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I'm try to compare the gear ratio of a IGH (Shimano Alfine 11) with a 10 speed cassette + 3 chainring setup.

I read Sheldon Brown's gain ratio definition.

I went to Sheldon Brown's gear calculator

I entered all the numbers from my bike and got this result

enter image description here

Here is my interpretation:

The first column group with heading 0.53 (low) shows the gear ratio of the 10x cassette and 3x chainwheel. Example: The number circled green is 34 / 11 = 3.1 Which to me is the gear ratio (correct me if I'm wrong). That first column group tells me the highest gear ratio is 3.8 (e.g. when going downhill), and the lowest gear ratio is 0.7 (not on the screenshot, e.g. when going steep uphill). The IGH has highest ratio 2.15 (not on the screenshot) and lowest ratio 0.53. To me that means on uphills I'll have an easier time with the IGH than with the cassette. However downhills I won't be able to go as fast with the IGH than with the cassette. Is my interpretation correct?

What do the other column groups mean? Consider the column group with heading 0.68 ? Where does the number circled in red come from (because 34 / 11 not equal 4.0) ?

Also where do the numbers 0.53, 0.68, 0.77 etc come from. I know they are from the Shimano specs. Are they really the gear ratios? Aren't the sizes of the single rear sprocket and the front chainwheel (that are installed on the bicycle) required to calculate the gear ratio of the IGH setup?

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    "0.53, 0.68, 0.77..." are the ratios built into an Alfine hub. You can't change the ratios, but you can change the chainring and cog, effectively moving the whole set of gears toward harder(higher) for going fast or easier(lower) for hills – Criggie Aug 21 '18 at 7:31
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I think you’ve told it to do an Alfine hub with all 3 chainrings and all 10 cassette sprockets, so the computer is obliging.

Just include one chainring and one sprocket value to get the Alfine table.

Then calculate another table with all 3chainrings and 10 sprockets but no Alfine 👍

You’ll get things more like this:

enter image description hereenter image description here

You’ll need to pick your own chainring and sprocket values for the Alfine, point being you can customise these to get the gearing you want. I put in random values (32,17) which give the Alfine something like the range of the 3x10 setup

Edit: a gain ratio of 1.9 may/will feel nothing like a gain ratio of 1.2 when you're climbing, so keep playing around with numbers for the IGH chainwheel and sprocket

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There are really two things to consider: can you get all the gear range you desire and what is the spacing between the gears? The Alfine has a range of just over a factor 4 from top to bottom and you can put that range anywhere you want by choosing the gears you put on it. The cassette you cite has a range of 3.3 all by itself and coupling it to any reasonable front triple will give a much wider range, say a factor 5. Do you need that range? I ride a 2x10 setup with 50/34 front and 12/30 rear which gives a range of 3.67. I don't miss a 50-11 combo which would increase my range. I might like a little lower gear at the bottom, but it hasn't been enough of a priority to do anything about. That would also give about a factor 4 range. Considering the overlap of the two chain rings I have effectively 13 different gears, so my spacing is on average closer than the Alfine. That hides the fact that some gaps are larger than others. In my cassette the gears go 14-15-17. The change from a one tooth gap to a two tooth gap is noticeable. The Alfine is more regularly spaced because they use so many more teeth that you can get the ratios desired. They are about a 13% increase for each gear which is almost as much as my 15/17 transition. I believe I would find the Alfine quite acceptable even though the gaps are a little large. If you need the range of the triple plus 11/36 I suspect you would be unhappy with the Alfine. You will be running out of gears at one end, the other, or both.

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To answer the questions properly

The 34/11=3.1 is a red herring. The 3.1 is the Gain Ratio, the whole ratio for each mm the pedal turns to each mm the bike moves. It's just coincidental that 34/11 is 3.1, resulting from the table doing the calculations effectively for a bike with the IGH strapped to the derailleur system.

The next interpretation is more like it, the higher the gain ratio, basically the harder the gear. Lower numbers give an easier time up hill. It's just that the numbers aren't correct yet. At the low end, small changes in gain ratio make for significant perceived differences, i.e. when you're running out of gears fast for that climb!

The 0.53, 0.68 numbers are multipliers for each of the IGH gears, think of them as gears 1 thru 11 for the Alfine. In the IGH table you'll see eleven of these headers, and one gain ratio for each.

The gain ratio circled in red is the gain ratio if you had gear two of the Alfine selected (0.68) and the 34/11 selected on the derailleur. At the same time.

Finalement, you do indeed need to specify the chain wheel and sprocket for the Alfine hub, putting their single values in to the calculator to make a separate table.

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