change sprocket or chainring to gear down?

[Euan Uzami]

if I go from an 18t to a 19t how far is it likely to move the wheel forwards by?

currently got a 48/18 which is 72", want to gear it down a bit, but not too much, and am slightly worried it might then sit right at the front of the dropouts and foul the mudguard, and putting an extra link in would be a bit of a PITA and I don't really want a string of powerlinks strung together.

so not sure if it's viable or would getting a 46t ring be better (albeit more expensive)

[Chris N]

A little less than 1/8", IIRC.  Easier and cheaper to change cogs than rings, and large ring/large cog is better than small ring/small cog.

[LittleWheelsandBig]

1 tooth = 0.5" chain length. The wheel will move forward half that, so 0.25".

[Euan Uzami]

ok cheers.

[jsabine]

Quarter of an inch or thereabouts ...

(One tooth difference; teeth are half an inch apart; quarter of an inch difference on both top and bottom run of chain.)

(The magic gear calculator at http://eehouse.org/fixin/fixmeup.php might be useful to confirm, though this isn't its intended purpose ...)

[Chris N]

Hmmm, I thought that because you are changing the circumference of the cog by 1/2", the centre-centre distance changes by less than half a pitch.

[alexb]

If you need new chainrings, the Stronglight 9/10 speed ones sold by Ribble and other places are very good and last really well.

[jsabine]

Hmmm, I thought that because you are changing the circumference of the cog by 1/2", the centre-centre distance changes by less than half a pitch.

I think you're right. Lazy repetition of a half-remembered rule of thumb on my part - actually doing the maths and reconfirming using the link I'd quoted suggests that your answer of a fraction under 1/8" is somewhat closer to the truth ...

[Jakob]

I was about to say...I go from 72" to 86" when changing to track config and certainly don't move the wheel 3-1/4"

[jsabine]

I was about to say...I go from 72" to 86" when changing to track config and certainly don't move the wheel 3-1/4"

You wouldn't even if I'd been right the first time - it's the difference in teeth that matters, not in gear inches.

(Now you'll tell me it actually is a 13 tooth difference, of course ... Serve me right for trying to be a smart arse.)

[Chris N]

Assuming the top and bottom runs of chain are parallel (i.e. the ring and cog are the same size) then:

Change in C-C distance in mm = (pi x difference in teeth x 12.7)/2

It's more complex than that though, because you need to take the change in angle of the chain in to account as you change the size of the cog or ring.  I'm sure I could work it out, but it might take a while.  Probably easier just to draw it in CAD.

[Euan Uzami]

Assuming the top and bottom runs of chain are parallel (i.e. the ring and cog are the same size) then:

Change in C-C distance in mm = (pi x difference in teeth x 12.7)/2

It's more complex than that though, because you need to take the change in angle of the chain in to account as you change the size of the cog or ring.  I'm sure I could work it out, but it might take a while.  Probably easier just to draw it in CAD.

I can't help thinking that jsabine is right in that it's equivalent to shortening the chain by exactly half a link, but I can't get it out of my head that that amount of shortening is "spread over the circumference of the sprocket AND the chainring."

And I can't get it out of my head that it's nothing to do with pi either since what if you tookthe link out of the MIDDLE of the chain?

it's worse than the monty hall paradox.

[Jakob]

I was about to say...I go from 72" to 86" when changing to track config and certainly don't move the wheel 3-1/4"

You wouldn't even if I'd been right the first time - it's the difference in teeth that matters, not in gear inches.

(Now you'll tell me it actually is a 13 tooth difference, of course ... Serve me right for trying to be a smart arse.)

Hah, you're right, sorry. It's a 5 tooth difference.

[Chris N]

I can't help thinking that jsabine is right in that it's equivalent to shortening the chain by exactly half a link, but I can't get it out of my head that that amount of shortening is "spread over the circumference of the sprocket AND the chainring."

Even more complicated than I thought: http://bicycles.stackexchange.com/questions/8608/what-would-be-the-definitive-formula-to-calculate-chainstay-length-from-sprock

And I can't get it out of my head that it's nothing to do with pi either since what if you tookthe link out of the MIDDLE of the chain?

If you take the link out of the middle of the chain then you're right, it's got nothing to do with pi.  But it's different to changing the number of teeth on the cog/ring.

it's worse than the monty hall paradox.

What's it got to do with marine biology?

[LittleWheelsandBig]

A calculation as easy as pi then?

[Euan Uzami]

i'll probably just try it   

[Nelson Longflap]

What a good question! I never realised it was so difficult.  My immediate answer was the same as LWAB's first response, above.

If we start by supposing the circumference of an 18T sprocket is 9" and that of a 19T sprocket is 9.5" (in practice this is a bit too much, what we need is the circumference around the chain rivets that is approximately halfway down the teeth of the sprocket, but I'll assume the error is negligible). It follows the difference in radius between 18T and 19T is (9.5 - 9)/2/PI or 1/4/PI = 0.08"

So I think the answer is that the wheel moves forward by the difference in radius of an 18T and 19T sprocket. The (fixed length) chain will just wrap to accommodate this difference.

Doesn't sound much does it? I'm not at all confident there isn't a mistake somewhere here.  Perhaps Ben T should just do it, take measurements and let us know; making sure there's no change in chain tension of course 

[Nelson Longflap]

PS I assume we are dealing with horizontal track ends here. Otherwise we'll have to measure the angle of slope of the fork ends and do some trigonometry.  Gulp!!

[jsabine]

Assuming the top and bottom runs of chain are parallel (i.e. the ring and cog are the same size) then:

Change in C-C distance in mm = (pi x difference in teeth x 12.7)/2

I think you've got pi in the wrong place there - that would give 19mm odd ... (Difference*12.7)/2pi gives about 2mm, which feels more like it - and is in line with the 0.08in suggested above by joro.

[Crumbling Nick]

Assuming the top and bottom runs of chain are parallel (i.e. the ring and cog are the same size) then:

and that they they stay the same size, which can't be true but is a small enough error that it's irrelevant to OP.

Change in C-C distance in mm = (pi x difference in teeth x 12.7)/2

Disagree here (that's the first time with Chris N). Change is (difference in teeth)/2 {because only half of each sprocket is involved} x (chain pitch in inches){one half}. Conversion to 20th century units needs multiplication by 25.4, but is optional.

It's more complex than that though, because you need to take the change in angle of the chain in to account as you change the size of the cog or ring.  I'm sure I could work it out, but it might take a while.  Probably easier just to draw it in CAD.

You need to learn to use a slide rule

[jsabine]

Change in C-C distance in mm = (pi x difference in teeth x 12.7)/2

Disagree here (that's the first time with Chris N). Change is (difference in teeth)/2 {because only half of each sprocket is involved} x (chain pitch in inches){one half}. Conversion to 20th century units needs multiplication by 25.4, but is optional.

Doesn't this take us back to 1/4"?

LWaB and I suggested this some way up the thread - I've been persuaded that I was wrong.

[Nelson Longflap]

I'm not at all confident there isn't a mistake somewhere here.

I was right to be unconfident.  Moving the wheel forward by 0.8" (*) will put the back of the 19T sprocket in the same place as the original 18T. But the chain has further to climb (and fall) as it wraps around the bigger sprocket.

Let's assume the chain wraps around half the sprocket, that would be 4.5" of chain around the 18T and 4.75" around the 19T, so we have an extra quarter inch of chain wrapped around the sprocket. I think this means the wheel has to go forward 0.25". So yes, I think we are back to quarter of an inch!

(*) sorry about the antediluvian unit of length. It seems to me the appropriate length unit here is the chain 

[Euan Uzami]

Well tried it and it is ever so slightly noticeable but not much at all.I would guess at an eighth to a quarter of an inch. Sorry that's not very scientific

[jsabine]

Let's assume the chain wraps around half the sprocket, that would be 4.5" of chain around the 18T and 4.75" around the 19T, so we have an extra quarter inch of chain wrapped around the sprocket. I think this means the wheel has to go forward 0.25". So yes, I think we are back to quarter of an inch!

Doesn't that work out as the wheel moving forward by 1/8"? There's an extra quarter of inch of chain wrapped around the socket, but this is taken up by both upper and lower runs of chain.

Well tried it and it is ever so slightly noticeable but not much at all.I would guess at an eighth to a quarter of an inch. Sorry that's not very scientific

Sounds like it's worked out though ...

(And I like the way your guess leaves the rest of us all still able to continue arguing.)

[Nelson Longflap]

Well tried it and it is ever so slightly noticeable but not much at all.I would guess at an eighth to a quarter of an inch. Sorry that's not very scientific

So we may conclude the answer to your OP is 'sprocket' 

You sure the chain wasn't a bit slack when you made your first measurement?