Funny Chain Lubricant Story

On Fri, 13 Jun 2008 00:43:04 -0600, wrote:

On Thu, 12 Jun 2008 21:21:27 -0700 (PDT), Frank Krygowski
wrote:

On Jun 12, 6:34 pm, wrote:


The chief effect of lubrication on bicycle chains is to keep grit out.

I'd have said the chief effect of lubrication is to trap the grit on
the chain, and distribute it on other parts of the bike. And the
rider's leg.

That's been true of every wet lube I've tried, anyway.

- Frank Krygowski

Dear Frank,

Wet lube initially keeps road dust out. (Nothing larger will fit
between pins and rollers.)

Any wet lube traps the road dust flung up by the tires, so the wet
lube turns black within a few miles.

After that, the outside of the chain is covered with an extremely fine
polishing sludge, which gradually mixes with the thin film of clean
lube inside the rollers as the minuscule pumping action draws it in
and out.

Eventually, the area between the pins and rollers builds up a thin
layer of polishing paste.

Chain wear rates suggest how long the process takes.

Each roller turns a tiny bit as it engages the top of the front
sprocket, a tiny bit as it exits, and ditto for the rear sprocket and
any idler pulleys.

But only two of the turns are under any significant load, when the
chain is pulled onto the front sprocket and pulls off the rear
sprocket.

At 100 rpm on a 53-tooth front sprocket, the chain moves at a mere 2.5
mph. (At the same 100 rpm on a 175 mm crank, the rider's foot whirls
at a blistering 4.1 mph.)

At 100 rpm on a 53-tooth sprocket, an individual roller on a
106-roller chain makes its small partial turn under load (entering the
front or leaving the rear sprocket) at only a rate of once every
3/5ths of a second.

How small is that turn?

As it pulls onto the front 53-tooth, the roller turns and locks in
1/53rd of a circle--a bit less than 7 degrees. (About 9 degrees for a
39-tooth.) Then it just sits there until it eases off the sprocket.

The extreme case is an 11-tooth rear, where the chain pulling off has
its pin and roller turn about 32 degrees.

So an hour of 100 rpm riding produces only 6,000 partial polishing
rotations (7 to 32 degrees) on any single pin and roller, amounting to
much less than 400 full turns per hour.

That's about 0.25 rpm.

(The 106-roller chain is a convenient figure that's easy to calculate
and produces a slightly inflated result compared to the typical
~114-roller chain.)

In other words, most bicycle chains last over a thousand miles, even
on a diet of polishing paste made from oil and road dust, because the
individual pins and rollers turn so little and because the polishing
paste can contain only the grains of extremely hard road dust small
enough to fit between the pins and rollers, whose clearance is below
what a typical micrometer can measure.

As a crude example, a 53x19 at 91.5 rpm on a 2124 mm tires is doing 20
mph. Each pin on a 106-roller chain makes its partial turns under load
at 91.5 rpm, about 5500 partial polishing turns every hour or every 20
miles. That's 27,500 slight "grinds" averaging only about 20 degrees
in a thousand miles and fifty hours of steady riding at about 90 rpm.

When 25 of these pins (the ends of a foot-long ruler) wear 0.0025",
the chain elongates a full 1/16th of an inch (0.0625") and should be
replaced. The 0.0025" wear on each pin-roller combination amounts to
about the thickness of a sheet of flimsy phone-book paper.

***

Such incredibly tiny wear explains why it's almost impossible to clean
real wet-lube chains that have gotten dirty.

Dunk a dirty, oily chain in solvent in an ultrasonic cleaner, shake it
in a bottle, do whatever you please--

Eventually, you'll probably run out of patience before fresh solvent
stops producing wisps of filth from what looks like an immaculate
chain.

The solvent acts only on the incredibly thin exposed edge of the film
of oil-and-grime trapped between each pin and roller, a surface that
isn't much wider than a human hair. Given such poor access, the
solvent takes forever, even with shaking or ultrasonic action, to eat
into the mess trapped between the pins and rollers.

***

Dry wax has the advantage that it draws no road dust into the
pin-roller interface. Instead of a oily film pumping in and out, the
dry lube flakes outward under pressure from between the pin and roller
and never returns.

The price for this is that the dry lube needs to be re-applied more
often than a wet lube (with exceptions of all kinds for different
lubes and conditions).

Frank is quite happy with wax that has some oil added, others swear by
various oils, and I've been reasonably pleased with Dupont Teflon
spray wax.

(I can't recommend it over oil or melted wax, but it's fairly cheap,
easy to apply, and has a pleasant new-toy effect that hasn't worn off
yet.)

***

As far as I know, lubrication makes no significant difference to chain
friction in terms of power transmission. Spicer's article explains the
theory behind this unexpected result, which could be grossly
simplified to a matter of how little actual polishing action takes
place in the lazily moving chain of a bicycle.

Even a dry chain that squeaks like a box full of bats still transmits
almost exactly the same power as a brand-new factory-lubed chain--the
noise is annoying, but it's apparently all out of proportion to the
increase in friction.

Cheers,

Carl Fogel


Aaargh! Off by more than order of magnitude!

Absolutely no idea where I came up with 0.25 rpm--probably just
looking at the wrong figure or not noticing that a numeral was missing
from a number when I punched enter. That'll teach me not to show my
work.

Slightly short 106-roller chain on 53x11, 100 rpm, single pin-turn
with each pedal stroke, once as it pulls onto front 53, once as it
exits rear 11.

Average turn in degrees is:

( (1/53 * 360) + (1/11 * 360) ) / 2

or (6.8 + 32.7 ) / 2

or ~20 degrees

At 100 rpm, there are 6,000 20-degree turns per hour, the equivalent
of (20/360) * 6,000, or 333.3 full turns in 60 minutes, which is 5.5
rpm, not the mysterious and mistaken 0.25 rpm.

Of course, 5.5 rpm is still pretty slow for polishing chain rollers.

***

A equally embarrassing pair of mistakes in basic arithmetic involve
the 53x19 at 91.5 rpm and 20 mph on a 2124 mm rear tire.

At 91.5 rpm, any pin on the slightly short 106-roller chain makes
about 5500 partial turns (5,490), so in fifty hours (1,000 miles at 20
mph) any pin goes through about 275,000 partial turns (274,500).

That's 275,000 partial turns, ten times the 27,500 that I scribbled
due to my careless, dim-witted reading of a calculator.

The other mistake is that with a 53x19, the average turn isn't ~20
degrees, it's ~13 degrees.

The average degrees for the two turns:

( (1/53) * 360 ) + ( (1/19) * 360 ) ) / 2

or (6.8 + 18.9) / 2

or only 12.9 degrees average turn for 53x19, not 20 degrees.

At 91.5 rpm, that's about 5500 13-degree turns per hour

or (13/360) * 5500 = ~200 full turns per hour, about 3 rpm.

Careless but detail-obsessed nitwits should always show their work.

Cheers,

Carl Fogel

On Fri, 13 Jun 2008 09:33:13 -0700 (PDT), Frank Krygowski
wrote:

On Jun 13, 3:50 am, Ben C wrote:


It is said that cross-chaining increases rate of wear. Why is that? Are
the pins still only worn as they pull on and off the front and rear
sprockets, and it's made worse by having to pull them back into line, or
do they get worn continuously in some way in a cross-chaining situation?

My guess would be this: With the chain running at an angle, the loads
transmitted between links and pins (at the same parts of the chain
travel Carl describes) are not supported by the entire width of the
pin. They're supported by a larger pressure load applied to the end
of the pin, while the rest of the pin gives little help. More
pressure leads to more wear. Similar problems exist when mechanical
shafts are supported by plain bearings that are not in proper
alignment; and for shafts that are insufficiently rigid, and deflect
under load as they spin. All this stuff works better when things are
straight.

In addition, IIRC, chain efficiency is lower when the chain doesn't
run in a straight line. I imagine this is partly due to the effect I
just described, and partly because a laterally-bent chain generates
more friction between the side plates.

- Frank Krygowski

Dear Frank & Ben,

As Frank points out, the twisting concentrates the force at one side
and puts things out of line, which is always bad for wear--you want
the load distributed as evenly as possible.

This twisting and sideways rocking also tends to squish more of the
oil-and-dust (or water-and-mud) in and out of the chain crevices,
which encourages chain wear. Sideways flex is just plain bad because
it helps work road dust into the chain guts.

As for the related matter of efficiency, there is some loss with
cross-chaining, but it's small compared to the penalty for using
smaller gears.

The testing already mentioned by Spicer showed that offsetting
(cross-chaining 52x11, for example) produced only about 0.5% power
losses, while smaller sprockets lost about 3% more power than larger
sprockets (52x11 was about 3% less efficient than 52x21).

Big sprockets good, small sprockets bad.

The details are near Table 1 and the conclusion, after the statistics
are pondered, is that "it appears that the offset has a negligible
effect on efficiency."

http://www.ihpva.org/HParchive/PDF/hp50-2000.pdf

Cheers,

Carl Fogel

wrote:
On Thu, 12 Jun 2008 15:16:05 -0700, "Tom Kunich" cyclintom@yahoo.
com wrote:

wrote in message
...
Spicer tested lubricated and unlubricated bicycle chains in 2000 and
found that lubrication had no significant effect on transmission
efficiency--even when the lubricant was removed by cleaning.

After testing a chain with Castrol Wrench Force Dry Lube, Pedro's Syn
Lube, Generation 4 White Lightning, Spicer thoroughly cleaned the
chain and tested it dry.

No significant differences were noted by his testing equipment:
http://www.ihpva.org/HParchive/PDF/hp50-2000.pdf
That's pretty interesting. You do understand that the idea of testing a
CLEAN chain isn't of much use? Or that lubrication is supposed to allow the
chain to run low friction despite dirt etc. in the mechanism?

Dear Tom,

As Spicer's testing showed, lubrication has next to no effect on
bicycle chain transmission efficiency.

The chief effect of lubrication on bicycle chains is to keep grit out.

it's there to lubricate. it can't and doesn't keep grit out. if
anything, lube retains it.



Anyone can read Spicer's test:
http://www.ihpva.org/HParchive/PDF/hp50-2000.pdf

while that article sincerely seeks to address the causes, it's
incredibly naive in terms of reality. "degreasing" new chains is highly
ineffective because:

1. surface adsorption still retains a layer of grease/lube.

2. even if a chain were assembled without lube at the factory, it would
still have the processing lubes on it used during each component's
forming process.

the chain therefore runs with this surface layer until such time as it
wears out or otherwise becomes contaminated. this is far removed from
real world service where abrasives and water can destroy surface
lubrication and thus allow friction to become much more significant.

"true" degreasing basically involves removing a surface layer of the
material that was previously greased. if that were to be done, surface
friction welding will follow in double-quick time and friction would
become very significant very quickly. real world service in fact sees
two "true" degreasing mechanisms in action - physical abrasion and
chemical action. road grit performs the former, water the latter once
it undercuts and corrodes any surface layers.




Maybe you can tell us more about whatever test you had in mind.


http://en.wikipedia.org/wiki/Adsorption

surface chemistry has attracted a lot of attention in recent years. in
fact, i believe there was even a nobel prize for one of its research
pioneers recently.

On Jun 13, 8:49 pm, jim beam wrote:
wrote:
On Thu, 12 Jun 2008 15:16:05 -0700, "Tom Kunich" cyclintom@yahoo.
com wrote:

wrote in message
. ..
Spicer tested lubricated and unlubricated bicycle chains in 2000 and
found that lubrication had no significant effect on transmission
efficiency--even when the lubricant was removed by cleaning.

After testing a chain with Castrol Wrench Force Dry Lube, Pedro's Syn
Lube, Generation 4 White Lightning, Spicer thoroughly cleaned the
chain and tested it dry.

No significant differences were noted by his testing equipment:
http://www.ihpva.org/HParchive/PDF/hp50-2000.pdf
That's pretty interesting. You do understand that the idea of testing a
CLEAN chain isn't of much use? Or that lubrication is supposed to allow the
chain to run low friction despite dirt etc. in the mechanism?

Dear Tom,

As Spicer's testing showed, lubrication has next to no effect on
bicycle chain transmission efficiency.

The chief effect of lubrication on bicycle chains is to keep grit out.

it's there to lubricate. it can't and doesn't keep grit out. if
anything, lube retains it.



Anyone can read Spicer's test:
http://www.ihpva.org/HParchive/PDF/hp50-2000.pdf

while that article sincerely seeks to address the causes, it's
incredibly naive in terms of reality. "degreasing" new chains is highly
ineffective because:

1. surface adsorption still retains a layer of grease/lube.

2. even if a chain were assembled without lube at the factory, it would
still have the processing lubes on it used during each component's
forming process.

the chain therefore runs with this surface layer until such time as it
wears out or otherwise becomes contaminated. this is far removed from
real world service where abrasives and water can destroy surface
lubrication and thus allow friction to become much more significant.

"true" degreasing basically involves removing a surface layer of the
material that was previously greased. if that were to be done, surface
friction welding will follow in double-quick time and friction would
become very significant very quickly. real world service in fact sees
two "true" degreasing mechanisms in action - physical abrasion and
chemical action. road grit performs the former, water the latter once
it undercuts and corrodes any surface layers.



Maybe you can tell us more about whatever test you had in mind.

http://en.wikipedia.org/wiki/Adsorption

surface chemistry has attracted a lot of attention in recent years. in
fact, i believe there was even a nobel prize for one of its research
pioneers recently.

The discussion hasn't mentioned protection from corrosion, but it
should have. Wear of corroded surfaces, with their dramatically
greater surface area, is much greater.

Calculations of chain efficiency are interesting, and no doubt well
done. But, they are beside the point if little energy is needed to
remove material, with abrasives, from the wearing parts of the chain.

And consider the noise. If the wear on the chain were as bad as the
noise of a squeeking drive train is offensive, you'd certainly lube
your chain.

Great feature of this group is that Carl might find the numbers to
measure just how efficiently a dry, unlubricated chain, can drive the
next rider nuts. smile Hint: Requires truly minimal energy.

Harry Travis

Harry Travis wrote:


The discussion hasn't mentioned protection from corrosion, but it
should have. Wear of corroded surfaces, with their dramatically
greater surface area, is much greater.

I'm not sure what sort of corrosion you have in mind, but my chain
sees nothing but oil and on occasion rain water, that in time washes
all oil out of the chain. Water works as a good lubricant but
unfortunately evaporates readily and leaves the chain unlubricated.

http://www.sheldonbrown.com/brandt/chain-care.html

Calculations of chain efficiency are interesting, and no doubt well
done. But, they are beside the point if little energy is needed to
remove material, with abrasives, from the wearing parts of the
chain.

I think you are looking in the wrong place. The smaller the sprocket,
the larger the articulation angle and proportionately the wear and
minuscule energy loss in the hinge-pin. For instance, two 60t
sprockets make the chain bend 24° in one revolution of the chain. a
53t-11t combination make the chain bend 79°.

And consider the noise. If the wear on the chain were as bad as the
noise of a squeeking drive train is offensive, you'd certainly lube
your chain.

If it squeaks it must be clean. Grit does not allow metal-to-metal
stick-slip squeak.

Great feature of this group is that Carl might find the numbers to
measure just how efficiently a dry, unlubricated chain, can drive
the next rider nuts. smile Hint: Requires truly minimal energy.

Do your own analysis if you have a grasp of the subject that you feel
allows you to write these lines.

Jobst Brandt

wrote:
snip for cleanliness


If it squeaks it must be clean. Grit does not allow metal-to-metal
stick-slip squeak.

that's not true, unless you're talking earth-mover quantities of dirt.
grit very effectively removes surface layers, and thus allows
metal-to-metal contact. asperity welding follows, with squeaking.



Great feature of this group is that Carl might find the numbers to
measure just how efficiently a dry, unlubricated chain, can drive
the next rider nuts. smile Hint: Requires truly minimal energy.

Do your own analysis if you have a grasp of the subject that you feel
allows you to write these lines.

bothering to do analysis never stopped you!

In article ,
wrote:

Harry Travis wrote:


The discussion hasn't mentioned protection from corrosion, but it
should have. Wear of corroded surfaces, with their dramatically
greater surface area, is much greater.

I'm not sure what sort of corrosion you have in mind, but my chain
sees nothing but oil and on occasion rain water, that in time washes
all oil out of the chain. Water works as a good lubricant but
unfortunately evaporates readily and leaves the chain unlubricated.

http://www.sheldonbrown.com/brandt/chain-care.html

Calculations of chain efficiency are interesting, and no doubt well
done. But, they are beside the point if little energy is needed to
remove material, with abrasives, from the wearing parts of the
chain.

I think you are looking in the wrong place. The smaller the sprocket,
the larger the articulation angle and proportionately the wear and
minuscule energy loss in the hinge-pin. For instance, two 60t
sprockets make the chain bend 24° in one revolution of the chain. a
53t-11t combination make the chain bend 79°.

And consider the noise. If the wear on the chain were as bad as the
noise of a squeeking drive train is offensive, you'd certainly lube
your chain.

If it squeaks it must be clean. Grit does not allow metal-to-metal
stick-slip squeak.

Great feature of this group is that Carl might find the numbers to
measure just how efficiently a dry, unlubricated chain, can drive
the next rider nuts. smile Hint: Requires truly minimal energy.

Do your own analysis if you have a grasp of the subject that you feel
allows you to write these lines.

Jobst Brandt

Admittedly, there's little to no tension in the rear derailleur idlers,
but wouldn't that be where the greatest chain bend angle would be found?

On 15 Jun 2008 23:19:10 GMT, wrote:

I think you are looking in the wrong place. The smaller the sprocket,
the larger the articulation angle and proportionately the wear and
minuscule energy loss in the hinge-pin. For instance, two 60t
sprockets make the chain bend 24° in one revolution of the chain. a
53t-11t combination make the chain bend 79°.

[snip]

Do your own analysis if you have a grasp of the subject that you feel
allows you to write these lines.

Jobst Brandt

Dear Jobst,

Aha! A chance to test the newest part of my spreadsheet.

A chain bends only twice under load, not four times.

It bends under load twice on the top run, as it pulls off the rear and
pulls onto the front.

There's no significant load on the lower run as the chain exits the
front or engages the rear sprocket, unless it's a fixie and the rider
brakes through the pedals.

Nor is there any significant load as the chain wraps around the two
idler pulleys--which would have been 8 bends.

(That's one reason why derailleur chains don't wear out twice as fast
as single-speed chains.)

For a 60x60 (a silly but easily calculated example), that's (360/60) +
(360/60) degrees, a total of only 6 + 6 = 12 degrees of rotation under
load as a pin makes a trip around the sprockets.

For a 53x11 (verging on silly, but I pedal it and it exercises a
spreadsheet), that's (360/53) + (360/11) degrees, a total of only 32.7
+ 6.8 = 39.5 degrees of rotation under load.

For a 39x20 (just an example for those grinding up hills), that's
(360/39) + (360/20) degrees, a total of only 9.2 + 18.0 = 27.2 degrees
of rotation under load.

On the other six bends of a derailleur, there is the slight load of
the feeble derailleur spring and the weight of the chain.

Just how little load exists on the lower chain-run was shown by some
early riders who happily let their lower chain-runs dangle loose, with
only an unsprung roller to guide the chain onto the rear sprocket, a
strange approach known as a floating chain:
http://i16.tinypic.com/4gj8g2c.jpg

For true nit-pickers, the length of the chain and the size of the
sprockets affects the rotation-under-load RPM as compared to the pedal
cadence, meaning that longer chains wear at a lower rate.

For a 52x12 derailleur 114-link at 90 RPM, the pins turn under load at
4.21 RPM.

For a 52x12 fixie with a shorter 108-link, the bike goes the same
speed at the same 90 RPM, but the pins turn under load slightly
faster, 4.44 RPM.

Switch to a giant double-length 232-link chain for recumbents and
tandems, and the 52x12 at 90 RPM turns the pins under load at only
2.07 RPM.

***

Incidentally, the real loss of chain efficiency is not so much the
tiny bending of the chain at the pin, but what's called chordal
action. As any chain run (slack or under load) enters the sprocket, it
abruptly decelerates as the link moving in a straight line snaps down
and takes a short-cut to form a chord across the inside of the
"circle" of the sprocket.

The greater the angle, the greater each link decelerates as it enters
the sprocket, and the more the chain run vibrates, which is why small
sprockets are less efficient.

Here's a nice explanation of chordal action, with equations and the
vibratory point:
http://chain-guide.com/basics/2-2-1-chordal-action.html

The vibration wastes far more power than the amazingly tiny friction
that takes thousands and thousands of miles to wear the pin-roller
interface the 0.0025" that adds up to 1/16th of an inch elongation in
a foot of chain.

Using the chordal action equation, here are some sample chain speed
variations for X teeth.

teeth
chordal action
53 0.1756%
52 0.1824%
50 0.1973%
46 0.2331%
42 0.2776%
39 0.3243%
38 0.3146%
34 0.4266%
32 0.4815%
30 0.5478%
28 0.6288%
24 0.8555%
21 1.1169%
20 1.2312%
19 1.3639%
18 1.5192%
17 1.7027%
16 1.9215%
15 2.1852%
14 2.5072%
13 2.9058%
12 3.4074%
11 4.0507%
10 4.8943%
9 6.0307%

That's why big sprockets are more efficient at transmitting power--the
heavy chain run isn't being sped up and slowed down as much every time
a new link engages the sprocket. Wear is more a matter of how gritty
the debris in the polishing paste--

Er, how dirty the chain oil is.

As someone said, "Do your own analysis if you have a grasp of the
subject that you feel allows you to write these lines."

:-)

Cheers,

Carl Fogel

On Mon, 16 Jun 2008 00:18:01 GMT, Ralph Barone
wrote:

In article ,
wrote:

Harry Travis wrote:


The discussion hasn't mentioned protection from corrosion, but it
should have. Wear of corroded surfaces, with their dramatically
greater surface area, is much greater.

I'm not sure what sort of corrosion you have in mind, but my chain
sees nothing but oil and on occasion rain water, that in time washes
all oil out of the chain. Water works as a good lubricant but
unfortunately evaporates readily and leaves the chain unlubricated.

http://www.sheldonbrown.com/brandt/chain-care.html

Calculations of chain efficiency are interesting, and no doubt well
done. But, they are beside the point if little energy is needed to
remove material, with abrasives, from the wearing parts of the
chain.

I think you are looking in the wrong place. The smaller the sprocket,
the larger the articulation angle and proportionately the wear and
minuscule energy loss in the hinge-pin. For instance, two 60t
sprockets make the chain bend 24° in one revolution of the chain. a
53t-11t combination make the chain bend 79°.

And consider the noise. If the wear on the chain were as bad as the
noise of a squeeking drive train is offensive, you'd certainly lube
your chain.

If it squeaks it must be clean. Grit does not allow metal-to-metal
stick-slip squeak.

Great feature of this group is that Carl might find the numbers to
measure just how efficiently a dry, unlubricated chain, can drive
the next rider nuts. smile Hint: Requires truly minimal energy.

Do your own analysis if you have a grasp of the subject that you feel
allows you to write these lines.

Jobst Brandt

Admittedly, there's little to no tension in the rear derailleur idlers,
but wouldn't that be where the greatest chain bend angle would be found?

Dear Ralph,

Yes, there's no load on the chain on the bottom run, except for its
own weight and the feeble derailleur spring.

Jobst mistakenly included the lower run in his explanation, using 4
turns, instead of just the upper run's 2 turns, where the chain is
under load.

The upper run is where the wear occurs because the pins turn under
load as the chain exits the rear and engages the front.

Power loss is different than wear.

The power lost polishing the pins under load is quite small. It takes
thousands of miles to polish each pin interface about 0.0025" and
elongate a foot of chain a whole 1/16th of an inch.

Most of the loss occurs because of what's called chordal action, which
is why lubrication makes little difference to power transmission.

When the chain engages the sprocket, the speed changes. In crude
terms, the link snaps down as it pulls onto the front sprocket and
takes a shortcut across the "circle" of the sprocket, a tiny chord
across the inside of the circle.

So the long, heavy chain run is constantly speeding up and slowing
down a little bit, which means that it vibrates. Accelerating that
mass in a twanging motion takes power.

The smaller the sprocket, the greater the shortcut. The bigger the
shortcut the link takes across the inside of the sprocket "circle",
the greater the change in chain speed, vibration, and power loss.

Here's a page that gives the equation for such chordal action:
http://chain-guide.com/basics/2-2-1-chordal-action.html

As the graph at the bottom shows, the chain speed variation due to
chordal action is almost nothing at 53 teeth (0.1756%), but is about
twenty times as much at 11 teeth (4.0507%).

Keep in mind that the % of chain speed variation is not a direct
measure of power loss--that's a different percentage. But the two are
fairly well related, which is one reason why small sprockets lose more
power than large sprockets.

The speed-change rises very steeply as the tooth count approaches 11
teeth:

teeth
chordal-speed-variation
increase-from-16-teeth

16 1.9215%
15 2.1852% +13.7%
14 2.5072% +30.5%
13 2.9058% +51.2%
12 3.4074% +77.3%
11 4.0507% +110.8%

That's why land-speed-record bikes with two chains connected by a
jackshaft use much bigger sprockets than necessary to obtain their
high gearing.

A pair of ordinary 52x12's coupled by a jackshaft would produce
18.7-to-1 gearing, roughly what's used.

But the two chains would be vibrating badly because of the 12-tooth
sprockets, whose average chain-speed variation is 3.4%.

So Rompelberg used a 70x15 and 60x16 (only 17.5-to-1 gearing) at first
and then 70x15 and 60x14 (20-to-1 gearing) for his land-speed records.
That reduced the average chain-speed-variation down to around 2% and
2.3%, with the mismatched tooth-counts avoiding the two chains
vibrating in synchronization.

Cheers,

Carl Fogel

wrote:
On Mon, 16 Jun 2008 00:18:01 GMT, Ralph Barone
wrote:

In article ,
wrote:

Harry Travis wrote:


The discussion hasn't mentioned protection from corrosion, but it
should have. Wear of corroded surfaces, with their dramatically
greater surface area, is much greater.
I'm not sure what sort of corrosion you have in mind, but my chain
sees nothing but oil and on occasion rain water, that in time washes
all oil out of the chain. Water works as a good lubricant but
unfortunately evaporates readily and leaves the chain unlubricated.

http://www.sheldonbrown.com/brandt/chain-care.html

Calculations of chain efficiency are interesting, and no doubt well
done. But, they are beside the point if little energy is needed to
remove material, with abrasives, from the wearing parts of the
chain.
I think you are looking in the wrong place. The smaller the sprocket,
the larger the articulation angle and proportionately the wear and
minuscule energy loss in the hinge-pin. For instance, two 60t
sprockets make the chain bend 24° in one revolution of the chain. a
53t-11t combination make the chain bend 79°.

And consider the noise. If the wear on the chain were as bad as the
noise of a squeeking drive train is offensive, you'd certainly lube
your chain.
If it squeaks it must be clean. Grit does not allow metal-to-metal
stick-slip squeak.

Great feature of this group is that Carl might find the numbers to
measure just how efficiently a dry, unlubricated chain, can drive
the next rider nuts. smile Hint: Requires truly minimal energy.
Do your own analysis if you have a grasp of the subject that you feel
allows you to write these lines.

Jobst Brandt
Admittedly, there's little to no tension in the rear derailleur idlers,
but wouldn't that be where the greatest chain bend angle would be found?

Dear Ralph,

Yes, there's no load on the chain on the bottom run, except for its
own weight and the feeble derailleur spring.

Jobst mistakenly included the lower run in his explanation, using 4
turns, instead of just the upper run's 2 turns, where the chain is
under load.

The upper run is where the wear occurs because the pins turn under
load as the chain exits the rear and engages the front.

Power loss is different than wear.

The power lost polishing the pins under load is quite small. It takes
thousands of miles to polish each pin interface about 0.0025" and
elongate a foot of chain a whole 1/16th of an inch.

Most of the loss occurs because of what's called chordal action, which
is why lubrication makes little difference to power transmission.

When the chain engages the sprocket, the speed changes. In crude
terms, the link snaps down as it pulls onto the front sprocket and
takes a shortcut across the "circle" of the sprocket, a tiny chord
across the inside of the circle.

So the long, heavy chain run is constantly speeding up and slowing
down a little bit, which means that it vibrates. Accelerating that
mass in a twanging motion takes power.

The smaller the sprocket, the greater the shortcut. The bigger the
shortcut the link takes across the inside of the sprocket "circle",
the greater the change in chain speed, vibration, and power loss.

Here's a page that gives the equation for such chordal action:
http://chain-guide.com/basics/2-2-1-chordal-action.html

As the graph at the bottom shows, the chain speed variation due to
chordal action is almost nothing at 53 teeth (0.1756%), but is about
twenty times as much at 11 teeth (4.0507%).

Keep in mind that the % of chain speed variation is not a direct
measure of power loss--that's a different percentage. But the two are
fairly well related, which is one reason why small sprockets lose more
power than large sprockets.

The speed-change rises very steeply as the tooth count approaches 11
teeth:

teeth
chordal-speed-variation
increase-from-16-teeth

16 1.9215%
15 2.1852% +13.7%
14 2.5072% +30.5%
13 2.9058% +51.2%
12 3.4074% +77.3%
11 4.0507% +110.8%

That's why land-speed-record bikes with two chains connected by a
jackshaft use much bigger sprockets than necessary to obtain their
high gearing.

A pair of ordinary 52x12's coupled by a jackshaft would produce
18.7-to-1 gearing, roughly what's used.

But the two chains would be vibrating badly because of the 12-tooth
sprockets, whose average chain-speed variation is 3.4%.

So Rompelberg used a 70x15 and 60x16 (only 17.5-to-1 gearing) at first
and then 70x15 and 60x14 (20-to-1 gearing) for his land-speed records.
That reduced the average chain-speed-variation down to around 2% and
2.3%, with the mismatched tooth-counts avoiding the two chains
vibrating in synchronization.

Cheers,

Carl Fogel


good informative post.