Gear Ratios

[wildeny]

pinkbikes, I do not disagree with your reason for using gear inch. As you already pointed out.

My previous reply was to explain the dimensionless quantity and the principle behind the gain ratio.

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?

Thanks for pointing it out. I should say that that is the minimum force you need to apply so that the wheels can start to turn. The minimum force is just to let the object remain at its status (if it's at rest, it's still at rest; if it's moving, it still moves with the same speed).

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.

I checked the definitions in "The Long Distance Cyclists’ Handbook" by Simon Doughty before writing the previous post. There it said the gear size in meters is "development", i.e. the "roll-out" distance. Also in Sheldon's page. Maybe I shouldn't use the term of gear meter here.

Even though gear inch does not include "pi" in the formula, it is based on the same idea without multiplying "pi". (imo, neglecting the multiplication of pi is jut to make the calculation easier)

What I'm trying to say is that gain ratio is not more complicate than gear inch. Their formulas only differ by the crank length, although the thinking is slightly different:

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).

That difference is important when comparing the gear inches from different bikes. Of course, for someone who always uses the same crank length, he/she doesn't need to consider the effect from the crank length, as you already mentioned. But, why not try to understand the effect of the crank length in gear size and know how to quantify it? [so that one can understand why his/her taller fellow can pedal with ease by the same gear inch]
(Note: the crank length is related to bike fitting too)

My intention in my first post was only to point out Sheldon's gain ratio. I'm sorry if my following explanations confuse people or make people feel more uncomfortable with gain ratio.