Novel flight style and light wings boost flight performance of tiny beetles

Flight speed generally correlates positively with body size in animals. However, miniature featherwing beetles (Ptiliidae) exhibit exceptional flight capabilities, surpassing larger insects in speed and acceleration. This anomaly contradicts the expected scaling laws of flight. Previous research has highlighted the surprisingly high flight performance of these tiny beetles, but the underlying mechanisms remain unclear. Miniaturization in the biological world presents unique challenges, as physical forces influencing flight (e.g., viscous drag versus inertial forces) shift their relative importance at smaller scales. While larger insects are generally faster fliers, certain miniature insects, including Ptiliidae, demonstrate unexpectedly high performance. This study aims to uncover the structural and kinematic adaptations responsible for this exceptional flight performance in *Paratuposa placentis*, one of the smallest insect species.

Existing literature extensively examines flight mechanics in larger insects, providing insights into wing motion and aerodynamics. Studies on unsteady aerodynamics in millimeter-sized insects like fruit flies and mosquitoes are abundant. However, research focusing on the flight of tiny insects remains scarce. Two-dimensional numerical simulations have investigated the aerodynamics of bristled wings, but these studies often lack the detail and comprehensive approach needed to fully understand the complex interplay of forces at work in such miniature creatures. While some studies suggest that bristled wings may offer slight advantages in the clap-and-fling phase, a complete understanding of their role in the entire wingbeat cycle, especially in the context of miniaturization, is lacking. Previous work on the smallest beetles demonstrated their extraordinary flight performance, but the precise mechanisms were not fully elucidated.

This study combined multiple advanced techniques to analyze the flight of *Paratuposa placentis*. Firstly, a morphological model was created based on data obtained through light, confocal, and electron microscopy. This provided detailed information about the beetle's wing structure, including the arrangement of bristles and their secondary outgrowths. Secondly, a kinematic model was developed using high-speed videography to record and analyze the wing movements during flight. This provided precise data on wingbeat frequency, stroke amplitude, and the detailed trajectory of the wingtips. Thirdly, a dynamical model employing computational methods of solid and fluid mechanics was used to simulate the aerodynamic forces generated by the wings. This involved simulating the flow of air around the wings and calculating the lift and drag forces generated during different phases of the wingbeat cycle. This allowed for a comprehensive quantitative analysis of the forces and power requirements associated with this unique flight style. The aerodynamic calculations incorporated added mass effects, accurately reflecting the impact of the surrounding air on wing motion. Both bristled and membranous wing models were simulated to compare performance characteristics and quantify the mass savings achieved through ptiloptery.

The study revealed several key features contributing to *P. placentis*' exceptional flight performance. First, the beetle exhibits a novel figure-of-eight wingbeat cycle, distinct from larger insects. This cycle consists of two powerful strokes generating upward force and two recovery strokes involving wing clapping above and below the body. The elytra (modified forewings) act as an inertial brake, counteracting the pitching moment generated by the large wing excursions and enhancing stability. The bristled wings of *P. placentis* are exceptionally lightweight, approximately 1% of the body mass, significantly less than comparable membranous wings (estimated 10-20 times heavier). The secondary outgrowths on the bristles further reduce wing mass by 44%, minimizing inertial forces. Aerodynamic analysis showed that approximately 68% of the vertical force is generated through lift, with drag contributing 32%. While instantaneous forces generated by a membranous wing exceed those of the bristled wing, the cycle-averaged vertical force is comparable. Crucially, the low inertia of the bristled wings keeps the mechanical power required for wing actuation positive throughout the wingbeat cycle. This eliminates the need for elastic energy storage, which is necessary for membranous wings to manage the high inertial forces during their movement. The cycle-averaged power consumption in *P. placentis* is remarkably low (28 W per kg body mass), despite instantaneous peaks reaching 110 W kg−1. The benefits of the bristled wing design are most apparent at low Reynolds numbers, typical of miniature insects, where the advantage of reduced inertial costs outweighs the slight reduction in aerodynamic force.

The findings demonstrate how *P. placentis* overcomes the challenges of flight at low Reynolds numbers. The unique figure-of-eight wingbeat cycle, coupled with the lightweight bristled wings and the inertial braking effect of the elytra, results in a highly efficient flight system. The elimination of elastic energy storage simplifies the flight mechanism and reduces the power demands on the flight muscles. This combination of kinematic strategies and structural adaptations explains the high flight performance of this tiny beetle, despite its miniature size. The significant mass reduction achieved through ptiloptery allows for high-amplitude wing strokes without excessive inertial forces, thereby enhancing flight maneuverability and efficiency. The study suggests that these mechanisms may be widespread among miniature beetles, contributing to their evolutionary success.

This study unveils a novel flight strategy employed by miniature featherwing beetles, highlighting the intricate interplay between wing morphology, kinematics, and aerodynamics. The lightweight bristled wings, the figure-of-eight wingbeat, and the inertial braking function of the elytra constitute a highly efficient flight system at low Reynolds numbers. Future research should investigate the prevalence of this flight style in other miniature insects with bristled wings to better understand the convergent evolution of ptiloptery and its role in miniaturization.

The study focuses on a single species, *Paratuposa placentis*. While this species is representative of the smallest beetles, further studies on a wider range of Ptiliidae and other microinsects with bristled wings are needed to determine the generality of the observed mechanisms. The computational models, while sophisticated, are still simplifications of the complex reality of insect flight. Factors such as the exact details of bristle flexibility and interactions between individual bristles were not fully captured in the simulations.