Supplementary material from "Allometric Scales Underlying Animal Flight: A Mechanics-Based Approach"

Over the years, numerous studies have attempted to deduce scaling laws for the parameters associated with animal flight. These have been primarily empirical, and have, moreover, tended to focus on one of the three volant groups, viz., birds, bats or insects, with few attempts to seek common scaling behaviours. On the premise that there are underlying fundamental scales enabling animal flight regardless of species, a unified approach based on the mechanics of flight is developed. It is shown that the primary physical phenomena can be described in terms of 4 morphological parameters, the mass-scalings of which are allometric. Comparison with data demonstrates that the theoretical scales hold across a broad range of extant species spanning 8 orders of magnitude in size. The scales are found to also apply to extinct animals, suggesting that they are a necessary requirement for animal volancy. Additionally, the theory enables the determination of scales for other quantities, including the density, muscle strain and various aspects of the power. These scales are found to be consistent with previous, hitherto unexplained, observations. Finally, the present approach enables conclusions to be drawn regarding certain features of extinct animals, including their size and mode of flight.