How did extinct giant birds and pterosaurs fly? A comprehensive modeling approach to evaluate soaring performance - PubMed (original) (raw)

How did extinct giant birds and pterosaurs fly? A comprehensive modeling approach to evaluate soaring performance

Yusuke Goto et al. PNAS Nexus. 2022.

Abstract

The largest extinct volant birds (Pelagornis sandersi and Argentavis magnificens) and pterosaurs (Pteranodon and Quetzalcoatlus) are thought to have used wind-dependent soaring flight, similar to modern large birds. There are 2 types of soaring: thermal soaring, used by condors and frigatebirds, which involves the use of updrafts to ascend and then glide horizontally; and dynamic soaring, used by albatrosses, which involves the use of wind speed differences with height above the sea surface. Previous studies have suggested that P. sandersi used dynamic soaring, while A. magnificens and Quetzalcoatlus used thermal soaring. For Pteranodon, there is debate over whether they used dynamic or thermal soaring. However, the performance and wind speed requirements of dynamic and thermal soaring for these species have not yet been quantified comprehensively. We quantified these values using aerodynamic models and compared them with that of extant birds. For dynamic soaring, we quantified maximum travel speeds and maximum upwind speeds. For thermal soaring, we quantified the animal's sinking speed circling at a given radius and how far it could glide losing a given height. Our results confirmed those from previous studies that A. magnificens and Pteranodon used thermal soaring. Conversely, the results for P. sandersi and Quetzalcoatlus were contrary to those from previous studies. P. sandersi used thermal soaring, and Quetzalcoatlus had a poor ability both in dynamic and thermal soaring. Our results demonstrate the need for comprehensive assessments of performance and required wind conditions when estimating soaring styles of extinct flying species.

Keywords: birds; dynamic soaring; pterosaurs; thermal soaring; wind.

© The Author(s) 2022. Published by Oxford University Press on behalf of the National Academy of Sciences.

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Figures

Fig. 1.

Fig. 1.

A size comparison and soaring styles of extinct giant birds (P. sandersi and A. magnificens), pterosaurs (Pteranodon and Quetzalcoatlus), the largest extant dynamic soaring bird (wandering albatross), the largest extant thermal soaring terrestrial bird (California condor), a large extant thermal soaring seabird (magnificent frigatebird), and the heaviest extant volant bird (kori bustard). The icons indicate dynamic soarer, thermal soarer, and poor soarer, and summarize the main results of this study. The pink arrows indicate the transition from a previous expectation or hypothesis to the knowledge updated in this study.

Fig. 2.

Fig. 2.

Schematics of dynamic soaring and thermal soaring. (A) Example of a 3D track of dynamic soaring. Dynamic soaring species repeat an up and down process with a shallow S-shaped trajectory at the sea surface. By utilizing wind gradients, a species can fly without flapping. (B) Example of a 2D dynamic soaring trajectory of 1 soaring cycle. The travel speed averaged over 1 cycle is defined as the travel distance in 1 cycle (d) divided by the soaring period, and the upwind speed averaged over 1 cycle is defined as the upwind travel distance in 1 cycle (dUp) divided by the soaring period. (C) Schematic of a thermal soaring cycle. (D) In the soaring up phase, a species soars in a steady circle. When there is upward wind that is greater than a species’ sinking speed, the species can ascend in the thermal. The upward wind is stronger in the center of a thermal; therefore, achieving a small circle radius is advantageous for thermal soaring. (E) In the gliding phase, a species glides in a straight line. The rate of horizontal speed to the sinking speed is equal to the rate of horizontal distance traveled to the height lost.

Fig. 3.

Fig. 3.

Wind shear models explored in this study. (A) Logarithmic wind gradient model. The wind speed at height 10 m was defined as _W_10. (B) Sigmoidal wind shear model with a wind shear thickness of 7 m (δ = 7/6) and a shear height (_h_w) of 1, 3, or 5 m. (C) Sigmoidal wind shear model with a wind shear thickness of 3 m (δ = 3/6) and a shear height of 1, 3, or 5 m. The maximum wind speed of the sigmoidal model is represented as Wmax. (D) Schematic of a soaring bird. Its height from the sea surface is represented as z and the height of the wingtip is represented as zwing. We constrained the models so that the wing tip did not touch the sea surface, i.e. _z_wing ≥ 0.

Fig. 4.

Fig. 4.

Minimum required wind speeds and dynamic soaring performances of extinct and extant animals. (A) Results of the logarithmic wind model. (B) Results of the sigmoidal wind model with a wind shear thickness of 7 m (δ = 7/6) and wind shear height (_h_w) of 3 m. The first row shows the minimum required wind speed for sustainable dynamic soaring. The second row shows the maximum travel speed averaged over 1 soaring cycle, in response to wind speed. The third row shows the maximum upwind speed averaged over 1 soaring cycle, in response to wind speed.

Fig. 5.

Fig. 5.

Glide polars (A) and circling envelopes (B) of extinct species, extant thermal soaring species, and the kori bustard, the heaviest rarely flying bird. In (A), the maximum glide ratios of each species are shown on the right side of species names. Points represent the horizontal speed and sinking speed at the maximum glide ratio of each species. Gray lines represent glide ratios (5, 10, 15, 20, 25, and 30). (B) Shows circling envelopes defined as the minimum sinking speed against the circle radius. The left end of the curve is for a bank angle of 40°. The smaller the bank angle, the larger the circle radius. A linear wingspan reduction is assumed for birds and a fixed wingspan is assumed for pterosaurs. The lift coefficient of circling envelope (formula image) is the maximum lift coefficient (1.8 for birds and 2.0 for pterosaurs).

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