Originally Posted by
Toddorado
My thinking was that if you started with link 'A' and followed it around for one revolution of the chain, fewer teeth in the entire system would result in more time on the drive wheel.
It depends a bit on how particular you want to be. Basic statement is that the only thing "really" influencing your gear inches are the number of teeth on your chainwheel compared to the number of teeth on your sprocket(s). On top of that the only part of the chain that's actually doing any work is the part that's under tension.
If you would park your bike with the front wheel against a wall, get on the bike and apply pressure to the pedals as if you were riding you could actually cut the lower run of the chain and nothing much would happen.(assuming sprockets are in decent shape...) That static position would also tell you how many of the teeth you're actually using at any given time. How many teeth and links you have above those under tension doesn't matter directly.
But of course things aren't quite that simple. Efficency is influenced by the number of teeth you're using even if the gear inches remains the same. A top gear of 56/14 would be more efficient by parts of a percent or so than a 44/11 even if the ratio remains the same. It'd wear out slower too.
Why? Don't know really. One theory states that more power is lost the smaller the radius you force the chain to follow, another states that you get more squirming between the chain rollers and the tooth flanks with fewer teeth to take the strain.
Originally Posted by
Toddorado
I understand why 11T is now the norm instead of an even number, 10.
The explanation I've seen on that particular issue is that with the even numbered pulley the teeth would always line up with the same links, and since inner and outer links wear differently this made the even-toothed pulley wear out faster. With odd numbers the elongated links end up on alternate teeth making them last longer.
Originally Posted by
Toddorado
What if you began with a single speed bike.
A SS (correctly set up) is the most efficient example of a (chain) drive there is. No losses through planar misalignment of the chain, a minimum number of parts. Maybe the chain itself can be more efficient when it doesn't have to accomodate sideways bending.
Originally Posted by
Toddorado
...added a 5-speed cassette.
Using the 5-spd cassette would force you away from the perfect chainline for 4 of the available ratios. But dependent on riding conditions the rider may gain more from the selection of ratios than what is lost through a less efficient system.
Originally Posted by
Toddorado
Also add in a derailleur with 20T pulleys for the sake of argument. How would that differ from a system with 9T pulleys?
20T would mean more teeth to distribute wear over, and a bigger radius to bend the chain around, both are potential advantages.