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The reason why you would use a suction cup is because with no air between the cup and your surface, there's no air pressure, and you get 14 pounds/square inch pressing down on your cup, increasing the force of friction. All you need is a large suction cup and use a pneumatic cylinder to press the air out. As for why airplanes fly, it's mostly conservation of momentum with a little Bernoulli, according to my competent physics teacher. I'd use ansi art to illustrate but I suck at it. Basically, air flows into the turned wing and exerts a force on it up. As air travels down the back of a curved wing, again, conservation of momentum the wing must move up to have no momentum gain.
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