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Singlespeed & Fixed Gear "I still feel that variable gears are only for people over forty-five. Isn't it better to triumph by the strength of your muscles than by the artifice of a derailer? We are getting soft...As for me, give me a fixed gear!"-- Henri Desgrange (31 January 1865 - 16 August 1940)

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Old 01-12-05, 11:36 PM   #1
Ken Cox
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Cog Spread

If a person has two cogs on his rear hub, how great a tooth spread between the two cogs can he have with the same length chain: 16 and 17; 16 and 18; 16 and 19; or...?
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Old 01-13-05, 01:08 AM   #2
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depends on how long your rear dropouts are.
i only run a difference of 2 teeth on my wheel, on dropouts that are 3cm effective adjustment.
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Old 01-13-05, 01:47 AM   #3
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If you are riding with the tools needed to flip your wheel around, why can't you carry a little chain tool and a few links, too? If you don't plan to make the switch on the fly, why care?
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Old 01-13-05, 06:48 AM   #4
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RobbieIG wrote:

"If you are riding with the tools needed to flip your wheel around, why can't you carry a little chain tool and a few links, too?"

Right now I ride a geared hybrid commuter.
I don't know about these things.
It hadn't occured to me that riders with two cogs would change their chain length.
I had assumed they would simply flip their wheel over and adjust the position of the axle in the dropouts for proper chain tension.

My question had to do with how great a spread in the number of teeth of the two cogs one could accomodate with typical horizontal dropouts, say as on a Bianchi Pista.

At 58 years of age, I presently follow a rather ambitious plan of exercise given to me by my physical therapist to overcome some earlier injuries.
The plan includes a lot of bike riding.
In order to keep myself motivated, I hold this image of a fixed gear bike out in front of me like a carrot.
This fixed gear carrot gets me up at 0430 in the morning and keeps me riding even in the snow and the ice.

I had hoped to start riding a fixed gear bike one day a week, starting some time this spring.
The key to my recovery and progress involves making slow, careful progress and listening to my body.
I had hoped to retain the ability to drop down in gear inches if my knees started to complain.

I can presently ride all day, anywhere in my community, at 72 inches without any pain issues.
I can do this about three days in a row before giving myself a break.
I can do a whole day at 81 inches without consequences, but not two days in a row.

Anyway, the fixed gear bike really motivates me.
I love beautiful machines and nothing, in my mind, compares in beauty to some of the fixed gear bikes I have seen in this forum.
I want to do this very much, and I want to do it the smart way without hurting myself.
I don't have too many more years left to do this.

So, if I have to carry addtional tools and some links, I will.
Or, if I can choose the right tooth spread, and carry fewer tools and parts and still meet my needs, I'll do that.

So, the question remains, on a bike like the Bianchi Pista, with a 48 tooth chain ring, how much of a tooth spread could I accomodate by moving the axle fore and aft?
I can figure it out myself, I guess, when I get the bike.
Maybe I can figure it out right now.
I understand from this forum that one tooth on a cog equals 1/8 inch axle travel.
I suppose then, I would build a chain that gave me the most rearward possible axle position in my drop outs, and then measure how far I could still move the axle forward, in inches, and divide by eight.
That would tell me how many more teeth I could have on my other cog.
Does that sound right?
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Old 01-13-05, 07:02 AM   #5
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I have set up a rear hub with a 16 and 18 tooth cog. I set the chain with the 18 tooth and the rear hub mounted close to the front of the dropout. When the wheel is flipped the hub only moves back about 1/2". If the bike had a rear brake it would be a drag. But without a rear brake it's a piece of pie.

Tony
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Old 01-13-05, 08:13 AM   #6
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Quote:
Originally Posted by Ken Cox
If a person has two cogs on his rear hub, how great a tooth spread between the two cogs can he have with the same length chain: 16 and 17; 16 and 18; 16 and 19; or...?
one tooth moves axle exactly 1/8", 2=1/4", 4=1/2", and so on. so if your drop-outs or track ends are an inch long, they will be able to take max 4, but 3 is probably more realistic. just measure the length of your track-ends, drop-outs, and subtract your axle width, then you know how much difference your bike can take.
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Old 01-13-05, 11:13 AM   #7
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another option is to set up your wheel with whatever cogs you want, and use a connex chain. figure out how much extra chain you need for the larger cog, and make up a little section of chain that long, with a connex link on it.
then, when you flip your wheel over just add in that length of chain, easy peasy, and no chain tool needed.
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Old 01-13-05, 11:26 AM   #8
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Or, set up a double front chainring and then use spacers and redishing on the rear hub so that you can get a straight chainline while running a different gear ratio with the same number of teeth. So, for example, you could run a 14t and 16t cog in back, and a 44t and 42t ring in the front.

(I'm actually not sure this is a useful idea.)
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Old 01-13-05, 02:16 PM   #9
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KC-

First off, congratulations on your interest in FG. I think you will find it to be the most satisfying bike riding experience of you life.

I think that I can safely get a 3 tooth difference from 15 to 18 on my Pista (48T front) without adjusting the chain length but I'm not sure right now. I will have to check when I get home. There is something that you should consider if you are going to run two fixed cogs:

A lot of Track hubs are inexplicably designed to accept a fixed cog on one side and a freewheel on the other(or two freewheels but not two fixed cogs), including the hub on the stock wheel of a Bianchi Pista. These are commonly referred to fixed/free flip/flop hubs. To run the setup you are speaking of you would need a fixed/fixed flip/flop hub which limits your options. You can go with Phil Wood or Shimano Dura Ace and break the bank or Surly which is significantly cheaper and the people in this forum will praise them up and down the street.

In any case you will need to purchase a rear wheel which can cost some $.

Or if your riding is going to be really low impact you can have a bum bike fixed setup(fixed cog lotsa locktite and a BB lockring) on the freewheel side of the stock Bianchi wheel. This may be dangerous and since you are a beginner I wouldn't recommend... although some would say you wouldn't have a problem.

Good Luck!
Neal
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Old 01-13-05, 02:35 PM   #10
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One thing you might want to consider is that with the fixed/free option you can give yourself coasting on the easier gear, which, if you really want to rest, is where its at. An easier uphill gear can turn into a leg mangling spinfest downhill.
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Old 01-13-05, 02:53 PM   #11
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Ken..

Nice to have you around. Proud of you for your upcoming fitness goals.

On your pista, are you rockin' a hub with two sides, both fixed? fixed/freewheel?

There's gotta be some super cheap chains out there that have master links. These allow removal/installation of chains with minimal tools. An easy fix to your "cog spread" dillemma would be to simply carry an additional chain in a zip loc bag.

Now, perhaps I misinterpreted your question. Are you interested in changing gear ratios while out on a ride? Are you interested in changing gear ratios throughout the week? Each scenario could have a completely different solution.

You could always be on the lookout for a cheap second wheel, too. In the fixed world, its always worth having an extra rear wheel...and chain...and cog.
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Old 01-13-05, 03:11 PM   #12
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Wow.
A person never knows how much he has to learn until he starts to learn it.

I don't have a fixed gear bike, yet.

I had thought about trying to put together a cost-effective Steamroller, but it kept coming out to more money than I expected.
My son suggested a Bianchi Pista and upgrading the parts as they wore out.
That made sense to me, but what do I know?

I had thought of the Pista with two cogs because, even though I have practiced riding around town in one gear, I have had the advantage of free wheeling and I didn't know how much that might have enabled me to pull more gear inches than I really could.
So, I thought, since the Pista had two sides (I didn't know one side favored a freewheel) I could have the option of an easier gear to learn with, and, similarly, an easy gear to get me home from work if my knees complained.

My physical therapist and my knee doc think I can do this if I approach it very carefully.
I just want to stack the deck for success.
Thechamp's post got me to thinking a freewheel option in the beginning might serve me very well on the careful side.

Many good options presented and much to learn.
Thanks.

I cannot remember anything that has captured my imagionation as much as has this fixed gear bike idea (I mean, other than girls in my younger days).
The concept and the bikes themselves radiate beauty.
It amazes me how many variations riders can come up with such a simple idea.
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Old 01-13-05, 03:16 PM   #13
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Quote:
Originally Posted by Ken Cox
Wow.

Thechamp's post got me to thinking a freewheel option in the beginning might serve me very well on the careful side....
that would probably be the best option, (assuming you're putting a brake on there anyways), just about every basic stock track bikes such as the pista comes with the rear hub as a fixed and then freewheel on the other side
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Old 01-13-05, 03:22 PM   #14
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Quote:
Originally Posted by Ken Cox
I cannot remember anything that has captured my imagionation as much as has this fixed gear bike idea (I mean, other than girls in my younger days).
The concept and the bikes themselves radiate beauty.
It amazes me how many variations riders can come up with such a simple idea.
It amazes me that in the world of 10 speed durace, campy shifty crap, and carpet fiber shiz bikes there are plenty of people content with riding a 1 speed fixed gear steel bike, just as they did 100 years ago...
Makes you wonder about the value of technology.
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Old 01-13-05, 03:25 PM   #15
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Quote:
Originally Posted by VeganDave
that would probably be the best option, (assuming you're putting a brake on there anyways), just about every basic stock track bikes such as the pista comes with the rear hub as a fixed and then freewheel on the other side
A small caveat with the bianchi pista track bike. The bike is not drilled for a rear brake, so you would have to drill the hole your self, or have your shop do it... some shops will not do it for liability reasons, like a shop near me when I inquired about having them drill the frame for a rear brake....
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Old 01-13-05, 04:59 PM   #16
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Well i got home and was motivated to check out the gear situation on my Pista but my new brand spankin' new Colnago fork was waiting for me so i'm a little preoccupied right now. I did however manage to drag myself away from my new best friend for a few minutes to do some measuring.

I think the 1/8" theory is a little flawed after measuring some things. It is true that the diameter of a cog changes by 1/8" per tooth. Here are my measurements for what I had lying around:

14T cog = 2 1/2"
16T cog = 2 3/4"

Difference = 2/8"

I then measured the dropout and the track nut to find the useable amount of space in the dropout and this is what I found:

Dropout = a little more than 1 1/2" so for arguments sake I will say 1 5/8"
Track nut = 3/4" diameter

Useable dropout space = 1"

In my calculation of useable space I figured that you wouldn't want any of the track nut hanging out the back of the dropout so I subtracted half of the diameter of the track nut from the total. I also figured you could get the track nut a little farther forward in the dropout so I only subtracted 1/4" for the front.

If you draw a line that is 1" long and mark it at each 1/8" you get a total of 9 marks. By the 1/8" theory you would be able to fit 9 different gears in my droputs without lengthening the chain!

3cm sounds a little more reasonable because 3cm is equal to 1.18" which would mean I could squeeze 3 different gears in if I was lucky.

This has piqued my interest but I lack the know-how and the motivation to dust off the scientific calculator to figure out how to come up with a formula for exactly how far 1 tooth moves the axle in the dropout, any ideas? Any engineers out there?
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Old 01-13-05, 05:09 PM   #17
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Originally Posted by jinx_removing

This has piqued my interest but I lack the know-how and the motivation to dust off the scientific calculator to figure out how to come up with a formula for exactly how far 1 tooth moves the axle in the dropout, any ideas? Any engineers out there?
1/8" of an inch.
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Old 01-13-05, 05:20 PM   #18
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Quote:
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1/8" of an inch.
So are you saying I can fit 9 different gears on my hub without lengthening my chain or are you saying my calculations were wrong?
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Old 01-13-05, 05:21 PM   #19
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Quote:
Originally Posted by BostonFixed
A small caveat with the bianchi pista track bike. The bike is not drilled for a rear brake, so you would have to drill the hole your self, or have your shop do it... some shops will not do it for liability reasons, like a shop near me when I inquired about having them drill the frame for a rear brake....
some shops will go as far as saying that they won't install a front brake on a track bike because the track forks aren't designed to take the intense forward/rearward stresses braking requires of forks.

but, anyways...

track bikes are a lot like a blind man in an orgy. you just gotta get into and feel your way around.
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Old 01-13-05, 05:32 PM   #20
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LOL well put. Where is my cane?
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Old 01-13-05, 06:05 PM   #21
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Meet my friend pi.

Each tooth adds 1/2" linearly (the length of half of a link). However that 1/2" is wrapped around a circle. If you remember from geometry class, the circumference of a circle is 2(pi)r where r is the radius. So if our first cog has circumference x, a cog with one more tooth will have circumference x+1/2".

2(pi)r = x
r = x/2(pi)
d = x/pi (the diameter of the cog)

2(pi)r' = x+0.5 (we'll assume x is a quantity in inches).
(x+0.5)/2(pi) = r' (the radius of the new cog)
(x+0.5)/pi = d' (the diameter of the new cog)

d' - d = (x+0.5)/pi - x/pi = 0.5/pi (difference in diameter which will be how much your chainline will shorten).

So now we've determined the difference in diameter between a cog and a cog with one more tooth to be (x+0.5/pi) - (x/pi) = 0.5/pi = some irrational number approximately 0.159 which is sort of close to 1/8 = 0.125.

Actually, maybe your chainline shortens by pi/4 as it's only affected by radial distance... right? So then it would be about 0.0796 which is not at all like 1/8.

Last edited by bostontrevor; 01-13-05 at 06:10 PM.
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Old 01-13-05, 06:09 PM   #22
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Quote:
Originally Posted by bostontrevor
Meet my friend pi.

Each tooth adds 1/2" linearly (the length of half of a link). However that 1/2" is wrapped around a circle. If you remember from geometry class, the circumference of a circle is 2(pi)r where r is the radius. So if our first cog has circumference x, a cog with one more tooth will have circumference x+1/2".

2(pi)r = x+0.5 (we'll assume x is a quantity in inches).
(x+0.5)/2(pi) = r (the radius of the new cog)
(x+0.5)/pi = d (the diameter of the new cog)

So now we've determined the difference in diameter between a cog and a cog with one more tooth to be (x+0.5/pi) - (x/pi) = 0.5/pi = some irrational number approximately 0.159 which is sort of close to 1/8 = 0.125.
You know the funny thing was I almost ended that post with "bostontrevor I know you know the answer." and then another cheesy Pi/Pie reference which you were so set up for but failed to deliver.

edit: even though the difference in diameter is 1/8" that does not necessarily mean that the axle moves 1/8" right?

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Old 01-13-05, 06:11 PM   #23
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Dammit! I blew it!

"Ok, let's assume that you start with a cherry pie with 6 slices. Now compare this to a peach pie with 7 slices...."

No good?
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Old 01-13-05, 06:13 PM   #24
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Anyhow, I just did a little back of the envelope with a 14 & 15 tooth cog and I'm pretty sure the right answer is each tooth adds pi/4 inches to your chain line.

Hmmm.. But it's also more complicated than that because the amount of chain you need is actually the boundary of the shape defined by the hemispheres of your cog and chainwheel connected by straight lines (the pie wedge). So the angles of that wedgish shape will change and it may not be a strictly pi/4 change.... Hmm...
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Old 01-13-05, 06:29 PM   #25
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See that's what I was thinking. This seems like it would be pretty complicated to figure out. Even though the diameter of the cog may be 1/8" larger the chain is engaging it at more than one point so it must be more. Also if you go by the 1/8" theory the chainline would only move back approximatley 1/2 of that (1/16") since the chain is only engaging a little more than half of the cog at one time.

Wouldn't you would need to find the length of the arc around the cog at which the chain engages it and subtract it from that of the arc at which the chain engages the larger cog? This would be pretty hard to figure out since the arc will change slightly depending on which chainring you have on the front and the size of the cog in the back.

BTW. Nice try with the pie thing but it seemed a little forced

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