I tried building a "pad" that would allow my Kerbals to fly around at moderate altitudes, hovering in the air; something like a quadcopter, just with jet engines.
I made sure the center of thrust is above the center of mass, that way the thing should be self-stabilizing. Well, it isn't. It flips over a few seconds after take-off.
I thought the center of mass may be still too high. I strapped the huge Roxkomax X200-64 fuel tank on the bottom to weigh it down, and still - it managed to take off despite the very heavy load, and promptly flipped over.
What should I do for a hovering contraption so that it can hover unattended without flipping over?
11 Answer
You've managed to stumble upon the pendulum rocket fallacy. Don't worry, you're in good company; Robert Goddard, the inventor of the liquid-fueled rocket, famously made the same mistake.
Here's a nice video by Scott Manley demonstrating the issue:
Scott's video also suggests one potential solution; if you can mount your engines on flexible supports, in such a way that they'll tend to preferentially flex towards the ground, you may be able to get your vehicle to stay upright. It may be somewhat difficult to plan a configuration that will work, though.
Alternatively, just turn on the SAS and make sure your vehicle has some control mechanism (gimbaled engines, RCS thrusters or reaction wheels; you probably don't want aerodynamic surfaces if you're trying to hover) for it to steer with. Note that older KSP versions had a bug where gimbaled engines mounted above the center of mass would steer the wrong way. That should be fixed in KSP 1.0, however.
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