A team of mathematicians has determined the ideal wing shape for fast flapping – a discovery that promises better methods of extracting energy from water and increasing airspeed.
The work, published in the journal Proceedings of Royal Society A is based on a technique that mimics evolutionary biology to determine which structure gives the best tempo.
"We can simulate biological evolution. In the lab, make a population of wings of different shapes, let them compete with each other to achieve a desired goal, in this case speed, and then have the best wings grown "To make related forms even better," says Leif Ristroph, assistant professor at New York University's Courant Institute of Mathematical Sciences and senior author of the newspaper.
In these determinations, researchers conducted a series of experiments at NYU's Applied Math Lab. Here they created three-dimensionally printed wings that mechanically fluttered and ran against each other, with winners "bred" using an evolutionary or genetic algorithm to create ever-faster flyers.
In order to mimic this breeding process, the researchers began the experiment with 10 different wing shapes whose driving speed was measured. The algorithm then selected pairs of the fastest wings ("parents") and combined their attributes to create even faster "daughters", which were then 3-D printed and tested. They repeated this process to create 15 generations of wings, with each generation bringing off more progeny than the previous one.
"This" survival of the fastest "automatically discovers a fastest drop-shaped wing that manipulates the flows most effectively to generate thrust," explains Ristroph. "Because we explored a wide variety of shapes in our study, we were also able to pinpoint which aspects of the shape were most responsible for the strong performance of the fastest wings."
Their results showed that they were the fastest wing The shape has a wafer-thin trailing edge that helps to create strong swirls or swirling currents during beating. The wing leaves a trail of these vortices as it expels the fluid to propel forward.
"We view the work as a case study and proof of concept for a much broader class of complex technical problems, especially those that involve" objects in rivers, such as rivers. For example, optimizing the shape to minimize the resistance of a structure, "notes Ristroph." We believe that this could be used, for example, to optimize the shape of a structure for generating energy in water waves. "
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Improving the Driving Speed of a Floating Wing by Artificial Form Development, Royal Society A rspa.royalsocietypublishing.or … .1098 / rspa.2018.0375