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My calculation was purely based on a series of gear ratios. Torque at cranks creates torque at chainrings creates tension in the chain creates torque at the cog creates torque on the ground through the back wheel. The upward component of the force on the ground from the back wheel has to offset the weight of rider and bike.
You could almost certainly do the calculation with energy though... Perhaps comparing the GPE of the rider with the cranks parallel to the ground to GPE of rider and bike with the cranks perpendicular to the ground but further up the slope? That would give you a vertical ascent. Then you can derive a maximum gear ratio based on the ground covered at a given gradient. Interesting idea! I'd be keen to see what you find! Might even do some more calculations myself tomorrow.
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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.