# Changing the rear sprocket size (single rear sprocket)

#### GuyBoden

##### Fat bloke, pedalling slowly and enjoying the ride.
I am trying to select a rear socket for my Wife's bike, so it is easier for her to pedal.

Currently my Wife's bike has a 45T front and a 18T rear sprocket.

The chainstay length is 435mm.

The current chain is 51 links (51inch), which includes about a 3/4 inch slack.

The bike has vertical drop outs, so there is no room for moving the wheel backward/forwards.

There is no chain tensioner on the bike and I don't really want to install one.

I've been using this chain length calculator:

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18T (Current sprocket)
For a 18T sprocket the recommendation is:
Recommended length = 51 inches or 51 links (Which is what is currently on the bike.)
Unrounded result = 50.2706255585656 inch
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22T
For a 22T sprocket the recommendation is:
Recommended length = 52 inches or 52 links
Unrounded result = 51.197128486344006 inch

Do you think the result for the 22T sprocket would work, with enough slack?
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24T
For a 24T sprocket the recommendation is:

Recommended length = 52 inches or 52 links
Unrounded result = 51.664740048919334 inch
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The 24T does not seem to have enough slack.
But, would a half link chain work with the 24T?

Subtract the Unrounded result from the Actual chain size give the slack.

52.5 - 51.67 = 0.83 inch slack

So, am I correct in thinking that a 52 link chain plus a half link would be ok for a 24T sprocket?

Thanks
Guy

#### rogerzilla

##### Legendary Member
You need to use a magic gear calculator - there are plenty on the Internet. They work up to a point; you have to change the chain sooner than normal as a small amount of chain elongation translates into a lot of slack. Half links give a bit more flexibility and are ok for lighter/less powerful riders.

OP

#### GuyBoden

##### Fat bloke, pedalling slowly and enjoying the ride.
Got a Half link chain and a 24T rear sprocket, been for a short ride, it seems to work very well..................

#### silva

##### Well-Known Member
Got a Half link chain and a 24T rear sprocket, been for a short ride, it seems to work very well..................

#### ColinJ

##### Puzzle game developer
Seconded!

I am thinking of trying a half link on my singlespeed bike. A new chain doesn't really need the chain tensioner. After a few hundred kms of use a fair amount of chain tensioning is needed. I reckon taking one full link out of the chain at that point and replacing it with a half-link might take up the slack.

(The chain runs quieter when the tensioner is slack and the chain is running almost straight.)

OP

#### GuyBoden

##### Fat bloke, pedalling slowly and enjoying the ride.
It's my wife's Alfine 8 geared hub, I changed to a larger sprocket size and used a half link chain.

All is fine, she's not complained and the chain has never come off, but it has got a bit more sag over time.

#### rogerzilla

##### Legendary Member
Half links work best when the rider is of modest power! Powerful riders, granny rings and steep hills can straighten out the links slightly, giving "real" chain stretch.

#### ColinJ

##### Puzzle game developer
Half links work best when the rider is of modest power! Powerful riders, granny rings and steep hills can straighten out the links slightly, giving "real" chain stretch.
Ah - probably not the best thing for a singlespeed bike sometimes used on 7-10% gradients by an 85 kg rider then! (I have to put an awful lot of force into the chain to get up those hills.)

PS Surely there is less strain on the chain in a granny gear - high cadence/low force? I am doing low cadence/high force when climbing in my 72" gear.

#### rogerzilla

##### Legendary Member
There's more leverage with a small ring (it's much smaller than the crank length). This is why MTBs had vertical dropouts before road bikes - the extra chain tension can pull the wheel over in horizontal dropouts.

#### Ajax Bay

##### Veteran
I am doing low cadence/high force when climbing in my 72" gear.
I am doing low cadence/high force when climbing (aren't we all), but in my 25" gear, and that gearing allows me to get up hard climbs (eg Hard Knott, Rosedale Chimney, Bwlch y Groes) without stalling.
I haven't measured the forces, but I'd assume one can apply a force of 1.5 x bodyweight on the pedal, and my crank is (more or less exactly) 3 x the radius of the inner ring (28t). That implies a tension in the chain of (for me @ 75kg) 1100N. Every tooth less than 30 on the chainring implies an increase in tension of 3+%. As @rogerzilla says this means an MTB chainset with a 22t inner ring results in a much higher chain tension ceteris paribus and therefore higher forward force on the rear wheel hub's right side.

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#### ColinJ

##### Puzzle game developer
I not only should have worked that out for myself, I actually already knew it but had forgotten... Lazy thinking on my part!

It probably also explains why it is much easier to get the rear wheel to slip on steep, damp roads when in a very low gear?

#### rogerzilla

##### Legendary Member
Well, chain tension and rear wheel torque are obviously related but rear sprocket size also comes into it.

On a fixie or singlespeed you can choose between something like 52 x 20 or 39 x 15. Same ratio, but they feel very different. The option with the bigger sprockets results in a higher chain speed and lower chain tension. It feels a lot smoother. The 39 x 15 option has more "bite" when accelerating and is lighter, but isn't as smooth (and is also less tolerant of a bit of eccentricity in components). It's a trade-off.

#### ColinJ

##### Puzzle game developer
Well, chain tension and rear wheel torque are obviously related but rear sprocket size also comes into it.

On a fixie or singlespeed you can choose between something like 52 x 20 or 39 x 15. Same ratio, but they feel very different. The option with the bigger sprockets results in a higher chain speed and lower chain tension. It feels a lot smoother. The 39 x 15 option has more "bite" when accelerating and is lighter, but isn't as smooth (and is also less tolerant of a bit of eccentricity in components). It's a trade-off.
Interesting... I actually had a singlespeed in the Midlands with a 39x15 gear. I now ride a different bike up here with 52x19 and I do prefer it. I know the ratio is slightly different, but I don't think it is that - it does feel better. I was surprised at how much better the bike feels with a new chain too. Chain wear seems to make more difference on the singlespeed than on my multi-geared bikes. I suspect that is because I hardly need the chain tensioner with a new chain so I am pretty much getting a direct run for the chain.

#### rogerzilla

##### Legendary Member
I ran 39 x 14 fixed for a while on an MTB frame (these have to use rather small rings because of chainstay clearance issues, unless you get one of those On-One hubs with a 50mm chainline) and it certainly felt "harder" and less smooth than a more conventionally-sized fixie setup.