Span efficiency of flying animals

Span efficiency, a metric representing the efficiency of lift generation in flying animals, has been measured for birds, bats, and insects using particle image velocimetry over the past two decades. However, inconsistencies in capture and data analysis methods have introduced systematic biases, preventing a unified and fair comparison across diverse taxonomic groups and body sizes. Here, we quantify the impact of these methodological discrepancies using a computational fluid dynamics method, then standardise and synthesise span efficiency data from all thirty species measured to date. We apply a phylogenetic comparative method to evaluate how morphological and kinematic parameters affect span efficiency. Our analysis reveals that efficiency strongly correlates with body mass, suggests that larger flying animals may face stronger selective pressure for high span efficiency. Furthermore, simple theoretical span efficiency predictions for gliding and rotating flight—derived from wing planform and theoretical models—are correlated empirical values enabling reliable predictions of span efficiency in species that have not been measured. As an example of this morphology-based theoretical prediction, we compare the orange oakleaf butterfly, which has a wing planform that closely resembles a leaf for cryptic camouflage, with the migratory monarch butterfly. The monarch butterfly has a substantially higher predicted efficiency, quantifying the aerodynamic cost associated with mimicry. Ultimately, this study sheds new light on the interplay between physical constraints and lineage-specific adaptive strategies in biological flight, while providing a versatile framework to evaluate an aspect of flight performance from wing morphology without the need for intensive wind tunnel experiments.