Many species of owl are able to hunt without being heard by their prey by suppressing the noise of their wings at sound frequencies above 1.6 kilohertz (kHz) - including the range at which human hearing is most sensitive.
Owl wing porosity (the quality that allows air to pass resistively through the wings) helps in suppressing noise.
Numerous aero-acoustic studies have examined the effect of wing porosity, inspired by the quiet plumage features of owls.
However, much less is known about how wing porosity affects the aerodynamics of these wings, which likely competes with the acoustic benefits of porosity.
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Their mathematical formula uses arbitrary realistic porosity distributions, which may be used in conjunction with an aero-acoustic theory, to determine the aerodynamic trade- off of porous wing designs.
The work, published in the journal Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, could ultimately be used to improve man-made aerodynamic design of wind turbines and specialised aircraft or autonomous drones, researchers said.
"Exploratory experimental work by other researchers has measured the noise and aerodynamics of airfoils constructed from various porous materials over a range of flow speeds," said Justin W Jaworski, assistant professor at Lehigh University.
"Our general result has the potential to be integrated into the aerodynamic/aero-acoustic design of the wings and blades of small air vehicles, wind turbines, or drones seeking to minimise their noise footprint through passive means," he said.