Chain Ring/Cog impact on chain length.

bigW

Well-Known Member
#1
Super simple question that I think I had the wrong answer to:

What will the impact to chain length of switching the number of teeth on chain ring and/or cog? This question is important for single speeders like me who have to get it exactly right. I had always assumed that removing two teeth from either the cog or the chain ring would require removing a pair of links from the chain. However I just switched from 39x22 to 42x15 ( net down four teeth and knocked out four links from the chain only to discover that was twice as many as I should have done. 😡

Fortunately I had an extra chain to save the day but I struggled to think how removing four teeth would not shorten the chain by four ......

Eventually it occurred to me that the chain is only in contact with the ring/cog for 50% of the circumference so the addition/subtraction of a link only has 50% of the impact on the chain length.

Make sense? Alternate thoughts?

W
 

Patrick

aka Fidodie
Staff member
#2
mentally, you decreased teeth but increased the length of the hypotenuse of the triangles (symmetric about the center line of the drive train.)

imagine that if you ran 24x24 - the chain would be flat. then big ring, small cog, makes for a longer length to to get from the
cog to the ring. once there, it is a tooth count.

1567044009079.png
 
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Paul H

Fearless OOS Poser
#3
mentally, you decreased teeth but increased the length of the hypotenuse of the triangles (symmetric about the center line of the drive train.)

imagine that if you ran 24x24 - the chain would be flat, big ring, small cog, makes for a longer length to to get from the
cog to the ring. once there, it is a tooth count.

View attachment 103775
Sounds like you enjoyed this one....
 

Patrick

aka Fidodie
Staff member
#6
BTW - are you riding across the pine barrens with that? or are you just going animal?

that ratio is affecting my heart!
 

JDurk

Well-Known Member
#10
Super simple question that I think I had the wrong answer to:

What will the impact to chain length of switching the number of teeth on chain ring and/or cog? This question is important for single speeders like me who have to get it exactly right. I had always assumed that removing two teeth from either the cog or the chain ring would require removing a pair of links from the chain. However I just switched from 39x22 to 42x15 ( net down four teeth and knocked out four links from the chain only to discover that was twice as many as I should have done. 😡

Fortunately I had an extra chain to save the day but I struggled to think how removing four teeth would not shorten the chain by four ......

Eventually it occurred to me that the chain is only in contact with the ring/cog for 50% of the circumference so the addition/subtraction of a link only has 50% of the impact on the chain length.

Make sense? Alternate thoughts?

W
Any reason you didn't fit the old chain to the new chainring/cog to see how many to remove before breaking?
 

1speed

Incredibly profound yet fantastically flawed
#12
Not sure if you intended to say you won't adjust the stay length or not, but you can almost never guarantee your chain will fit different combinations cleanly without adjusting. There's a well known formula for this:

Let L = Chain Length, C = Chainstay length, F = # teeth on front ring, R = # teeth on cog. Then


L = 2*C + F/4 + R/4 +1

And most of that makes perfect sense at a quick glance, but that "+1" is where the practical problem presents itself if you are trying to apply this with no effective adjustments to C. All tensioning on a singlespeed involves adjusting C to some degree. The "+1" defines the tolerance - if you didn't have it, your chain might reach perfectly, but it could be an inner-to-inner link join, which is impossible - two inner links need to be joined by an outer link, thus "+1". But the moment you do this, you end up with an extra link leaving your tension too loose. So you need to adjust "C" with a maximum adjustment of one full link to ensure full tension if you've used the equation. How you adjust it depends on your bike - EBB, sliders, pivoting rockers, even "singulators" are all effectively doing the same thing: adjust the length of C necessary for proper tension. Typically, you wouldn't need to adjust the full extra link beyond the rest of the equation since most ratio changes fall somewhere between nice rational values of L, and some people like to use "half links" (which from what I hear is a recipe for disaster from a functional standpoint.) Of course, you always just can experiment with different lengths if you've got an easy set-up (like rear sliders or pivots - experimenting with an EBB can be a PIA), but if you start with this equation it can save you time.
 

Magic

Formerly 1sh0t1b33r
Team MTBNJ Halter's
#14
Not sure if you intended to say you won't adjust the stay length or not, but you can almost never guarantee your chain will fit different combinations cleanly without adjusting. There's a well known formula for this:

Let L = Chain Length, C = Chainstay length, F = # teeth on front ring, R = # teeth on cog. Then


L = 2*C + F/4 + R/4 +1

And most of that makes perfect sense at a quick glance, but that "+1" is where the practical problem presents itself if you are trying to apply this with no effective adjustments to C. All tensioning on a singlespeed involves adjusting C to some degree. The "+1" defines the tolerance - if you didn't have it, your chain might reach perfectly, but it could be an inner-to-inner link join, which is impossible - two inner links need to be joined by an outer link, thus "+1". But the moment you do this, you end up with an extra link leaving your tension too loose. So you need to adjust "C" with a maximum adjustment of one full link to ensure full tension if you've used the equation. How you adjust it depends on your bike - EBB, sliders, pivoting rockers, even "singulators" are all effectively doing the same thing: adjust the length of C necessary for proper tension. Typically, you wouldn't need to adjust the full extra link beyond the rest of the equation since most ratio changes fall somewhere between nice rational values of L, and some people like to use "half links" (which from what I hear is a recipe for disaster from a functional standpoint.) Of course, you always just can experiment with different lengths if you've got an easy set-up (like rear sliders or pivots - experimenting with an EBB can be a PIA), but if you start with this equation it can save you time.
I an neither confirm nor deny this math because math sucks, but this sounds better than whatever @Patrick came up with.
 

serviceguy

Well-Known Member
#18
Not sure if you intended to say you won't adjust the stay length or not, but you can almost never guarantee your chain will fit different combinations cleanly without adjusting. There's a well known formula for this:

Let L = Chain Length, C = Chainstay length, F = # teeth on front ring, R = # teeth on cog. Then


L = 2*C + F/4 + R/4 +1

And most of that makes perfect sense at a quick glance, but that "+1" is where the practical problem presents itself if you are trying to apply this with no effective adjustments to C. All tensioning on a singlespeed involves adjusting C to some degree. The "+1" defines the tolerance - if you didn't have it, your chain might reach perfectly, but it could be an inner-to-inner link join, which is impossible - two inner links need to be joined by an outer link, thus "+1". But the moment you do this, you end up with an extra link leaving your tension too loose. So you need to adjust "C" with a maximum adjustment of one full link to ensure full tension if you've used the equation. How you adjust it depends on your bike - EBB, sliders, pivoting rockers, even "singulators" are all effectively doing the same thing: adjust the length of C necessary for proper tension. Typically, you wouldn't need to adjust the full extra link beyond the rest of the equation since most ratio changes fall somewhere between nice rational values of L, and some people like to use "half links" (which from what I hear is a recipe for disaster from a functional standpoint.) Of course, you always just can experiment with different lengths if you've got an easy set-up (like rear sliders or pivots - experimenting with an EBB can be a PIA), but if you start with this equation it can save you time.
I have 2 questions:

a) what measuring unit do you use for the chainstay lenght ? Is it links?
b) why F/4 and not F/2, R/4 and not f/2 ? Is that to compensate the chain ring and cog radius that would be otherwise overlapping the chainstay lenght?
 

Patrick

aka Fidodie
Staff member
#19
I have 2 questions:

a) what measuring unit do you use for the chainstay lenght ? Is it links?
b) why F/4 and not F/2, R/4 and not f/2 ? Is that to compensate the chain ring and cog radius that would be otherwise overlapping the chainstay lenght?
full links, not half links ?

this formula fails as F and R diverge. but in most cases they aren't running 53x11......