Originally Posted by
hobkirk
Hmm right back at you, Danno. Thoughtful answer. I will need to think about this and examine the geometry. Your logic seems reasonable, although I am not sure where "bending the chain 4x per revolution" comes from - wouldn't extreme cross-chaining would be 34/11 or 53/28? And is the wear most evident on the chain, gears, or rings? Or all? And if gears, on the smallest and/or largest?
Imagine that looking down over the chain & rings from above. All of the chainrings and cogs are in parallel planes. When the chainring and cog are in the exact same plane, then there's no cross-chainring.
In the extreme cases of cross-chainring, imagine 4 points where the chain meets and releases from a cog & chainring. This is where it bends. The parts on the cog/chainring themselves will be perfectly straight while the parts in between will have to go through a lateral bend in order to reach the out-of-plane next part.
The wear on the rings won't be significant relative to the wear that occurs from shifting. The chain is bent even more severely then and there are spots where the chain-plates meets the teeth at an angle. This cuts the corners of the teeth and removes some material. You can really see this occur when you install a brand-new chainring. SuperGlide chainrings have this wear "pre-cut" into the rings at certain spots to help improve shifting.