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It doesn't feel possible that the propeller is enough to provide such forward motion that is also used to push the vehicle up

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Why not? That's exactly what happens in a plane (or a microlight, or powered parachute).

Well I'm by no means well versed in physics, but my mental model of lift would suggest wings + forward velocity generate a lot more than rotors + forward velocity, and that planes move a lot faster than autogyros, so there's more forward velocity to utilize for lift.

Given how much power appears to go into making helicopters rise, its surprising to see an autogyro do it without actually powering the main rotor.

(fwiw, I'm not arguing that I'm correct. obviously I'm wrong).

There is another push/pull propeller that moves plane forward and that one is driven by engine.

Well, the seeds of a maple tree fall a lot more slowly when they're rotating so clearly there's some kind of lift being generated. To fly you 'just' need to replicate that effect and forcibly push more air through the rotor than just gravity would.

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