Humans have long drawn inspiration from bird wings to design mechanical ones—and now a team of mathematicians has taken this biomimicry to a new level. By 3-D-printing a variety of wing shapes, racing them in a laboratory and feeding the data into an algorithm that simulates evolution, the researchers found that a teardrop-shaped wing is fastest for both flapping flight and swimming.
This is the first time such a combined process has been used to find an optimal wing shape for fast flight, says Leif Ristroph, a mathematician at New York University’s Courant Institute of Mathematical Sciences and senior author of the new study.
Specific aspects of the teardrop shape help to make the optimal wing faster than its competitors, Ristroph says. These include its front-to-back asymmetry (when viewed from the side), characterized by a rounded front, forward placement of its thickest point and a slender, trailing tail. The razor-thin back edge resembles that of a bird wing, which typically narrows to a single feather. The finding suggests birds’ wings have evolved to be as thin as possible, the researchers write in the study, which was published in January in the Proceedings of the Royal Society A.
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Ristroph and his collaborators 3-D-printed a first “generation” of 10 plastic wings. They attached each wing to a motor-driven horizontal rod that caused it to flap up and down in water. They measured its swimming speed and extrapolated its flying speed. They tested a variety of shapes, including ones based on conventional airplane wings, flattened spheres and a peanutlike structure, Ristroph says.
The researchers fed the wing speed data into the evolutionary algorithm, which produced a second generation of eight “daughter” wings. Faster wing shapes were more likely to be passed on to the next generation, but the algorithm also allowed “mutations” that could yield new shapes. The two fastest wings from the first generation were also added to the second. The process of 3-D printing and laboratory racing was then repeated with the second generation of 10 wings. Altogether the researchers created 15 generations of wings. The fastest wing—the teardrop shape—evolved in the 11th generation and persisted in the following ones. The algorithm’s attempts to improve this shape in subsequent generations yielded ones that were too slender to 3-D-print.
The study “is tremendously interesting,” says Geoffrey Spedding, an aerospace engineer at the University of Southern California, who was not involved with the work. He notes that the optimal wing is “more like a fish fin,” which makes it better suited for swimming or propelling objects forward than for generating lift, as in airplane flight.
