The answer is a resounding sorta. Scientists at Harvard have done that calculations and found that "the aerodynamics of a flexible, rippling sheet moving through a fluid" ... should make it "possible to make one that will stay aloft in air." However,
No such carpet is going to ferry people around, though. The researchers say that to stay afloat in air, a sheet measuring about 10 centimetres long and 0.1 millimetres thick would need to vibrate at about 10 hertz with an amplitude of about 0.25 millimetres. Making a heavier carpet 'fly' is not forbidden by the laws of physics. But the researchers say that their "computations and scaling laws suggest it will remain in the magical, mystical and virtual realm", as the engine driving the necessary vibrations would need to be so powerful.
How about those hover boards from Back to the Future then? I want one of those!
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it would be hard to design a flying carpet compared to a hover board. A flexible panel like a flying carpet is an aerodynamic nightmare.
When I was a child, I have a big carpet. And I play with it like aladdin. hehe...