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God, this conversation again.
Spin works because if the magnus effect. When it spins sideways (on a sphere) the air wants to hold on to the surface. It is the angular velocity cross the velocity, which gives the bb an upward force. Having sideways spin on a bb (stupid) will curve your bb sideways. Having hopup and sideways spin will curve your bb diagonally.
As said before by a few people, the tk barrel creates a "vortex" of air around the edges of the barrel. This causes the bb to want to be in the center of the barrel more because it is pushed towards the center because that is the location of lowest energy. (potential)
As to the bb "spiraling", I don't see how this would be possible. That's like throwing a baseball with so much spin it comes back to you. With a frisbee, maybe.. with a bb ball or a bullet, no. If you're saying that the bb is spinning on two axes, then yes, but I don't know if this is possible. (hopup with rifling is still spin on one axis, but one that is diagonal) That means the spin of the bb is changing directions, and this would only work for something that looks like a gyroscope/gimble thing.
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