Inspired by this Grand Theft Auto gif, an aircraft with its engines initially idling is dropped from a high altitude (such as from the top of a building) with no or minimal horizontal velocity. Can it successfully throttle up and fly to safety? How about for
Rather obviously, both of these situations are far from likely to occur. As a result, the following is just idle (but hopefully informed!) speculation — I don't recommend experiments!
If we assume that you’re a free-falling body, Newton (in the form of $v=u+at$) says that it’ll take about 1.8 seconds to reach that speed, and you’ll fall ($v^2=u^2+2as$) about 16 meters during that time.
Of course, you’ll be pointing nose down at the ground, accelerating, and needing to do something about it — which will take time, and, more importantly distance. But, in the grand scheme of sky-scrapers, mountains and cliffs, 16.2 m isn’t that high. Incidentally, for this reason, bungee launching is a traditional method of getting gliders airborne in parts of the world with big hills — a team of runners using glorified elastic bands shoot brave pilots into the blue yonder, as illustrated by the picture below (at the Long Mynd).
So, given that a hill is enough height for a sailplane to take off, possibly for a few hours on a good day, I’m reasonably sure that something like the John Hancock Centre would provide more than enough time for a pilot to recover from an odd attitude, loop forward to a nose-down dive, recover smoothly from it, and fly away (from the big building behind him).
The gif you linked to featured what looked a lot like a small private jet. I defer to the others on this site with a lot more turbofan experience than I, but I’ll just say this: given an hour that I spent in a 777 simulator, twenty minutes were spent going from “cold and dark” to pushback, I suspect you’d have a much harder time doing it. Of course, rapid engine starts are possible in some aircraft. It depends a lot on the exact circumstances you're asking (and passenger jets tend not to be designed for inverted flight, for example).
Unlike in a RC or a maple tree seed, recovering from zero-RPM rotor is not possible in a helicopter because the "driving region" of the rotor system can't produce enough rotation to generate lift in the "driven region."
In fact, once a heli rotor RPM is reduced below about 80%, it stops flying
Blade stop autos can be done with model helicopters, proving it is theoretically possible. There are a few differences in a model helicopters rotor design that make it more likely, but here is a video showing it done.
At 1:55 the blades are slowed to the point they are no longer spinning and the helicopter drops like a shot duck, until the operator reduces pitch enough to get them spinning again - without power.You'd probably not be able to physically withstand the stresses, but I think it's technically possible.
As long as you have enough altitude it's perfectly possible to pick up speed in a vertical or near-vertical dive in a fixed wing aircraft then convert that vertical speed into forward speed.
Red bull recently did a stunt where they landed a fixed wing plane on a skyscraper helipad and then took off again.
Since the helipad was small, the pilot wasn't able to gain much speed before leaving the helipad, so he dived picked up speed and then pulled out of the dive.
The plane was heavily customised for the stunt, a more normal plane would likely need substantially more altitude to acheive a similar feat.
In a fixed wing aircraft this is a common aerobatic maneuver called a tailslide. Many airplanes can safely perform this maneuver, and if you google around, you can easily find video.
