Gear Ratios

[wildeny]

I'm not sure why anybody would prefer a "dimensionless" answer because frankly a dimension is much more meaningful in outright terms.

A dimensionless quantity is more universal. No matter where you live, you get the same gain ratio from the same configuration.

In US/UK, you use gear inch: gear size = Wheel diameter (in inch) x Chainring teeth/Cassette teeth
but people in other places may use gear meter, which is the "roll-out" distance (or gear centimeter )

Gain ratio is about leverage. More precisely, the torque produce by your feet vs the torque by the rolling friction. The minimum torque you need to apply is equal to the torque by the rolling friction.

Torque = force * lever arm, which leads us to the minimum force you apply:

F_c = gain ratio * F_r [c = cyclist, r = rolling friction]

For the same rolling friction, the higher the gain ratio, the more forceful your pedaling. (or just consider F_r = 1)

This combines with the cadence is related to your power (that's what the power meter measures).

Gear inch/Gear meter tells you how far you can go when pedal one turn, while gain ratio tells you how much effort(work) you make(do).

However, no matter which method you use for gear size, all of them don't consider the effect from the tire (surface roughness, pressure).