Originally Posted by Ken Cox
All skidding aside, I have a mechanical intuition that larger chainring and sprocket pairs have lower stresses and greater efficiencies. I say intuition because I can't prove it with numbers.
I believe this has been experimentally demonstrated.
Does the size of the gear pairs matter in all of this?
Nope. Assume the ring is x teeth, one cog is y teeth, and the other is z teeth. The first gear ratio can be expressed as x/y and the second as x/z. To compare the second gear to the first, we would look at (x/y)/(x/z). Expand this to get xz/xy. The x's cancel out and we have z/y.