AlexS wrote:
The lateral forces don't really come into play because the track pushes back as much as you are pushing into the track (else you would sink into or float above the track - hence there is no work done in that direction). It's the additional rolling resistance that matters and that's proportional to "weight" felt at the track, which of course varies depending on where you are on the track and COM velocity but can be considered to be an average value per lap. Add 20kg and all you do is up the average rolling resistance by whatever proportion 20kg is of your original mass.The conservative assumption you're making is only valid if the bank angle of the track is solely responsible for the centripetal force, in which case there is no lateral tire force on the track and the only extra multiplier is the increased normal load to crr as you mention.
But, If the required centripetal acceleration does not satisfy a_c = g*tan(track angle)= V^2/R, then there must be a lateral force on the tire otherwise the cyclist will not go through the ground obviously, but ride up or down the slope of the track. The better the cyclist is at keeping corrections smooth or minimal relative to the "conservative" requirement, the less "non-conservative" lateral force there will be on average and thus the more efficient they will be.
It will always take some work to turn, as the total energy of the cyclist is approximately 1/2 mV^2 + 1/2 (m*R^2) omega^2 for an instantaneous radius R, where R >> human length scales. The lowest energy trajectory would be something like the path a coin would take if thrown into a banked turn if it also left the banked turn in the desired trajectory, but this will not likely be the least distance path.
Edit - (Corrected Quote Blocks)