Originally Posted by Kontact

In my example, the chainstays are essentially twisting into a helix by the alternating pedal strokes - clockwise, counterclockwise. That makes the chainstays shorter. So when the twist is taken out the chainstays elongate increasing the distance from the top of the cassette to the top of chainwheel. The rider is loading the chainwheel and the tire has traction on the road, so the only place the elongation can go is by pulling on the cassette cog and forcing the rest of the bike forward.

This doesn't do anything significantly different than an oval chainring in that it lowers the effective gearing at peak load and increases the effective gearing by adding to the amount of chain pulled by the chainwheel at low load. And that is a very simplified example of how a flexible bike stores and releases energy. Which is not "planing", but a contribution to the whole system (I would think). My Merlin does this in a fairly obvious way (to me) when climbing out of the saddle. I do not know if that means I experience planing per se, but I don't see why not.