I have a 26 FS that was running 3×10.
On my default local trail, i did all the climbs in the middle ring 32T, and didnt use the bottom 2 sprockets of my 11-36 xt cassette. Its not the only place i ride, so when i went 1×10 i used a 34T Hope retainer ring and a 40t t-rex. It was great to ride, and i seldom bailed out into to 40T.
I then got a 650b frame, and when i built it up, i swapped the 1×10 drivetrain onto it. A trip to 7Stanes showed me that unless i was a bit less fit then i was in need of a slightly lower bottom gear as i was finding i was struggling to climb with my usual riding buddies.
Ive got a 29er thats going 1×10, so i started to do some ‘shed maths’.
I got all 3 wheelsets with their tyres fitted, and i measured the radius of each wheel in cm. I appreciate that rolling radius will alter when the rider is sat on the bike, but i chose to ignore it.
so, i got 34cm for a 26″ wheel, 36cm for a 650b wheel and 36cm for a 29er wheel.
using C=2×Pi x R, this gave the following wheel and tyre circumferences, for a 26″ wheel it was 213.6 cm, for a 650b it was 226.2cm and for a 29er it was 238.8cm.
so using equation for distance moved per crank revolution, = C x Fr ÷ Rr
on 26″ with 34Fr and 40 Rr, a crank revolution moves bike 181.6cm
on 650b, same gearing moves bike 192.3cm, however 32Fr and 40Rr moves the bike 180.9cm
and on the 29er 32Fr and 40Rr moves the bike 191.0cm, but order is restored with 30Fr and 40Rr, as this moves the bike 179.0cm
So im guessing i have just worked out what the rest of the world knew, but it was a joy that the experience of riding them tallied with the maths. However if id done the maths first i may not have bought so much redundant kit!