How does it hover upside down?
Okay, i'll preface this by saying i'm no expert in this area by any means. But the blades don't change rotation direction, they pivot around their own axis. The blades in a 'copter can tilt and each can rotate around it's Z axis. Imagine taking a ceiling fan, grabbing the end of the blade, and twisting it so the blade tilts in the opposite direction. That's what's happening with the RC helicopter. As for whether or not real helicopters are capable of inverted hover... I remember reading somewhere that the recently scraped Comanche was supposed to be capable of pretty impressive maneuvering such as inverted flight. I've seen helicopters do barrel rolls but as far as i'm aware there hasn't been any inverted flying helicopters. But, again, i don't know squat about helicopters.

Correct me if i'm wrong those in the know.
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