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Short of try it and see, anyway to calculate chain lengths based on number of teeth?
Running 32/20 just now and wondering what larger chainring/smaller sprocket combo would run with exact same (or near as damnit) chain.
I.e. Higher gearing but same chain length
I love maths!!
Inexact geometry would say that the top and bottom runs are going to be broadly the same for both from 12 o clock to 12 o clock on the F&R rings (and 6 o'c to 6 o'c on the bottom) - the chainstay distance from centre of BB to centre of axle is a constant (but there is a bit of triangulation to take into account - more of that later*).
Then you have the chain running over half of each ring at F&R
So 32:20 - you have 16T at the front (which we'll say = F/2) plus 10T at the rear (= R/2) = 26T
If you change the rings, the top and bottom runs will be still broadly the same, so you just need your rings to meet the same equation, F/2 + R/2 = 26, F+R = 52
So next obvious one would be 34:18, although you can get 33T fronts if you search hard enough so 33:19 is also do-able.
* clearly if F=R, then the top and bottom run are parallel and also equiv to the chainstay length. As F increases and so R decreases (since F+R is a constant, in this case 52), the length of the top and bottom runs increases in a pythagorean manner, where L^2 = C^2 + D^2 (L= length of chain, C= chainstay length and D is the difference in radius of the rings) - hence if D = 0, L = C; but as D increases with C being constant, so L increases as well. But what you're looking at is actually the difference in the radiuses as you change chainring sizes and by doing it one or two teeth at a time, the actual difference will be minor, and you'll compensate it by adjusting C with a chaintug or track ends or whatever, so in fact L remains constant while C changes.
TL:DR
try 34:18 or 33:19 if you can find a 33T front.
this might help
Oh god I'm 15 again and about to fail higher maths. Thanks (I think). Shall re-read many times!
Depends on the chainstay length as that'll affect the change in angle when going from medium-medium to large-small sprockets.
I just make sure the number of teeth add up to the same and hope there is a bit of slack to accomodate the wider angle of the bigger front ring.
On my singlespeed 29 plus i run it as a dingle so 32/20 for lumpy stuff and 34/18 for the 10 mile bimble to the lumpy stuff.