Crikey, this is getting heavy now.
The original question was:-
Q1. Help me settle an argument - is a diff ratio a function of the size of the crownwheel versus the size of the pinion?
A1. It is the number of teeth that determines the ratio, not diameters. Standard gears have a calculated diameter, but gear tooth geometry can be "corrected", for many reasons, but mainly small number of teeth, pinions are corrected positively for strength purposes, so this increases the outside diameter of the blank. Generally the wheel is corrected negatively, but not always. This would make the diameter smaller, so the proportion of the diameter of the gears would alter but the ratio stays the same as the number of teeth is the same.
Q2. And can you make the teeth on a pinion smaller without making the pinion smaller *or* increasing the number of teeth on the pinion?
A2. Yes, but you need to modify the wheel geometry to suit, you would alter the pitch. Then as you later said
"I mean the teeth on the pinion. I've been told that a pinion is always the same size, and that the teeth are simply made smaller without changing the number of teeth when mated to a crownwheel with more (and therefore smaller) teeth.
I argued that it's impossible to make the teeth smaller without either making the pinion smaller, or increasing the number of teeth (to take up the excess surface area created by making the teeth smaller). If you had a 10/50 ratio and changed the gears for a 10/52 set for the same diff, the pitch would change, the pinion would generally be slightly smaller, and the wheel larger, but you wouldn't be able to fit the 10t pinion, even in an emergency to the other set, as the geometry would be VERY wrong.
Your analogy to the fair ground ride is good, but those diameters (tyre and drum), are similar to the pitch diameters of gears, which is a point somewhere down the tooth. Usually about mid tooth depth, not the outside diameters.
All this said, I hope you won the argument
