Well i got home and was motivated to check out the gear situation on my Pista but my new brand spankin' new Colnago fork was waiting for me so i'm a little preoccupied right now. I did however manage to drag myself away from my new best friend for a few minutes to do some measuring.
I think the 1/8" theory is a little flawed after measuring some things. It is true that the diameter of a cog changes by 1/8" per tooth. Here are my measurements for what I had lying around:
14T cog = 2 1/2"
16T cog = 2 3/4"
Difference = 2/8"
I then measured the dropout and the track nut to find the useable amount of space in the dropout and this is what I found:
Dropout = a little more than 1 1/2" so for arguments sake I will say 1 5/8"
Track nut = 3/4" diameter
Useable dropout space = 1"
In my calculation of useable space I figured that you wouldn't want any of the track nut hanging out the back of the dropout so I subtracted half of the diameter of the track nut from the total. I also figured you could get the track nut a little farther forward in the dropout so I only subtracted 1/4" for the front.
If you draw a line that is 1" long and mark it at each 1/8" you get a total of 9 marks. By the 1/8" theory you would be able to fit 9 different gears in my droputs without lengthening the chain!
3cm sounds a little more reasonable because 3cm is equal to 1.18" which would mean I could squeeze 3 different gears in if I was lucky.
This has piqued my interest but I lack the know-how and the motivation to dust off the scientific calculator to figure out how to come up with a formula for exactly how far 1 tooth moves the axle in the dropout, any ideas? Any engineers out there?