Physiology of Fixed

[Dvt]

Carl Fogel wrote:
> ...peering at my plain-jane Shimano mish-mash and failed to discern any hop in my two front gears
> or seven rear gears.

You won't see any hop in a derailer equipped bike. The spring tension in the derailer takes
that away.

Are you saying that when you pedal the bike, the rear derailer cage does not move fore and aft to
compensate for the change in chain tension? I'd say that your sample of one was pretty fortuitous if
this is the case.

Dave dvt at psu dot edu

 

[Dvt]

Carl Fogel wrote:
> You measured a front-sprocket hop of about .3mm and a rear-cog hop of about 0.1mm on your fixed-
> gear bike.
>
> This suggests a maximum variation in the distance between the teeth grabbing the top chain run of
> about 0.04mm, which rounds up to about 0.016 inches.
>
> My bike measures about 17 inches from the center of the bottom bracket to the rear axle, but let's
> round it down to 16 inches.
>
> (Both roundings exaggerate the effect of chain hop on chain tension.)
>
> A variation of 0.016 inches in 16.000 inches works out to 0.1%. (See why I rounded in your favor?)

Take this calculation further. Assuming the chain runs straight, it covers a distance of 16.000
inches. But the chain is adjusted such that the drivetrain does not bind at the longest point, so
the chain is adjusted to have 16.016 inches length. Doesn't seem like a big deal, but let's
calculate the sag in the middle of the chain run with that amount of error.

Assume the chain sags in a simple V to make the geometry simple. That's a bad assumption, and it
will give an overestimate of the chain sag. But the error will be less than a factor of 2, I think.

The chain sag (using the V assumption) is given by
8.008" * sin( arccos( 16/16.016 ) ) = 0.36"

If the chain hops up and down 0.2 to 0.3", it's noticeable to the eye. It's not enough to cause the
chain to derail, so it's definitely in the "don't care" regime.

Thermal expansion coefficient of steel is approximately 12e-6 m/m/°C. Assume a temperature
differential of 30°C between usage conditions and adjustment conditions, you get an expansion of
0.006" on a 17" chainstay. But the chain expands and contracts at approximately the same rate, since
it's also steel. Aluminum, on the other hand, has a coefficient of nearly double that of steel. So
the chain might tighten by around 0.003". I don't know of anyone that uses an Al frame in a winter
beater fixie, but I'm sure someone does.

Dave dvt at psu dot edu

 

[David L. Johnso]

On Wed, 10 Dec 2003 20:24:09 +0000, Carl Fogel wrote:

> You measured a front-sprocket hop of about 0.3mm and a rear-cog hop of about 0.1mm on your fixed-
> gear bike.

I just looked at my own bike, which has a Dura-Ace flip-flop hub, Shimano cheapie cranks with a
42tooth chainring, a 16t old British cog from about 1970, and a 15t Campy cog from about that
same vintage.

The chainring had a high spot (measured as Sheldon suggested, by the chain, but since it was over
several revolutions any chain irregularities would have averaged out), of less than a mm. Let's
call it 0.5mm

The cheap British cog had no noticeable out-of roundness, but the Campy cog was about as far out of
round as the chainring. So, with the two we are talking 1mm --- radius.

Note that I am talking about the tolerance that most people have for wheel roundness. Any further
out of round than that, and on a wheel it would be noticable. As I spun the crank/wheel, I could see
and feel the out-of roundness, just as I would with a rim. Were a rim this out of round, I would
keep working on it.

What would you expect the chain to do under those conditions? Let's presume that, for the sake of
argument, half of the sprocket is round with one radius, the other half with the larger radius. I
know that is not the situation, but modeling non-concentric circles will be more of a headache and
will not really increase the accuracy.

That results in about a 3mm difference in chain length on the two half-circles, 1.5mm difference on
the chainring, and about the same on the cog. When the top is under tension, that 3mm would be all
on the bottom run of the chain. On a 450mm run of chain (taught), that 3mm would change the chain
from a straight line, or nearly so, to a graph with a considerable dip to it. The shape of the chain
is the solution to the hanging cable problem, just like the utility wires on a rural road. But if
you grabbed it and pulled down in the middle, so that the chain was again straight with an angle at
your finger, it would pull down x mm. There is a triangle, with base 225mm (the straight path),
hypoteneuse
(226.5mm), and height x formed by the straight-path versus pulled-down path of the chain to the mid-
point. By the Pythagorean theorem, x = sqrt(226.5^2 - 225^2), which is a whopping 26mm.

So, if under these conditions you adjusted the chain to be taut at the tightest position, it would
sag over 2.5cm at the loosest.

Now, my back-of-the-envelope calculation makes a worst-case scenario, and also doesn't let the chain
just sag, it pulls it tight. But certainly half that much sag might well occur based just on these
measurements. That is certainly enough to explain what we see.
>
> This suggests a maximum variation in the distance between the teeth grabbing the top chain run of
> about 0.04mm, which rounds up to about 0.016 inches.

I don't get that bit. It's not a variation in the distance between the teeth, it's that there would
be fractionally more teeth on one side than another, measured by using a line through the center of
the bottom bracket as the dividing line. I think my 1.5mm figure is more common than your .04. The
slack/loose difference comes from how much chain is wrapped around the sprocket -- a half
circumference of the slightly off circle. If one half is longer than the other, as would happen in
an out-of-round chainring, that would change how much chain it takes to get half-way around. That
difference in chain length is what you see.

If you presume instead that both sprockets are perfect circles, but the axles are not concentric
by that 0.5mm, then instead the length of the spans between sprockets would change by as much as
1mm. That would give a 2mm extra length of chain at the loosest point, which would look pretty
much the same.

> Elsewhere, Sheldon Brown has suggested that, with good-quality modern parts like the ones that he
> used today to build a fixed-gear bike, the chain-tension variation vanishes.

I don't know whether you consider Dura-Ace or Campagnolo to be good quality, but they work pretty
well. The only thing that might be better now is if you consider a CNC machined chainring, which
might be a truer circle and have the bolt circle very close to concentric with the teeth. But CNC
machined chainrings are not the best for other reasons, and we still have to deal with out-of round
crank spiders and attachment variation (the largest source of error for the chainring).

>
> Try not to be too snippy if I've goofed a calculation. I really am curious about this matter
> because I can't make it add up. Possibly someone who remembers geometry

I remember a bit of it.

> will step in and explain that the thickness of four sheets of paper really can make a practical
> difference in chain tension.

Your analysis that led to the 4-sheets of paper is off, in any event.

--

David L. Johnson

__o | To announce that there must be no criticism of the president, or _`\(,_ | that we are to
stand by the president right or wrong, is not (_)/ (_) | only unpatriotic and servile, but is
morally treasonable to the American public. --Theodore Roosevelt

 

[Dvt]

David L. Johnson wrote:
> If you presume instead that both sprockets are perfect circles, but the axles are not concentric
> by that 0.5mm, then instead the length of the spans between sprockets would change by as much as
> 1mm. That would give a 2mm extra length of chain at the loosest point, which would look pretty
> much the same.

That was the assumption Carl used. I don't think it's too bad, since I could use Sheldon's technique
to get rid of much of the variation in chain tension. That means (in my case, at least) that the
chainring mounting was the largest source of error. And that seems to agree with your experience.
That assumption and Muzi's "rounder" sprockets still result in about a cm of sag in the bottom run.
Definitely noticeable.

Dave, whose fixie is still 2000 km away from home dvt at psu dot edu

 

[Carl Fogel]

dvt <[email protected]> wrote in message news:<[email protected]>...
> Carl Fogel wrote:
> > You measured a front-sprocket hop of about .3mm and a rear-cog hop of about 0.1mm on your fixed-
> > gear bike.
> >
> > This suggests a maximum variation in the distance between the teeth grabbing the top chain run
> > of about 0.04mm, which rounds up to about 0.016 inches.
> >
> > My bike measures about 17 inches from the center of the bottom bracket to the rear axle, but
> > let's round it down to 16 inches.
> >
> > (Both roundings exaggerate the effect of chain hop on chain tension.)
> >
> > A variation of 0.016 inches in 16.000 inches works out to 0.1%. (See why I rounded in your
> > favor?)
>
> Take this calculation further. Assuming the chain runs straight, it covers a distance of 16.000
> inches. But the chain is adjusted such that the drivetrain does not bind at the longest point, so
> the chain is adjusted to have 16.016 inches length. Doesn't seem like a big deal, but let's
> calculate the sag in the middle of the chain run with that amount of error.
>
> Assume the chain sags in a simple V to make the geometry simple. That's a bad assumption, and
> it will give an overestimate of the chain sag. But the error will be less than a factor of 2,
> I think.
>
> The chain sag (using the V assumption) is given by
> 8.008" * sin( arccos( 16/16.016 ) ) = 0.36"
>
> If the chain hops up and down 0.2 to 0.3", it's noticeable to the eye. It's not enough to cause
> the chain to derail, so it's definitely in the "don't care" regime.
>
> Thermal expansion coefficient of steel is approximately 12e-6 m/m/°C. Assume a temperature
> differential of 30°C between usage conditions and adjustment conditions, you get an expansion of
> 0.006" on a 17" chainstay. But the chain expands and contracts at approximately the same rate,
> since it's also steel. Aluminum, on the other hand, has a coefficient of nearly double that of
> steel. So the chain might tighten by around 0.003". I don't know of anyone that uses an Al frame
> in a winter beater fixie, but I'm sure someone does.
>
> Dave dvt at psu dot edu

Dear Dave,

Regardless of thermal expansion rates, you nailed it by pointing out that the chain is steel, too.
Scrap that dumb theory! (It seemed so charming when I typed it.)

I don't know an arc from a cosine, much less how to calculate a V-sag from an assumed straight run,
so unless someone else who eats pi for breakfast disputes your calculation, I plan to believe it
(try not to abuse my trusting nature).

So it sounds as if we take Andrew Muzi's about 0.1mm and 0.3mm measurement of cog-hop (so far, I see
no one calling him crazy and I like his sheets-of-paper scheme for trying to measure something
tricky as accurately as he could).

Then we take my crude assumption that this suggests 0.4mm or 0.016 inches of lengthwise chain-
distance variation (runout? play? I'm not sure what it's supposed to be called), an assumption
questioned elsewhere in a nearby post that suggests a 0.4mm cog hop may require more than 0.4mm more
chain to stay at the same tension. (Since it was my assumption, let's agree to blame me if 0.4mm is
smaller than it should be, not you.)

Then you do something with some formula (frantic hand-waving on my part) and figure .36" of sag
would result, but rather handsomely knock this down to maybe 0.20" to 0.30" because the chain sag
will not be an angular V, but rather a graceful and hideously difficult-to-calculate catenary
curve, right?

You place this small sag in the not-enough to derail and don't-care category. But to be fair,
Andrew's measurements might be on the low side and his particular bike might be closer to Sheldon
Brown's high-quality, just-assembled, no-apparent chain-tension variation bicycle than to the kind
of fixed-gear bikes that other posters are riding.

That is, this one example might be way over toward the best-fit side of the spectrum and another
post questions my assumption that a 0.4mm combined cog-hop produces a 0.4mm chain-stretch. I'd love
to see more people reporting whatever cog-hop they can measure.

Now for a timid question. One of the few physics details that I remember from a class taught more
for entertainment than anything else by a famous physicist was his loud claim that all the devils in
hell can't pull a chain or rope straight horizontally by pulling on the ends, given gravity acting
at right angles.

Does this practical detail help your decision to cut the idealized V-calculation of chain-sag down
from 0.036 to 0.020-0.030? That is, how much real-world sag already exists in a taut, heavy chain as
compared to a mason's line snapped across the tops of the two gears? I haven't done this yet, but
I'm trying to think of a way to do it.

Thanks for doing the heavy lifting in the math. Sorry if my assumption about 0.4mm turns out to be
significantly wrong.

Carl Fogel

 

[David L. Johnso]

On Thu, 11 Dec 2003 15:36:18 +0000, Carl Fogel wrote:

> I don't know an arc from a cosine, much less how to calculate a V-sag from an assumed straight
> run, so unless someone else who eats pi for breakfast disputes your calculation, I plan to believe
> it (try not to abuse my trusting nature).

That would be me.

> Then you do something with some formula (frantic hand-waving on my part) and figure 0.36" of sag
> would result, but rather handsomely knock this down to maybe 0.20" to 0.30" because the chain sag
> will not be an angular V, but rather a graceful and hideously difficult-to-calculate catenary
> curve, right?

Here I have trouble, as my other post indicates. You actulally get far more sag from that 0.4mm
of "runout".

> Now for a timid question. One of the few physics details that I remember from a class taught more
> for entertainment than anything else by a famous physicist was his loud claim that all the devils
> in hell can't pull a chain or rope straight horizontally by pulling on the ends, given gravity
> acting at right angles.

This is, of course, true. But I can pull it tight enough so that the sag does not matter. That is
also not relevant.

--

David L. Johnson

__o | Enron's slogan: Respect, Communication, Integrity, and _`\(,_ | Excellence. (_)/ (_) |

 

[Carl Fogel]

David Reuteler <[email protected]> wrote in message news:<[email protected]>...
> Carl Fogel <[email protected]> wrote:
> : David Reutler -- no measurement
>
> ahem. Reuteler.
>
> geez, carl you're brutal -- i gotta job and stuff (and happy to have one despite being put through
> bea java training all week. cack. kill me. gui IDEs).
>
> well, i duplicated (or tried to anyway) andrew's paper method as well as eye- balling it with grid
> paper taped on behind it (not as accurate obviously, but i looked at the valleys). on my chainring
> (a 47t suntour superbe pro track ring) in the valleys (by eye-balling it) i can find no
> perceptible difference. for the tops (w/ the paper) maybe .1mm or so. i dunno, it's pretty damn
> small. ditto for the rear cog.

Dear David,

Ahem. Reut-e-ler, Reut-e-ler. Sorry about that--I googled and found that this is my second offense.
My problem with names is becoming harder and harder to conceal, as Benjamin Lewis and Benjamin
Weiner know to their sorrow.

I appreciate your taking the trouble to look into how much your cogs actually hop. I suspect that
many people who do this will find surprisingly little variation, particularly when they use Andrew
Muzi's clever trick and have fairly modern equipment.

But to be fair I have to add that this is just some data. How 0.1mm hop affects chain tension is
another matter, so I don't take this as any endorsement of my theory that either the chain tension
isn't varying as much as many people think or else the chain itself should share much of the blame.

Reuteler, Reuteler, Reuteler!

(Sorry, just practicing.)

Good luck with your Java training. I've got a new idea about the chain tension that involves me and
everyone else being wrong, but it'll have to wait until tomorrow.

Carl Fogel

 

[A Muzi]

>>>Carl Fogel wrote: You measured a front-sprocket hop of about .3mm and a rear-cog hop of about
>>>0.1mm on your fixed-gear bike.-snip-

> dvt <[email protected]> wrote in message news:<[email protected]>...
>>Take this calculation further. Assuming the chain runs straight,
-snip-

Carl Fogel wrote: -snip-
> Andrew Muzi's about 0.1mm and 0.3mm measurement of cog-hop
-snip-

Before this goes too far,
1) I measured something Carl asked for repeatedly
2) I clearly noted that measuring the tops of the teeth was not in any way relevant ( Sheldon
concurred)
3) I do not have any way to measure accurately the actual errors of concentricity in cones, cups,
hubshells and the roots of teeth in situ, where they combine.

I still maintain that what we're doing here is indulging Carl's belief that there is some easily-
improved shortcoming in component machining which, corrected, would obviate tight and loose spots in
fixed-length chain. I do not believe that.

The errors are small but significant to chain tension. They are not easily avoided given current
machining practice. ( at least Phil and Campagnolo haven't) At any rate the world has adapted chain
tensioning technique to avoid setting the chain when loose which would risk a tight spot. At least
users seem only to do that once!

--
Andrew Muzi www.yellowjersey.org Open every day since 1 April, 1971

 

[David Reuteler]

Carl Fogel <[email protected]> wrote:
: chain tension is another matter, so I don't take this as any endorsement of my theory that either
: the chain tension isn't varying as much as many people think or else the chain itself should share
: much of the blame.

well, for the record i've never really had a "problem" with chain tension. as i said before (at
least i think i remember saying so) i more or less just tension, bolt, test and go.

: Reuteler, Reuteler, Reuteler!

ahh, a dutch co-worker once told me that in dutch reutelen was the sound a car makes when it can't
turn over. so reutelen-reutelen-reutelen was not something you wanted to hear on a cold morning.
maybe he was messing with me, i don't know for sure.

: (Sorry, just practicing.)
:
: Good luck with your Java training.

last day tomorrow!
--
david reuteler [email protected]

 

[Carl Fogel]

dvt <[email protected]> wrote in message news:<[email protected]>...
> Carl Fogel wrote:
> > What I'm wondering is whether the observed fluctuation in chain tension on these two-sprocket
> > devices is caused by everything but the chain (the prevailing wisdom), the chain (which everyone
> > seems to assume has no problems, despite having more moving parts), or both.
>
> After thinking about it a little more, I will point out some facts that indicate the chain is
> *not* the cause of varying tension in the chain of a fixie. Then the measurements become a moot
> point. As D. Johnson said, it's cold out there (just above freezing and raining pretty hard on top
> of several inches of snow).
>
> 1. In my experience, the variation in tension is often periodic with the rotation of the crank.
> The chain is tight at a specific point in the rotation of the crank, and loose at another
> point. This also indicates that the cog is not a significant contributor. Maybe I've just been
> lucky with cogs.
>
> 2. I have been able to adjust most of the variation in tension out using Sheldon's method to
> center the chainrings. That indicates that the chainrings are round, but the mount to the crank
> is not perfectly centered. And it implies the same general conclusions I mentioned in point 1.
>
> 3. Replacing chains does not affect the degree to which the chain tension varies. Again, my
> experience is much more limited than guys like Sheldon and Muzi, but I've replaced a few chains
> and it just doesn't make a noticeable difference.
>
> Enough data?
>
> Dave dvt at psu dot edu

Dear David,

Actually, that was no data at all.

You could have taken your wet, cold bicycle inside, placed it on the dining room table, and measured
the cog hop in the time that it took to type all that.

(I'm long-winded, so I sympathize.)

As for your previous post that mentioned watching the derailleur as you work the pedals backward, I
see it every day as I clean and oil my chain, but I bravely looked again, despite freezing
temperatures in my garage.

On an upside-down derailleur bike (another exception to Jobst's belief that the inverted position is
of no use), you can peer at the pulleys as they hesitate and jerk with the chain running backwards--
it appears to be more a matter of the chain running far from smoothly as it wraps in two sharp
curves around tiny gears.

I'm belatedly working my way through various replies. I think that you have another one off in
another part of this thread, so I'll see you there in a few minutes.

Carl Fogel

 

[Carl Fogel]

John Dacey <[email protected]> wrote in message news:<[email protected]>...
> "In virtute sunt multi ascensus." - Cicero On 10 Dec 2003 09:36:23 -0800, [email protected]
> (Carl Fogel) wrote:
>
> >This is becoming fascinating.
>
> <snip. See how easy that is, Carl?>
>
> >Again, how far do the gear teeth actually rise and fall on your front sprocket?
> >
> >The fixed-gear crowd is now 0-for-6 answering a question that I expected would produce a welter
> >of measurements.
>
> Here's one for the Home Team:
>
> Sugino is the only manufacturer I've seen to have the moxie to put numbers on the accuracy of some
> of their chainrings.
>
> Documentation that accompanies selected models of their track chainrings contain graphs that show
> that to meet the J.I.S. standard, there can be no more than .5 mm runout. They're happy to go on
> to point out that the chainring models they designate as the "S3" series have less than one tenth
> that amount (no more than .05 mm runout).
>
> -------------------------------
> John Dacey

Dear John,

Do you have a web address for this? Apart from the numbers, anyone who measures this sort of thing
might have all sorts of fascinating stuff about how they make the chainrings and what it all means.

Frankly, I can't even figure out what the right words are--runout, play, tension, and so forth
are trickier than I expected. There's the vertical play in the middle of the chain run that
indicates tension, but most of what's being measured by people pandering to my curiosity is cog-
hop, which might affect horizontal chain-play. Damned if I know what runout means here, but I
like the looks of it.

If a maximum runout of 0.50mm on Sugino's ordinary track sprockets is the same as (or corresponds
roughly to) an idealized cog-hop of 0.50mm, then that sounds plausibly close to Andrew Muzi's 0.30mm
tooth-tip measurement. He might have gotten a slightly better than usual sprocket, his measurement
might be off plus-or-minus 0.05mm or so, and the accumulated eccentricity of everything between the
sprocket and the frame might have aligned by sheer luck to cancel out some of the sprocket's
variation.

Whatever Sugino means by runout, that 0.05mm S3 sprocket sounds impressively accurate. But I have to
wonder how many laps lasts under a gritty chain. It seems to convert to 0.0019 inches. But perhaps
track bikes running indoors on wooden floors escape the polishing effect of outdoor dust?

Carl Fogel

 

[Carl Fogel]

"David L. Johnson" <[email protected]> wrote in message news:<[email protected]>...
> On Wed, 10 Dec 2003 20:24:09 +0000, Carl Fogel wrote:
>
> > You measured a front-sprocket hop of about 0.3mm and a rear-cog hop of about 0.1mm on your fixed-
> > gear bike.
>
> I just looked at my own bike, which has a Dura-Ace flip-flop hub, Shimano cheapie cranks with a
> 42tooth chainring, a 16t old British cog from about 1970, and a 15t Campy cog from about that same
> vintage.
>
> The chainring had a high spot (measured as Sheldon suggested, by the chain, but since it was over
> several revolutions any chain irregularities would have averaged out), of less than a mm. Let's
> call it 0.5mm
>
> The cheap British cog had no noticeable out-of roundness, but the Campy cog was about as far out
> of round as the chainring. So, with the two we are talking 1mm --- radius.
>
> Note that I am talking about the tolerance that most people have for wheel roundness. Any further
> out of round than that, and on a wheel it would be noticable. As I spun the crank/wheel, I could
> see and feel the out-of roundness, just as I would with a rim. Were a rim this out of round, I
> would keep working on it.
>
> What would you expect the chain to do under those conditions? Let's presume that, for the sake of
> argument, half of the sprocket is round with one radius, the other half with the larger radius. I
> know that is not the situation, but modeling non-concentric circles will be more of a headache and
> will not really increase the accuracy.
>
> That results in about a 3mm difference in chain length on the two half-circles, 1.5mm difference
> on the chainring, and about the same on the cog. When the top is under tension, that 3mm would be
> all on the bottom run of the chain. On a 450mm run of chain (taught), that 3mm would change the
> chain from a straight line, or nearly so, to a graph with a considerable dip to it. The shape of
> the chain is the solution to the hanging cable problem, just like the utility wires on a rural
> road. But if you grabbed it and pulled down in the middle, so that the chain was again straight
> with an angle at your finger, it would pull down x mm. There is a triangle, with base 225mm (the
> straight path), hypoteneuse
> (226.5mm), and height x formed by the straight-path versus pulled-down path of the chain to the
> mid-point. By the Pythagorean theorem, x = sqrt(226.5^2 - 225^2), which is a whopping 26mm.
>
> So, if under these conditions you adjusted the chain to be taut at the tightest position, it would
> sag over 2.5cm at the loosest.
>
> Now, my back-of-the-envelope calculation makes a worst-case scenario, and also doesn't let the
> chain just sag, it pulls it tight. But certainly half that much sag might well occur based just on
> these measurements. That is certainly enough to explain what we see.
> >
> > This suggests a maximum variation in the distance between the teeth grabbing the top chain run
> > of about 0.04mm, which rounds up to about 0.016 inches.
>
> I don't get that bit. It's not a variation in the distance between the teeth, it's that there
> would be fractionally more teeth on one side than another, measured by using a line through the
> center of the bottom bracket as the dividing line. I think my 1.5mm figure is more common than
> your .04. The slack/loose difference comes from how much chain is wrapped around the sprocket -- a
> half circumference of the slightly off circle. If one half is longer than the other, as would
> happen in an out-of-round chainring, that would change how much chain it takes to get half-way
> around. That difference in chain length is what you see.
>
> If you presume instead that both sprockets are perfect circles, but the axles are not concentric
> by that 0.5mm, then instead the length of the spans between sprockets would change by as much as
> 1mm. That would give a 2mm extra length of chain at the loosest point, which would look pretty
> much the same.
>
> > Elsewhere, Sheldon Brown has suggested that, with good-quality modern parts like the ones that
> > he used today to build a fixed-gear bike, the chain-tension variation vanishes.
>
> I don't know whether you consider Dura-Ace or Campagnolo to be good quality, but they work pretty
> well. The only thing that might be better now is if you consider a CNC machined chainring, which
> might be a truer circle and have the bolt circle very close to concentric with the teeth. But CNC
> machined chainrings are not the best for other reasons, and we still have to deal with out-of
> round crank spiders and attachment variation (the largest source of error for the chainring).
>
> >
> > Try not to be too snippy if I've goofed a calculation. I really am curious about this matter
> > because I can't make it add up. Possibly someone who remembers geometry
>
> I remember a bit of it.
>
> > will step in and explain that the thickness of four sheets of paper really can make a practical
> > difference in chain tension.
>
> Your analysis that led to the 4-sheets of paper is off, in any event.

Dear David,

I'm not sure that my analysis is off.

I think that you are assuming that the cog-hop is the result of a distorted sprocket and then doing
some admirable calculations.

But this assumption seems to be mistaken.

The amount that the tips of the gear teeth (or the crucial curve just below them) varies from an
ideal circle is what's being measured.

This variation partly reflects any distortion in the sprocket's circularity, but also any
distortion in:

a) how the sprocket is centered on the pedal arm
b) how the pedal is centered on the spline
c) how the straight the spline is
d) how circular the cone face of the spline is
e) how accurately machined the balls are
f) how smoothly machined the cups are
g) how parallel the two cups are to each other

I expect that these are all pretty darned good, but each minor inaccuracy is magnified from as we
progress outward toward the tips of the gear teeth.

If the tips of your sprocket are hopping 0.5mm as you turn it, I suspect that a significant amount
of the the hop is not the sprocket, but everything from its attachment point on down to the frame.

That is, your sprocket removed from the bike and measured just by itself seems unlikely to show
0.5mm of variation. So while I expect that your calculations make sense, I don't think that they
actually apply here.

I think that you're working on how a lumpy sprocket mounted on a perfect shaft would affect chain
tension and correctly concluding that X amount of lumpiness creates >X increase in chain-tension
variation.

I'm assuming that a much less lumpy sprocket that's mounted a little off center on a somewhat
eccentric. If that's the case, then X amount of hop may be a better rough-and-ready measurement.

Carl Fogel

 

[Carl Fogel]

A Muzi <[email protected]> wrote in message news:<[email protected]>...
> >>>Carl Fogel wrote: You measured a front-sprocket hop of about .3mm and a rear-cog hop of about
> >>>0.1mm on your fixed-gear bike.-snip-
>
> dvt <[email protected]> wrote in message news:<[email protected]>...
> >>Take this calculation further. Assuming the chain runs straight,
> -snip-
>
> Carl Fogel wrote: -snip-
> > Andrew Muzi's about 0.1mm and 0.3mm measurement of cog-hop
> -snip-
>
> Before this goes too far,
> 1) I measured something Carl asked for repeatedly
> 2) I clearly noted that measuring the tops of the teeth was not in any way relevant ( Sheldon
> concurred)
> 3) I do not have any way to measure accurately the actual errors of concentricity in cones, cups,
> hubshells and the roots of teeth in situ, where they combine.
>
> I still maintain that what we're doing here is indulging Carl's belief that there is some easily-
> improved shortcoming in component machining which, corrected, would obviate tight and loose spots
> in fixed-length chain. I do not believe that.
>
> The errors are small but significant to chain tension. They are not easily avoided given current
> machining practice. ( at least Phil and Campagnolo haven't) At any rate the world has adapted
> chain tensioning technique to avoid setting the chain when loose which would risk a tight spot. At
> least users seem only to do that once!

Dear Andrew,

Perhaps there are a few misunderstandings.

You did measure something tricky and showed everyone a clever way to do it--I appreciate the trouble
that you took to do it.

I agree with Sheldon that the tips are not bearing the actual load, but I disagree that measuring
the hop at the tips of the teeth is irrelevant.

Modern derailleur gears have subtly varying tooth-heights and wear may not be even on regular-
style sprockets, but the tips still look like an awfully good indicator of where the adjacent
curve that actually bears the load is. If one tooth-tip looks broken or deliberately shortened, it
can be ignored.

If the manufacturers can vary tooth-height so subtly and deliberately, it suggests considerable
machining accuracy.

The eccentricity of the cups, cones, and everything else is combined with any sprocket irregularity.
In fact, some may cancel others. Nothing matters to the chain except where the teeth are in relation
to the teeth of the other sprocket.

I appreciate how people are indulging my interest, but I'm not suggesting that there's any easily
improved situation.

What I'm wondering what actually causes the varying chain tension. All the explanations that I
browsed mentioned everything except the chain itself as a culprit and offered no measurements at all
to support the intuitive belief that it's the fault of everything between the tips of the gear teeth
and the bicycle frame itself.

Interestingly, Sheldon Brown indicates that the chains are okay (so much for my speculation)
because modern high-quality parts let him assemble a bike with no significant chain variation
during this thread.

(But then a modern high-quality chain itself may also have helped. Apart from finer tolerances,
modern chains may wrap more smoothly and therefore vary less in tension. One slightly tight link in
terms of swivelling may cause the chain-run to tighten.)

Forgive me, since I'm catching up and you may have already replied, but does Sheldon's post about
using more accurately machined components seem reasonable to you? (By "high-quality," I mean only
how accurately the gear-teeth describe ideal circles, not weight, durability, brand, cost, or
anything else.)

I'm just interested in the explanation of varying chain-tension, not in anything practical. I think
that some posters have been surprised by how tiny the measured cog-hop turns out to be.

Carl Fogel

 

[Carl Fogel]

[email protected] (Scott Hendricks) wrote in message news:<[email protected]>...

[snip Sheldon Brown--daring of me]

>
> Somehow, I don't think even this very well presented explanation will satisfy Carl's needs. He
> wants measurements, dammit! Not theory! ;->

Dear Scott,

Well, yes, Sheldon should have printed his results in numerical form, but I think that he was saying
zero observed cog-hop and zero chain-tension variation in the bike that he was putting together.

I want measurements, but I like theory, too. In fact, I like things all mixed up:

"The widow she cried over me, and called me a poor lost lamb, and she called me a lot of other name-
s, too, but she never meant no harm by it. She put me in them new clothes again, and I couldn't do
nothing but sweat and sweat, and feel all cramped up. Well, then, the old thing commenced again.
The widow rung a bell for supper, and you had to come to time. When you got to the table you could-
n't go right to eating, but you had to wait for the widow to tuck down her head and grumble a litt-
le over the victuals, though there warn't really anything the matter with them,--that is, nothing
only everything was cooked by itself. In a barrel of odds and ends it is different; things get mix-
ed up, and the juice kind of swaps around, and the things go better."
-- Huckleberry Finn

"Mixed-up" isn't a bad description of my posts, is it?

Carl Fogel

 

[Carl Fogel]

dvt <[email protected]> wrote in message news:<[email protected]>...
> Carl Fogel wrote:
> > ...peering at my plain-jane Shimano mish-mash and failed to discern any hop in my two front
> > gears or seven rear gears.
>
> You won't see any hop in a derailer equipped bike. The spring tension in the derailer takes
> that away.
>
> Are you saying that when you pedal the bike, the rear derailer cage does not move fore and aft to
> compensate for the change in chain tension? I'd say that your sample of one was pretty fortuitous
> if this is the case.
>
> Dave dvt at psu dot edu

Dear Dave,

Sorry for not making things clear.

I see no cog-hop when I flip my bike upside-down, crank the pedals, and watch the naked cogs spin,
sighting against various marks on the frame or distant objects. Shifting the gears to expose the
cogs that were under the chain gives the same results.

(I did this before Andrew Muzi showed us his trick for measuring with sheets of paper. Any variance
that small is pretty much beyond the ability of most people to eyeball accurately.)

The front is a splined Shimano 105 double 39 x 53, with the 53-tooth chain ring being a cheap non-
Shimano replacement.

The rear is a 7-speed 11 x 24 Shimano.

The sealed bottom bracket is Shimano.

The back wheel's hubs, cones, cups, and axle are a 1998 Schwinn LeTour.

As for the derailleur jerking, I suspect that much of this is not varying chain tension, but the
effect of wrapping the chain in too tight a curve around the two tiny jockey wheels.

I don't think that my apparently accurately tracking cogs are fortuitous--I think that you'll find
the same impressively smooth circles described by gear-teeth if you go down to the local bike shop
and amuse the employees by cranking pedals and peering at gears on half a dozen bikes.

I did.

Carl Fogel

 

[Carl Fogel]

"David L. Johnson" <[email protected]> wrote in message news:<[email protected]>...
> On Thu, 11 Dec 2003 15:36:18 +0000, Carl Fogel wrote:
>
> > I don't know an arc from a cosine, much less how to calculate a V-sag from an assumed straight
> > run, so unless someone else who eats pi for breakfast disputes your calculation, I plan to
> > believe it (try not to abuse my trusting nature).
>
> That would be me.
>
> > Then you do something with some formula (frantic hand-waving on my part) and figure 0.36" of sag
> > would result, but rather handsomely knock this down to maybe 0.20" to 0.30" because the chain
> > sag will not be an angular V, but rather a graceful and hideously difficult-to-calculate
> > catenary curve, right?
>
> Here I have trouble, as my other post indicates. You actulally get far more sag from that 0.4mm of
> "runout".
>
> > Now for a timid question. One of the few physics details that I remember from a class taught
> > more for entertainment than anything else by a famous physicist was his loud claim that all the
> > devils in hell can't pull a chain or rope straight horizontally by pulling on the ends, given
> > gravity acting at right angles.
>
> This is, of course, true. But I can pull it tight enough so that the sag does not matter. That is
> also not relevant.

Dear David,

Actually, it turns out that you probably can't pull it tight enough that it doesn't show significant
sag at the practical level.

I pondered the problem of how to measure how much a reasonably taut chain sags under its own weight
between the front and rear gears.

Let's see, punch two holes in a big piece of carefully carved cardboard, run a long string through
the holes, tighten the string for a straight line, insert the carboard rig between the chain and the
frame, line it up with the gears, and . . .

No, the string would sag under its own weight, just like the chain.

Okay, forget the string, just draw a straight line on the cardboard while it's flat on the table and
gravity doesn't interfere . . .

Too hard to draw a straight line with a string. Where's a big ruler?

Throw string and cardboard away, put knife used to carve carboard back in drawer with tape, take two-
foot metal carpenter's square out to garage, flip bike upside down, and lay L-shaped steel ruler on
top of the chain.

It sits there and balances fine by itself on the chain and gears. Nice straight edge, unaffected
by gravity.

Glad that Andrew Muzi is not watching all this and laughing himself sick at my incompetence. (See
why I wanted you guys to do the measuring?)

Measured with my dial calipers, chain sag appears to be 0.20 inches in the middle of the chain run
with just the tension of the elderly derailleur springs.

Pull hard on the derailleur and sag drops to about 0.10 inches.

This sag 0.10-0.20 inch gravity sag seems significant when someone else (not me) has calculated a
chain-sag of 0.20-0.30 inches for a 4mm cog-hop.

If anyone with a fixed-gear bike has a big steel carpenter's ruler, it would be interesting to hear
how much their chains are sagging in the middle under gravity.

Carl Fogel

 

[Dvt]

Carl Fogel wrote:
> Then you do something with some formula (frantic hand-waving on my part) and figure .36" of sag
> would result, but rather handsomely knock this down to maybe 0.20" to 0.30" because the chain sag
> will not be an angular V, but rather a graceful and hideously difficult-to-calculate catenary
> curve, right?

You hit the nail on the head. Except for the hideous part. I'm simply too lazy to roll my chair over
10', flip through my old physics book, and look for the formula. I don't know if it's hideous, but
it probably isn't.

> Does this practical detail help your decision to cut the idealized V-calculation of chain-sag down
> from 0.036 to 0.020-0.030?

First of all, you missed a decimal point in this sentence. You had it right in the earlier
paragraph. I computed 0.2-0.3", not 0.02-0.03".

> That is, how much real-world sag already exists in a taut, heavy chain as compared to a mason's
> line snapped across the tops of the two gears? I haven't done this yet, but I'm trying to think of
> a way to do it.

I think you miss another important point. As you ride a fixie, the top stays taut and fairly
straight unless you're going down a fast hill. So the bottom doesn't only sag, it bounces up and
down as you ride over bumps. That means that the observed bounce is 0.4-0.6".

Lest it be forgotten, the assumptions are 0.3mm and 0.1mm runout in cogs, 16" chainstay, and
perfectly round but imperfectly centered cogs. That sentence is for Google.

Dave dvt at psu dot edu

 

[David L. Johnso]

On Fri, 12 Dec 2003 10:15:15 +0000, Carl Fogel wrote:

> But this assumption seems to be mistaken.

??
>
> The amount that the tips of the gear teeth (or the crucial curve just below them) varies from an
> ideal circle is what's being measured.
>
> This variation partly reflects any distortion in the sprocket's circularity, but also any
> distortion in:
>
> a) how the sprocket is centered on the pedal arm

I did cover that.

b) how the pedal is
> centered on the spline

irrelevant

c) how the straight the spline is

Also not releveant.

> d) how circular the cone face of the spline is e) how accurately machined the balls are

Noise

d) how smoothly machined the cups are g) how parallel the
> two cups are to each other

All these are minor compared with out of roundness of the sprockets, and the sprocket not being
coaxial with the axle itself.

> If the tips of your sprocket are hopping 0.5mm as you turn it, I suspect that a significant amount
> of the the hop is not the sprocket, but everything from its attachment point on down to the frame.

Why would you assume that?
>
> That is, your sprocket removed from the bike and measured just by itself seems unlikely to show
> 0.5mm of variation. So while I expect that your calculations make sense, I don't think that they
> actually apply here.

Even if it is the hub, or the spider, the result is the same, isn't it?

>
> I think that you're working on how a lumpy sprocket mounted on a perfect shaft

The shaft defines the axis of revolution. Everything else is relative to that.

> I'm assuming that a much less lumpy sprocket that's mounted a little off center on a somewhat
> eccentric. If that's the case, then X amount of hop may be a better rough-and-ready measurement.

Forgive me, but that is precisely what we measured. Just what you wanted measured, if I recall
correctly. I suggest that the vast majority of this is in the assymetry or lack of concentricness of
the sprockets, front or rear. Anything else is for one, better machined, and for another, less
likely to be off while still being servicable.

--

David L. Johnson

__o | You will say Christ saith this and the apostles say this; but _`\(,_ | what canst thou say?
-- George Fox. (_)/ (_) |

 

[Carl Fogel]

dvt <[email protected]> wrote in message news:<[email protected]>...
> Carl Fogel wrote:
> > Then you do something with some formula (frantic hand-waving on my part) and figure .36" of sag
> > would result, but rather handsomely knock this down to maybe 0.20" to 0.30" because the chain
> > sag will not be an angular V, but rather a graceful and hideously difficult-to-calculate
> > catenary curve, right?
>
> You hit the nail on the head. Except for the hideous part. I'm simply too lazy to roll my chair
> over 10', flip through my old physics book, and look for the formula. I don't know if it's
> hideous, but it probably isn't.
>
> > Does this practical detail help your decision to cut the idealized V-calculation of chain-sag
> > down from 0.036 to 0.020-0.030?
>
> First of all, you missed a decimal point in this sentence. You had it right in the earlier
> paragraph. I computed 0.2-0.3", not 0.02-0.03".
>
> > That is, how much real-world sag already exists in a taut, heavy chain as compared to a mason's
> > line snapped across the tops of the two gears? I haven't done this yet, but I'm trying to think
> > of a way to do it.
>
> I think you miss another important point. As you ride a fixie, the top stays taut and fairly
> straight unless you're going down a fast hill. So the bottom doesn't only sag, it bounces up and
> down as you ride over bumps. That means that the observed bounce is 0.4-0.6".
>
> Lest it be forgotten, the assumptions are 0.3mm and 0.1mm runout in cogs, 16" chainstay, and
> perfectly round but imperfectly centered cogs. That sentence is for Google.
>
> Dave dvt at psu dot edu

Dear Dave,

Aaargh! Sorry about the decimal point--even adding zeros doesn't seem to stop my absent-mindedness.

You calculated 0.20 to 0.30 inches. Maybe if I repeat it, I'll get it right next time. (See why I
think any formula must be hideous?)

I'm sorry, but I don't see what's important about the lower slack chain run bouncing in terms of
chain tension--don't all slack lower chain runs do this?

That is, despite the modest springs of a derailleur, doesn't its comparatively slack lower chain run
also bounce more than its heavily loaded and taut top run?

(It's fascinating how many questions arise from what seems like such a simple matter.)

Carl Fogel

 

[John Dacey]

"Ille sinistrorsum hic dexrorsum abit, unus utrique error, sed variis
illudit partibus." - Horace
On 12 Dec 2003 10:34:40 -0800, [email protected] (Carl Fogel)
wrote:

>John Dacey <[email protected]> wrote:
>> Sugino is the only manufacturer I've seen to have the moxie to put numbers on the accuracy of
>> some of their chainrings.
>>
>> Documentation that accompanies selected models of their track chainrings contain graphs that show
>> that to meet the J.I.S. standard, there can be no more than .5 mm runout. They're happy to go on
>> to point out that the chainring models they designate as the "S3" series have less than one tenth
>> that amount (no more than .05 mm runout).

>Dear John,
>
>Do you have a web address for this? Apart from the numbers, anyone who measures this sort of thing
>might have all sorts of fascinating stuff about how they make the chainrings and what it all means.

Sugino has a modest web presence, but you won't find this kind of detail listed there. If you're
determined to look for yourself, the URL is http://www2.odn.ne.jp/suginoltd/. As I mentioned, the
measurements to which I referred are found on a written sheet included with some of Sugino's premium-
grade track 'rings. The .5 mm spec refers to _any_ chainring (road, mtn, track) that would aspire to
meet the JIS standard. Since even Sugino's least expensive track 'rings are quite good, I'd expect
them to consistently better the .5 mm criterion, but meeting the .05 mm accuracy standard is only
promised for their more elite S3 models.

To put this in perspective, there is one model of Sugino track chainring (called "Gigas") which
costs in excess of $300.00 per chainring. Gigas 'rings are ostensibly made to allow G1 professional
keirin racers (who are in a position to afford such things) to minimize the kind of chain tension
inconsistencies we've been discussing. Other models within their S3 series are somewhat more
modestly priced (but still not for the faint of heart) from about $100.00.

<snip>

>Whatever Sugino means by runout, that 0.05mm S3 sprocket sounds impressively accurate. But I have
>to wonder how many laps lasts under a gritty chain. It seems to convert to 0.0019 inches. But
>perhaps track bikes running indoors on wooden floors escape the polishing effect of outdoor dust?

By comparison to road bikes, most track chainrings, sprockets and chains lead lives that are far
more sheltered from environmental wear. Only a very small fraction of the worlds' velodromes are
indoor venues however, and professional keirin racing happens rain or shine.

-------------------------------
John Dacey Business Cycles, Miami, Florida http://www.businesscycles.com Now in our twenty-first
year. Our catalog of track equipment: eighth year online
-------------------------------