How many chain links for a 47 tooth sprocket?

[Shaharidan]

I'm going to a 47 tooth rear sprocket, anyone know how much longer a chain I'll need?

Thanks,
Mike

 

[Formula390]

With a 15 front and 47 rear you would need 114 links according to my math:


So, to solve for a 520 chain for the 390 we would use:
C == Shaft Center to Center distance in Pitches (520 is a 1/2" pitch): 40.5
n == Sprocket Tooth Count: 15
N == Sprocket Tooth count: 47

So to solve for L:
(2*C) + ((N+n)/2) + (((N-n) / 2*Pi)^2) * (1/C))
(2*40.5)+ ((47+15)/2) + (((47-15) / 6.28)^2) * (1/40.5))
(81) + ((62) /2) + (((32) / 6.28)^2) * (0.024691358))
(81) + (31) + (( 5.09541401)^2) * (0.024691358))
81 + 31 + (( 25.964542172 ) * 0.024691358)
112 + (0.641099807)
112 + 0.641099807
112.0641099807
and of course, we have to round up to the next even because we can't run an odd number of links:
L = 114

It's close enough that you MIGHT get away with using a stretched out chain with 112 links, but 114 is the "correct" answer. Feel free to check my math... it's been a while since I've had to show my work for something like this. LOL

 

[Tom]

Wait, why cant we just slap the sprockets on and adjust the tension? I did so with a 41T rear. Was I supposed to change my chain length?

 

[Shaharidan]

Thanks Matt.

Tom,
It depends, if your chain is fairly new and can be adjusted correctly on the new sprocket then you're fine.
In my case I went with a larger sprocket and the chain no longer fit.
Also if you have a lot of miles on the chain and sprocket, it's best to replace everything otherwise stuff is liable to wear unevenly.

 

[Formula390]

Wait, why cant we just slap the sprockets on and adjust the tension? I did so with a 41T rear. Was I supposed to change my chain length?

If you've got the adjustment length left, then you don't NEED to remove links. There are many schools of thought on if you "should" or not, but basically it boils down to the resulting change in your axle to axle length. A longer wheelbase will impact the bike being able to flick as easily and the like. With a shorter chain, you've got a shorter wheelbase, basically... so by going with a smaller sprocket and needing to adjust the chain out further, you are effectively lengthening your wheelbase. You've certainly see the Busa dudes with their stretched out swingarms and massively long chains. An extreme example, but that's effectively what you did when you put the 41T on and left the chain length the same. The link count is more how you determine what the minimum number of links are required based on the wheel all the way forward (shortest). In general, for high maneuverability (aka racing) a shorter swingarm is your friend. If you are cruising, or straight line only racing (drag, speed runs on the salt, etc) then you want a long wheelbase because the longer the wheelbase means the bike is more stable in a straight line.

So, if you are going UP in sprocket size, and keep the same 15T front, you can go from a 43 to 46, and still run the stock 112 links. If you are going UP from 47T to 49T (114 links) or higher, or DOWN from 39-42 (110 links), you would theoretically need more or less links to have the "correct" length of chain, as per the calculations with a NEW chain.

Like I had said, if you are running a used chain which is stretched out some already, you MIGHT get away with running a 47T rear with 112 links. It's RIGHT on the border. That said, -=*I*=- most likely wouldn't do it, but it's in theory possible. It would wear the sprocket out faster, but you could possibly make it work, if maybe only for a race weekend.

I mean c'mon, who here among us as young lads HASN'T (at least strongly considered) pulled a few links out of our stretched out (beyond safely usable) chain to get some adjustment back in it and get that chain to last "just a wee bit longer until payday." LOL Let's see those Hands of Shame!!!