Quote Originally Posted by wildeny View Post
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. Two should be equal to each other under the ideal condition.

Torque = force * lever arm, which leads us to

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).
As an engineer I am pretty comfortable with the physics of torque. But I think you may be a little confused in your explanation here. In ideal conditions I think you would certainly NOT want the torque created by your feet and the torque created by the rolling friction to be equal, or you would not overcome the rolling friction and you wouldn't go anywhere!

You then give a formula where you insert the gain ratio so that the torque produced by the cyclist is equal to the gain ratio multiplied by the torque from rolling friction. So what you say there is that in ideal cases they are NOT equal? Which is it?

Also I think that you may be a little confused - gear inch/metre does not tell you how far one revolution takes you because the formula does not involve pi, which is required to develop the circumference of the wheel from the diameter.

Wildeny, I don't disagree with you that Sheldon's formula is great and I am quite comfortable with the physics involved in its many applications. But the OP just wanted to know which gear was higher, not compare different rolilng frictions, surfaces etc, so gear inches is just a simpler method of doing what she wanted without all the rocket science!