How are Bamboo Copter Toys Stabilized?

[RubinLicht]

This is a Bamboo Copter: https://en.wikipedia.org/wiki/Bamboo-copter

So the key to building a stable one is that the "rod" part spun by the hand has to be heavy. However, a uniform force field cannot exert a torque on a rigid body. By elimination, I assume that external forces stabilize the system, so is it the "center of pressure"? the same as passively stabilized rockets? However, the fact that you want a heavier rod would seem to disagree with this, since a heavier rod pushes the CoM closer to the center of pressure at the center of the rod.

If so, does this mean that a bamboo copter that is spinning just fast enough to hover is not stable? or that a slower one (a falling bamboo copter) would flip over?

I don't have one on hand to test, and even if I did, I'm still more interested in the physical reasons for stability, since I'm trying to apply it to something else.

Thanks

 

[CWatters]

If the thing leans over it will move sideways through the air due to the inclined thrust. With a heavy rod the centre of area/drag is above the centre of mass and this causes a torque that acts to restore the rod to the vertical.