Hey all,

call me stupid, but i went ahead anyways and built my first fixed gear from a bike that has vertical dropouts with very little room to give. Amazingly, my first try with cog sizes fit perfectly. 18 rear, 42 front. It works, but its a little bit too easy and Im thinking　to up the size of the front cog. I thought, before i go and buy a bunch of cogs and find out they wont fit, there must be some sort of calculation i can run to find out which ones would fit. If such a calculation existed, it would be much easier making good single speeds from any frame, obviously a big help, so bear with me.

right now, i have 18 in the rear, and 42 in the front, for a total of 60.
next, i counted my number of tooth spaces in my chain: 93
so, given that the length of the frame is irrelevent since it is constant, i figured i coudl just simply use a comparative fraction. number of teeth/ number of tooth spaces in chain: 60/93
next, i divided 60/93 and got 0.6452
then, i took 0.6452 and multiplied it by the total number of teeth i plan to have with a different cog.
So, for example, if i wanted to run a 48 tooth cog in the front, boosting my total number of teeth to 66,
i would multiply 0.6452 x 66 and get 42.581
If my calculation is correct, since my variable is the chain length, this amount of teeth would have roughly 0.581 difference in chain length (too short or too long). In this calculation, an answer like xx.5 would be the worst, and xx.1 or xx.9 would be pretty good, but idealy, the best would be an even number with no decimal places. Get it? I ran a bunch of numbers and found that for my setup, the best fitting size up would be a 47 tooth cog (65 total teeth). 0.6452 x 65 = 41.935 The would only be a 0.065 difference, which i could probably deal with.

Does this make sence to anyone??? Im not a engineer, and pretty bad a math, but i have put a lot of thought into this and would really appreciate some feedback.

Thats too much for me to read.

Try the magic gear calculator to figure it out.

it might be close enough, but it does not take into account the longer run of chain between the front chain ring and the rear cog, as you increase the size of the chainring. Draw a scale picture with the different combinations of teeth, and you can measure the straight portions....to capture this impact

I agree with pyze - use the calculator. At best your math would only work on that exact frame.

chain length = trial and error

or

measuring up against your old chain.

i just put it on and take out links untill it fits. it works.