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Princeton's Magic Carpet
Princeton's magic carpet uses piezoelectrically deformed substrates to fly! Well, it just hovers for now.
"We use integrated piezoelectric actuators and sensors to demonstrate the propulsive force produced by controllable transverse traveling waves in a thin plastic sheet suspended in air above a flat surface, thus confirming the physical basis for a 'flying' carpet near a horizontal surface," wrote the three authors, Noah Jafferis, Howard Stone, and James Sturm. “Experiments are conducted to determine the dependence of the force on the height above the ground and the amplitude of the traveling wave, which qualitatively confirm previous theoretical predictions.”
The undulating ripples allow the sheet to move at a speed of a centimeter per second, and Jafferis believes it should be possible to increase the speed to about a meter per second...
The sheet hovers above the ground as electric ripples flow, moving air along its underside.

(Princeton's flying carpet)
SF fans still have their fingers crossed; this advance could lead to the hawking mats from Hyperion, the 1989 novel by Dan Simmons:
Dangerous to handle, a waste of shielded monofilaments, almost impossible to deal with in controlled airspace, hawking mats had become curiosities reserved for bedtime stories, museums, and a few colony worlds.
(Read more about Simmon's Hawking mat)
From Traveling wave-induced aerodynamic propulsive forces using piezoelectrically deformed substrates via Physorg.
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