SA 3-speed - dropping gearing procrastination

[Jezston]

I've been running my Sturmey Archer 3-speed based road bike as a commuter for a couple of years now, with a 48t chainring and 18t sprocket. I feel this gearing is a little bit too high as I virtually never use the top gear, often feel 2nd is a touch too grindy and 3rd sometimes not low enough.

I need a new chainring, chain and sprocket as mine are now worn out, so was thinking of dropping the gearing.

I'm thinking of doing this gear dropping chainring side as I feel I just want it a tiny bit lower (kind of half a gear's different) not a fairly big jump that I suspect putting a bigger sprocket on will do, but not sure how far I should go - obviously it will be difficult and/or expensive to try different sizes so wonder if I can get any opinions on how some ratio changes will feel.

Current 48/18 = 2.66:1
Possible 48/19 = 2.53:1
Possible 47/18 = 2.61:1
Possible 46/18 = 2.55:1

How big a jump will these feel? Erring towards 46/18 as I guess going 0.1:1 down isn't going to feel dramatically different, but that 0.15:1 might feel more like a whole gear step down? Agh, wish there was a way to try this without having to spend loads of money on chainrings!

 

[GrumpyGregry]

sturmey rear cogs are dirt cheap. (relatively speaking)

 

[RecordAceFromNew]

For most people the risk of guessing could be minimised by figuring out what the highest or lowest gear inch they would like to have, by e.g. comparing with specific gearing they have on a geared bike.

Currently assuming you have 27" nominal sized wheels your high/direct drive/low are 96", 72" and 54" respectively assuming you have a SA hub like the AW with 1.333 / 1 / 0.75 drives. I suspect most people would consider that well high even in London. I also suspect a reduction of 4% or so (by using a 46T chainwheel) is likely too little.

Anyhow suppose you want an 85" high the way to work out the rest is direct drive would then be 85"/1.333 or 64" while low is 64" * 0.75 or 48".

To calculate what the chainring and sprocket size need to be all one needs to do is to use either of the following formulae:
Chainring size = Direct Drive Gear Inch / 27" * Sprocket Size or
Sprocket size = 27" / Direct Drive Gear Inch * Chainring size

So assuming the retention of the 18T sprocket, the new chainring to achieve an 85" high above should be 64"/27" * 18T or 42.6T, which you can round up or down as you wish.