Originally Posted by
tomato coupe
Every 16 tooth cog will rotate 360 degrees with the passage of 16 chain links, regardless of the depth of the valley between the teeth. Likewise, it will rotate exactly 1,000,000 times with the passage of 16,000,000 chain links. It is not possible to get anything other than 1,000,000 rotations with the passage of 16,000,000 chain links unless the chain skips.
That would be correct but has no bearing on the actual distance traveled. If you have a cog with 16t and a diameter of 4" (made up number, didn't measure) and a 16t cog with a diameter of 4.15" the there will be a rotation of 16 teeth but the chain will still have traveled a different distance to travel that same 16 teeth. As an extreme example, if you were to cut the valleys shallow enough to match the bottoms of a 17t cog, besides being hard to avoid skipping, the chain would still travel a distance equivalent to a 17t cog, which means the bike would travel the distance of a 17t cog. And we're not always talking about a tiny bit. Take a Dura Ace cog as the average and hold one up that isn't cut as deep and another that's cut more shallow and the difference between the two can be a several mm in diameter and that matters.