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I'll dig out the code and post it tomorrow. Apologies in advance to anyone who tries to read it...
Either way it suggested that you could get up a 20% gradient with a 50/12 or something which I found a little hard to believe. I made it because I was wondering about the maximum gradient you could get up on a fixie/SS, given that the maximum torque you can apply is based on your body weight, and whether you could base your gear choice off that. There are a bunch of factors I didn't account for in my "model" though and I wonder whether anyone can devise anything better.
frankenbike-
So, my guess (and I've been drinking) is that the limit is when the vertical component of the propulsion (rider weight on the pedals causes bike to move forwards and up a slope) is counter balanced by the gain in gravitational potential energy from moving up the slope.
Lower gear = less forward motion (and therefore a smaller vertical component).
ICBA with the maths right now, will see if being sober in the morning helps.
Greenbank
Do share.