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New York Times

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The jellyfishlike flying machine. Leif Ristroph/New York University

With Math as Inspiration,

a New Form of Flyer

JAN. 15, 2014

Check out the video of the Ornithopter here: Ornithopter

When the Wright brothers pioneered powered flight, said Leif Ristroph, they “didn’t solve a lift problem; they solved a stability problem.” Dr. Ristroph, who works in applied mathematics at New York University’sCourant Institute, also solved a stability problem recently, with a small, hovering, flapping-wing flying machine that looks for all the world like a flying jellyfish.The lightweight, electrically powered machine, which seems to be the first of its kind, keeps itself right side up without the benefit of sensors or any righting mechanism. Its stability is completely a result of its shape and the movement of its three-inch wings.
As Dr. Ristroph and Stephen Childress, also at the Courant Institute, reported Wednesday in The Journal of the Royal Society Interface, their goal was to create a hovering flyer in a new form — not a helicopter, and not a robot based on reverse engineering insect flight. So they did not look to insects or birds, or to jellyfish for that matter, for inspiration. Instead, they first turned to mathematics and asked themselves, said Dr. Ristroph, “what is the simplest scheme that should generate upwards force?”

They began, he said, with “force diagrams in our heads.” But, he said, in his field pure calculations are not enough. “The aerodynamics involved in flapping wing flight are so complicated that we can’t just make predictions,” Dr. Ristroph said. Instead, he explained, they have to make physical models and see what happens. They calculated that pyramids and cones were the best shapes to try. Then they floated the actual objects in puffs of air to see how they behaved. Finally they constructed a machine with four flapping wings.
Only later, Dr. Ristroph said, did they realize that the ornithopter, as they call it, mimicked a jellyfish (although he noted that it is more difficult to hover in air than in water). As to the problem of stability, Dr. Ristroph said they solved it from an engineering perspective, but the math is still not settled. “We don’t really understand for the active flyers how this works,” he said. He and Dr. Childress published one mathematical model of how the flapping wings reorganize air flow to keep the ornithopter upright. But, Dr. Ristroph said, the model is not entirely satisfying. So, he said, “we are presenting this problem to the wider scientific community.” Dr. Ristroph said that he doesn’t know if the “jellyfishlike flying machine” will find a practical use. “If it’s going to be useful,” he said, “we’ll need to get engineers excited about it.”