Scaling and mechanical optimality of bristled wings in microinsects

Abstract

It is crucial for both animal evolution and engineering to optimize the relative size of structures. Animal wings are no exception, every structural design having its limits in terms of achievable size and performance. For instance, many microinsects have bristled wings, which are more efficient at small scales than the membranous wings common in larger insects. However, the limitations and the optimal characteristics of bristled wings remain largely underinvestigated. We collected morphological and kinematic data on a variety of beetles ranging between 0.3 and 5 mm in wing length. This was followed by a theoretical analysis to explain from the mechanical standpoint the morphological traits and allometric scalings observed in the data. We derived functional dependencies for parameters such as the number of bristles, bristle length and diameter, size of the wing blade, etc., from considerations of wing inertia minimization under the aerodynamic and structural stiffness constraints. The solution of the optimization problem reveals scaling relationships aligning with empirical trends, which suggests that the reduction of wing membrane during miniaturization can be explained by mechanical optimality. Thus, scaling of the number of bristles and the average gap width between bristles follows directly from the aerodynamic condition of maintaining low permeability, while the bristle diameter and length are determined mainly by the structural stiffness requirement. Similar mechanical arguments are likely applicable to other miniature animals that propel through fluids.