny insects [29]. The wings had little weight under the tested conditions because of neutral buoyancy resulting from the similar densities of the PVA (~1190-1310 Kg m −3 ) and the fluid used (glycerin, ~1260 Kg m −3 ).…”

“…This study used generic wings with bristle spacing similar to that of small insects (Figure 1a-g, Table 1) [29] instead of testing the bristled wings of any single specific species. Our synthetic wing shapes were constructed to consider three aspects: a resemblance to natural flapping bristled wings; a one-parameter family that determined wing permeability (bristle spacing); and an emphasis on aerodynamics and power.…”

“…Although secondary microstructures on bristles may have a significant effect on bristle drag, more realistic 3D printed bristles with cylindrical cores and secondary outgrowths generate the same aerodynamic drag as simple cylindrical rods with a wider diameter. More details on the development of wing design and kinematics were published previously [29].…”

“…To allow comparisons to previous studies in insect flight, the Reynolds number Re is typically determined from velocity u at the wing tip and wing length R. Following a numerical study on bristled wings [29], however, we here defined the Reynolds number as:…”

“…Most previous studies on bristled wing aerodynamics have not addressed the power requirements of flapping flight, leaving the question unanswered as to why bristle and solid wings co-occur in small insects but not in larger insects. A recently published numerical study suggests that Froude efficiency is key to the latter finding [29]. This experimental study employed the same kinematic pattern and wing design as the numerical study testing parameterized wing models with bristle densities that are typical of small insects.…”