Gear Ratios

[pinkbikes]

Sheldon's gain ratio takes the crank length into account. I think it's better than gear inch. Besides, it is dimensionless.

Sheldon's formula takes crank arm length into account and works on gain ratio, which gives the added benefit of taking into account the greater/lesser lever arm of longer/shorter cranks. Strictly speaking it sort of introduces a "feel meter" for two sets of identical gearing with different crank lengths.

I find this is only a useful add-on if you are using it compare perceived difficulty of the same gearing ratios on bikes with different lengths of crank arm. Which is of course completely valid and very useful, especially if you are thinking of changing your crank arm length and want to know how it may make your existing gearing "feel" compared to how it used to.

But if you have your set of gears already and you are already set up with a suitable crank arm length for your anatomy (or even have multiple bikes with the same length of crank arms) then all it adds is mathematical complexity and it obscures the straight comparison of the actual gear ratios on different bikes.

Don't get me wrong - Sheldon was an absolute genius and his formula has valid uses - but really most of the world talks gear inches when comparing apples with apples (even in Europe and Oz where metric is next to Godliness! Gear centimetres???).

I'm not sure why anybody would prefer a "dimensionless" answer because frankly a dimension is much more meaningful in outright terms. A gain ratio of 6.6 means very little unless you are comparing it to a gain ratio of 8.4 or 3.1. Whereas a 100inch gear is a gear where you will travel pi x 100inches for each time you turn your pedals through one rotation. And hell - that is a pretty long way whatever length your crank arm is!!!

So..... for the life of me I have always pondered why they didn't just slap the damned pi into the formula there and make the dimension of gear inches actually mean something more representative - like how many inches you will travel for the one full crank rotation (maths geek - quite the waste of time really to ponder these things)?

I guess it is just that the numbers would have been so much larger and the pi is only a constant anyway, so why bother? Hmm - still a waste of time to ponder.....