Originally Posted by
One Wheel
If no motion happens, no work happens. If motion, then work. When running in sand, work is done to move the sand that does not contribute to moving the runner forward: that's an inefficiency. When rocking a spinning wheel, work is done to overcome the gyroscopic force and move the wheel side-to-side. That work does not contribute to moving the bike and rider forward, and it is an inefficiency.
But you are only rocking the bike to maintain a dynamic balance as you exert force on the pedals. If the gyroscopic force was higher then the bike would simply rock less. It might actually be more efficient in this regard. But to put it into context we are talking about transient forces in the order of 10-20N. They are inconsequential in balancing the bike.