Optimizing Granny

Oct.23,2016 11m
Oct.mtd 142m ytd:2340

There's no time like a Steelers game to enjoy a nice quiet ride on local roads, which Frazz taught me a while ago.

I took the ECR out for a ride which involves a little bit of climbing. It's a fun bike and it works going uphill, but I found myself wishing for another level of Granny.

Gear Inches: TireDiameter x ChainRing Teeth / Cassette Teeth = _____

On my Surly LHT with 700Cx35 tires (27.2" outer diameter), my gear-inches calculation goes like this:
27.2 x 20 / 36 = 15.1 gear-inches, which is pretty low.

On my ECR with 29+ by 3inch tires (30.5" outer diameter), a 22/36 chainrings up front, and a 10-speed (11– 36t) cassette it looks like:
30.5 x 22 / 36 = 18.6 gear inches, which is still pretty low but not as low as I'm used to

So that's something that seems amenable to adaptation. The rear cassette is a Shimano HG50-10, 10-speed. I need to study what I can do with the rear cassette.
A 40-tooth cassette would get me to 16.8 gear-inches.
A 42-tooth cassette would get me to 15.97 gear-inches
A 44-tooth cassette would give me 15.25 gear-inches, which is very close to the LHT's 15.1

Or, attacking the front chainrings:
Replacing the 22-tooth with a 20-tooth, same cassette, would give me a 16.9 g-i granny.
20-tooth chain ring, 40-tooth cassette would give me a 15.25 g-i granny.

Documenting this for reference: rear derailleur Shimano DeoreLX RD-T670 SGS, 10-speed ;
front derailleur Shimano SLX FD-M676D, Problem Solvers direct mount adaptor(28.6);
crankset Surly O.D., 22/36t note: 64mm inner BCD and 104mm outer BCD