70sSanO

Is there a correct, or accepted, calculation for the percentage of change between 2 cogs? This question came about when I read an article that Pinion gearboxes have a consistent increase/decrease percent of change of 17.7%.

I've have always done a quick and dirty cog tooth difference/number of teeth of the "to" cog. 14t > 12t = 2/12 or 16.7%.

I've also seen the cog tooth difference/number of teeth of the "from" cog. 14t > 12t = 2/14 or 14.3%.

Sheldon Brown uses gear inches as a gear inch percentage using the from gear. Sheldon uses going from 80 GI to 88 GI which equals 110% or an incremental difference 10% increase. With an 8 GI difference it would seem that the 10% increase would be from the 80 GI.

Using a 40t chainring and 700x25, the 12t GI = 87.93 and the 14t GI = 75.37 which calculates to 116.7% or 16.7%.

The cog difference "from" and the GI "from" are 14.3% and 16.7%

Things seem to get more convoluted when calculating downshifting 12t > 14t.

John

Edit added: I also did calculations with gear ratios 40/14 (2.86:1) > 40/12 (3.33:1) and it is the same as GI, which makes sense based on how GI are calculated.

zaje

edit: wrong answer.

Andrew R Stewart 

Some of this seems to be a "which side of the mirror are you on" type of sound. I would just pick one formula and get comfy with that. Don't worry what others are doing unless you want to discuss with them gearing choices.

My method is to convert a gear combo into inches of development then calculate amounts of difference. Andy

FBinNY 

It's simple math, and whatever method you choose to use SHOULD yield the same result.

However, it's up to you whether to calculate the change up or down. For example 25 to 20 is 20% down, but going back is 25% up.

Keep in mind that smaller steps mean smaller differences, up vs. down. As a practical matter, these days steps are usually less than 10%, so it's reasonable to split the difference and round off. As long as you don't say anything, your legs will never know.

Hondo6

Ditto to what FBinNY and AndrewRStewart said above.

The calculated "answer" varies depending on whether you calculate percent increase or decrease (as FBinNY noted, 25/20 yields a different percentage change than 20/25 due to a different denominator for the fraction). But so long as you're consistent, your results will be directly comparable.

SoSmellyAir

Although 11 and 12 speed cassettes are now common, cassette ranges are also increasing. For example, for 11 speed road cassettes: (a) the currently largest 11-34 cassette has an 11T to 13T step, (b) the popular 11-32 cassette has a 14T to 16T step, and (c) even the previously more common (and smaller) Shimano 11-28 cassette has a 15T to 17T step. All of these steps >> 10%. The only two 11 speed road cassettes in which all steps < 12% (calculated using the physically larger cog as the denominator, which reduces the resulting %) are the 12-25 and the 12-28.

That is true. But your legs will definitely feel a shift that brings you outside your powerband. Instead of % increase or decrease in gear ratio, I find it more useful to (a) assume that I am pedaling at a cadence around the middle of my powerband (e.g., 80 rpm), then calculate the resulting cadence immediately after a gear shift (i.e., at the same speed and same wheel rpm). Of course, as a wimpy cyclist, I am sure that both my powerband and my optimal cadence decrease when I am heading uphill.

urbanknight

Yeah, I think what matters is what exactly you're comparing and why. That's why I like Sheldon Brown's gear calculator so much. You can get gain ratios, gear inches, meters development, and speed at various cadences.

KerryIrons

Absolutely! If you are calculating the decrease, you say so. If you are calculating the increase, you say so. This is (hopefully) grade school math.

wheelreason

LOL. -40 degrees is the same temperature in Celcius or Farenheit...

tFUnK

I start with the tallest gear (expressed as gear inches) and work down. I always felt that was more intuitive but you're right, one could start low and go high. But if we're talking overall range, that is just a ratio between the tallest gear and the smallest gear.

70sSanO

Thanks for all of the responses.

I agree that this discussion is somewhat academic and in the real world cog gapping comes down to rider preference. It is just simple math, but this thread did give me the light bulb moment.

In most cases an incremental increase or decrease when determined as a percentage it is an easy and straight forward calculation. If you ride at 10mph and increase by 2 mph the increase is a simple 20%. You pump up a tire to 100psi and a week later it is a 90psi, the decrease was 10%. The "from" is always a the denominator and the incremental (or "to" value) is always the numerator. Easy peasy. That works well because increase values are greater and decrease values are smaller.

But with a freewheel/cassette the smaller the cog the greater the increase in ratio, gear inches, and speed (at a consistent cadence). Going from a 14t to a 12t results in a decrease in cog teeth but an increase in ratio/gear inches. It would seem that using gear inches is the best method.

However, the result is the same to the gear inch "from" calculations if the difference in cog teeth is divided by the number of teeth in the "to" cog.

Upshifting 14t to 12t when 2 is divided by 12 (to) = 16.7% and 87.93 divided by 75.37 (from) = 1.167 (16.7%). It also works with downshifting 12t to 14t when 2 is divided by 14 (to) = 14.3% and 75.37 divided by 87.93 (from) = 0.857 (14.3%).

John