spoke tension changes under load

[carlfogel@comcast.net]

What happens to spoke tension on a motionless wheel when a normal load
is placed on the axle?

This page uses FEA to calculate spoke tension changes in newtons for a
36-spoke cross-3 symmetrical (front) wheel with a very heavy 1,000
newton (225 lb) load:

http://www.astounding.org.uk/ian/wheel/index.html

Here's an extrapolated graph of the spoke tension changes that Ian
predicts, in pounds rather than newtons and for a more reasonable 95
pound load, with the spokes re-numbered from 1 at the bottom at 6
o'clock:

http://i16.tinypic.com/47ca8fm

How well does Ian's theoretical wheel match a real wheel?

Here's a rig to load a front wheel with 95 pounds on a bathroom scale,
just an old frame with its seat post trapped in a bench vise and a
pole and board attached to the top tube to hold weights over the axle:

http://i9.tinypic.com/4p97ur7.jpg

First, I measured the tension changes in 36-spoke cross-3 aero rim
from a bike used by visitors. The wheel came nicely trued from the
factory.

Here's the graph of how spoke tension changed from that real wheel
with a tire inflated to 110 psi, first in the air and then standing on
a scale showing 95 pounds:

http://i8.tinypic.com/52at279.gif

Oops!

Obviously, twanging spokes on that wheel would not confirm the theory
that only the lowermost spokes change tension significantly when the
axle is loaded. It doesn't match Ian's predicted graph very well.
Instead of staying at about 3 pounds of increased tension, spokes are
jumping up and down between 30 pound gains and 20 pound losses.

What's the explanation?

A) Gross incompetence at Fogel Labs must account for some of the wild
variation--the pay is scandalously low and attracts only workers
unable to find more rewarding jobs.

But if the discrepancy was just the result of inaccurate measurements,
then the bottom spokes probably wouldn't match Ian's FEA prediction.
And a 50-pound variation where the graph is supposed to be nearly
level at a 3 pound gain would be amazingly inaccurate.

B) Theoretical wheel models don't include inflated tires constricting
the rim and lowering the spoke tension about 10% to 15%.

But I'm damned if I can see how that would change things. I just put
tires on the wheels to make them as real as possible.

C) Theoretical wheel models do not include one effect of cross-lacing,
namely that lowering the tension in any spoke must lower the tension
in the other spoke around which the first spoke bends at the crossing.

But this effect, however large it might be, should be fairly even and
diminishing, without one spoke gaining and the next spoke losing lots
of tension.

D) Theoretical wheel models assume absolutely uniform initial spoke
tension that real wheels never achieve.

In fact, many real wheels show very uneven tension. Significant random
variations in initial spoke tension on a true rim might lead to
significant random variations in spoke tension changes under load.

So I tested another 36-spoke cross-3 wheel, one that had more evenly
tensioned spokes than the first wheel, though nothing to boast about:

http://i12.tinypic.com/67n6o1c.gif

Aha! The more even the initial spoke tension, the more the spoke
tension changes resemble the idealized FEA prediction on Ian's page.
Here's a graph with all three spoke-tension changes:

http://i13.tinypic.com/4qro8qx.gif

And here are graphs showing how even the initial spoke tension was,
with a level line showing Ian's idealized wheel set to the average for
the two real wheels:

http://i11.tinypic.com/4lp55cl.gif

http://i15.tinypic.com/4zxw03t.gif

http://i6.tinypic.com/4u1lesl.gif

A few conclusions . . ..

A) Pay cuts may not be necessary at Fogel Labs, but workers should
still strive to improve accuracy. Marginal employees may be given more
suitable tasks, such as cleaning up after the guard dog.

B) On real wheels, spokes with uneven initial spoke tension may indeed
twang in very unexpected ways, even though the wheels are true.

Anyone sinfully proud of his evenly tensioned spokes can arrange to
have his wheel tested--you pay to ship it, I'll pay to ship it back.

C) Uneven initial tension may be a bigger problem than expected.

A real spoke that gains or loses more tension than expected as soon as
you sit on the bike may lead a very exciting secret life when the
wheel starts rolling, with more or larger tension changes per
revolution than an idealized spoke.

D) Real testing often produces curious results. I wonder what spokes
do on rear wheels, which have inherently uneven tension? Maybe someone
will email me about testing a really beautifully tensioned rear wheel?

Cheers,

Carl Fogel

[jobst.brandt@stanfordalumni.org]

Carl Fogel writes:

> What happens to spoke tension on a motionless wheel when a normal
> load is placed on the axle?

> This page uses FEA to calculate spoke tension changes in newtons for
> a 36-spoke cross-3 symmetrical (front) wheel with a very heavy 1,000
> newton (225 lb) load:

http://www.astounding.org.uk/ian/wheel/index.html

> Here's an extrapolated graph of the spoke tension changes that Ian
> predicts, in pounds rather than newtons and for a more reasonable 95
> pound load, with the spokes re-numbered from 1 at the bottom at 6
> o'clock:

http://i16.tinypic.com/47ca8fm

> How well does Ian's theoretical wheel match a real wheel?

> Here's a rig to load a front wheel with 95 pounds on a bathroom
> scale, just an old frame with its seat post trapped in a bench vise
> and a pole and board attached to the top tube to hold weights over
> the axle:

http://i9.tinypic.com/4p97ur7.jpg

> First, I measured the tension changes in 36-spoke cross-3 aero rim
> from a bike used by visitors. The wheel came nicely trued from the
> factory.

> Here's the graph of how spoke tension changed from that real wheel
> with a tire inflated to 110 psi, first in the air and then standing
> on a scale showing 95 pounds:

http://i8.tinypic.com/52at279.gif

> Oops!

> Obviously, twanging spokes on that wheel would not confirm the
> theory that only the lowermost spokes change tension significantly
> when the axle is loaded. It doesn't match Ian's predicted graph very
> well. Instead of staying at about 3 pounds of increased tension,
> spokes are jumping up and down between 30 pound gains and 20 pound
> losses.

> What's the explanation?

> A) Gross incompetence at Fogel Labs must account for some of the
> wild variation--the pay is scandalously low and attracts only
> workers unable to find more rewarding jobs.

> But if the discrepancy was just the result of inaccurate
> measurements, then the bottom spokes probably wouldn't match Ian's
> FEA prediction. And a 50-pound variation where the graph is
> supposed to be nearly level at a 3 pound gain would be amazingly
> inaccurate.

> B) Theoretical wheel models don't include inflated tires
> constricting the rim and lowering the spoke tension about 10% to
> 15%.

> But I'm damned if I can see how that would change things. I just put
> tires on the wheels to make them as real as possible.

> C) Theoretical wheel models do not include one effect of
> cross-lacing, namely that lowering the tension in any spoke must
> lower the tension in the other spoke around which the first spoke
> bends at the crossing.

> But this effect, however large it might be, should be fairly even
> and diminishing, without one spoke gaining and the next spoke losing
> lots of tension.

> D) Theoretical wheel models assume absolutely uniform initial spoke
> tension that real wheels never achieve.

> In fact, many real wheels show very uneven tension. Significant
> random variations in initial spoke tension on a true rim might lead
> to significant random variations in spoke tension changes under
> load.

> So I tested another 36-spoke cross-3 wheel, one that had more evenly
> tensioned spokes than the first wheel, though nothing to boast
> about:

http://i12.tinypic.com/67n6o1c.gif

> Aha! The more even the initial spoke tension, the more the spoke
> tension changes resemble the idealized FEA prediction on Ian's page.
> Here's a graph with all three spoke-tension changes:

http://i13.tinypic.com/4qro8qx.gif

> And here are graphs showing how even the initial spoke tension was,
> with a level line showing Ian's idealized wheel set to the average
> for the two real wheels:

http://i11.tinypic.com/4lp55cl.gif

http://i15.tinypic.com/4zxw03t.gif

http://i6.tinypic.com/4u1lesl.gif

> A few conclusions...

> A) Pay cuts may not be necessary at Fogel Labs, but workers should
> still strive to improve accuracy. Marginal employees may be given
> more suitable tasks, such as cleaning up after the guard dog.

> B) On real wheels, spokes with uneven initial spoke tension may
> indeed twang in very unexpected ways, even though the wheels are
> true.

> Anyone sinfully proud of his evenly tensioned spokes can arrange to
> have his wheel tested--you pay to ship it, I'll pay to ship it back.

> C) Uneven initial tension may be a bigger problem than expected.

> A real spoke that gains or loses more tension than expected as soon
> as you sit on the bike may lead a very exciting secret life when the
> wheel starts rolling, with more or larger tension changes per
> revolution than an idealized spoke.

> D) Real testing often produces curious results. I wonder what spokes
> do on rear wheels, which have inherently uneven tension? Maybe
> someone will email me about testing a really beautifully tensioned
> rear wheel?

Nice work. May I suggest measuring the same spoke as it is moved from
one position to the next, 10° at a time, with the graph going from 12:00
to 12:00 so that the "load affected zone" lies in the center of the plot.

Using the same spoke will avoid effects of varying initial spoke
tension that may confuse the diagram. It will show the continuity of
the salient feature in the center of the plot.

Thanks for the effort.

Jobst Brandt

[carlfogel@comcast.net]

On 13 Sep 2007 06:20:37 GMT, jobst.brandt@stanfordalumni.org wrote:

>Carl Fogel writes:
>
>> What happens to spoke tension on a motionless wheel when a normal
>> load is placed on the axle?
>
>> This page uses FEA to calculate spoke tension changes in newtons for
>> a 36-spoke cross-3 symmetrical (front) wheel with a very heavy 1,000
>> newton (225 lb) load:
>
> http://www.astounding.org.uk/ian/wheel/index.html
>
>> Here's an extrapolated graph of the spoke tension changes that Ian
>> predicts, in pounds rather than newtons and for a more reasonable 95
>> pound load, with the spokes re-numbered from 1 at the bottom at 6
>> o'clock:
>
> http://i16.tinypic.com/47ca8fm
>
>> How well does Ian's theoretical wheel match a real wheel?
>
>> Here's a rig to load a front wheel with 95 pounds on a bathroom
>> scale, just an old frame with its seat post trapped in a bench vise
>> and a pole and board attached to the top tube to hold weights over
>> the axle:
>
> http://i9.tinypic.com/4p97ur7.jpg
>
>> First, I measured the tension changes in 36-spoke cross-3 aero rim
>> from a bike used by visitors. The wheel came nicely trued from the
>> factory.
>
>> Here's the graph of how spoke tension changed from that real wheel
>> with a tire inflated to 110 psi, first in the air and then standing
>> on a scale showing 95 pounds:
>
> http://i8.tinypic.com/52at279.gif
>
>> Oops!
>
>> Obviously, twanging spokes on that wheel would not confirm the
>> theory that only the lowermost spokes change tension significantly
>> when the axle is loaded. It doesn't match Ian's predicted graph very
>> well. Instead of staying at about 3 pounds of increased tension,
>> spokes are jumping up and down between 30 pound gains and 20 pound
>> losses.
>
>> What's the explanation?
>
>> A) Gross incompetence at Fogel Labs must account for some of the
>> wild variation--the pay is scandalously low and attracts only
>> workers unable to find more rewarding jobs.
>
>> But if the discrepancy was just the result of inaccurate
>> measurements, then the bottom spokes probably wouldn't match Ian's
>> FEA prediction. And a 50-pound variation where the graph is
>> supposed to be nearly level at a 3 pound gain would be amazingly
>> inaccurate.
>
>> B) Theoretical wheel models don't include inflated tires
>> constricting the rim and lowering the spoke tension about 10% to
>> 15%.
>
>> But I'm damned if I can see how that would change things. I just put
>> tires on the wheels to make them as real as possible.
>
>> C) Theoretical wheel models do not include one effect of
>> cross-lacing, namely that lowering the tension in any spoke must
>> lower the tension in the other spoke around which the first spoke
>> bends at the crossing.
>
>> But this effect, however large it might be, should be fairly even
>> and diminishing, without one spoke gaining and the next spoke losing
>> lots of tension.
>
>> D) Theoretical wheel models assume absolutely uniform initial spoke
>> tension that real wheels never achieve.
>
>> In fact, many real wheels show very uneven tension. Significant
>> random variations in initial spoke tension on a true rim might lead
>> to significant random variations in spoke tension changes under
>> load.
>
>> So I tested another 36-spoke cross-3 wheel, one that had more evenly
>> tensioned spokes than the first wheel, though nothing to boast
>> about:
>
> http://i12.tinypic.com/67n6o1c.gif
>
>> Aha! The more even the initial spoke tension, the more the spoke
>> tension changes resemble the idealized FEA prediction on Ian's page.
>> Here's a graph with all three spoke-tension changes:
>
> http://i13.tinypic.com/4qro8qx.gif
>
>> And here are graphs showing how even the initial spoke tension was,
>> with a level line showing Ian's idealized wheel set to the average
>> for the two real wheels:
>
> http://i11.tinypic.com/4lp55cl.gif
>
> http://i15.tinypic.com/4zxw03t.gif
>
> http://i6.tinypic.com/4u1lesl.gif
>
>> A few conclusions...
>
>> A) Pay cuts may not be necessary at Fogel Labs, but workers should
>> still strive to improve accuracy. Marginal employees may be given
>> more suitable tasks, such as cleaning up after the guard dog.
>
>> B) On real wheels, spokes with uneven initial spoke tension may
>> indeed twang in very unexpected ways, even though the wheels are
>> true.
>
>> Anyone sinfully proud of his evenly tensioned spokes can arrange to
>> have his wheel tested--you pay to ship it, I'll pay to ship it back.
>
>> C) Uneven initial tension may be a bigger problem than expected.
>
>> A real spoke that gains or loses more tension than expected as soon
>> as you sit on the bike may lead a very exciting secret life when the
>> wheel starts rolling, with more or larger tension changes per
>> revolution than an idealized spoke.
>
>> D) Real testing often produces curious results. I wonder what spokes
>> do on rear wheels, which have inherently uneven tension? Maybe
>> someone will email me about testing a really beautifully tensioned
>> rear wheel?
>
>Nice work. May I suggest measuring the same spoke as it is moved from
>one position to the next, 10° at a time, with the graph going from 12:00
>to 12:00 so that the "load affected zone" lies in the center of the plot.
>
>Using the same spoke will avoid effects of varying initial spoke
>tension that may confuse the diagram. It will show the continuity of
>the salient feature in the center of the plot.
>
>Thanks for the effort.
>
>Jobst Brandt

Dear Jobst,

I think that might miss the point of loading and testing a motionless
wheel (the familiar plucking test fails for uneven tension) versus
what happens to any single spoke once the wheel has been loaded and
starts rolling.

Given a motionless and unloaded wheel, we can't predict what the
tension changes will be when we load the wheel _if_ the initial spoke
tension varies significantly.

The 31 spokes not under the axle, which would show only a tiny ~3-lb
rise in tension and tone on an evenly tensioned wheel, may gain or
lose 20 to 30 lbs in tension when the wheel is unevenly tensioned.

This may be why some posters are unconvinced by the motionless
plucking test--it really doesn't work if the wheel isn't tensioned
evenly, even though the wheel may be as true as anyone could wish.

But once a wheel is loaded and starts rolling, any single spoke should
start to behave as predictably as Professor Gavin's measurements
showed, whether the initial tension was even or not. Any single spoke
should lose considerable tension as it rolls under the wheel for about
50 degrees and then return to its "normal" level for the rest of the
cycle.

The evidence for this is Professor Gavin's real-world test with a
strain gauge on a bicycle ridden around a course. He didn't measure
the change in tension in many spokes as the wheel was loaded. In
figures 9 & 10, he measured what happened to a single spoke _after_
the wheel was loaded and began rolling around the course:

http://www.duke.edu/~hpgavin/papers/HPGavin-Wheel-Paper.pdf

I think that the test that you suggest will just duplicate Gavin's
results, which are better done with a strain gauge in real time, while
the motionless wheel test for unevenly tensioned spokes is probably
easier to do at my crude level.

Cheers,

Carl Fogel

[Ben C]

On 2007-09-13, carlfogel@comcast.net <carlfogel@comcast.net> wrote:
[...]
> Given a motionless and unloaded wheel, we can't predict what the
> tension changes will be when we load the wheel _if_ the initial spoke
> tension varies significantly.

We might be able to-- you could always jumble up the spoke tensions a
bit in the FEA and see what it came up with.

Or measure the actual spoke tensions, put those in the FEA, load the
wheel, measure them again, and compare against the FEA. This would help
validate the FEA and also the theory that it's the uneven spoke tension
that's the cause of the spikiness rather than some other unknown factor
or gremlin. I think Ron Ruff might have an FEA.

[jobst.brandt@stanfordalumni.org]

Carl Fogel writes:

>> Nice work. May I suggest measuring the same spoke as it is moved
>> from one position to the next, 10° at a time, with the graph going
>> from 12:00 to 12:00 so that the "load affected zone" lies in the
>> center of the plot.

>> Using the same spoke will avoid effects of varying initial spoke
>> tension that may confuse the diagram. It will show the continuity
>> of the salient feature in the center of the plot.

>> Thanks for the effort.

> I think that might miss the point of loading and testing a
> motionless wheel (the familiar plucking test fails for uneven
> tension) versus what happens to any single spoke once the wheel has
> been loaded and starts rolling.

> Given a motionless and unloaded wheel, we can't predict what the
> tension changes will be when we load the wheel _if_ the initial
> spoke tension varies significantly.

That may be so, but we can't assume a normal distribution from wheels
with uneven spoke tension, as you have shown. The more uniform the
wheel is the more it begins to operate as theory predicts. The effect
on each spoke is its initial tension and the variation it sees per
revolution and that is what would be shown moving the spoke around to
its different position that it experiences in use. That is ultimately
what counts for the individual spoke and its endurance.

If you take the loosest and tightest spoke for this measurement, I
believe the results would be fairly consistent, assuming the loosest
spoke does not go slack.

> The 31 spokes not under the axle, which would show only a tiny ~3-lb
> rise in tension and tone on an evenly tensioned wheel, may gain or
> lose 20 to 30 lbs in tension when the wheel is unevenly tensioned.

I haven't found that to occur. Whenever I use the plucking test, I
use the same spoke so there is a comparison. I think even if you
pluck random spokes, each before and after loading, you'll not get
increases where you should get decreases, nor audible changes in
spokes in any of the spokes not near the load zone. At least that is
what I experience when plucking spokes of clearly different tension by
tone.

> This may be why some posters are unconvinced by the motionless
> plucking test--it really doesn't work if the wheel isn't tensioned
> evenly, even though the wheel may be as true as anyone could wish.

As I said, this hasn't occurred with wheels I have tested by tone.

> But once a wheel is loaded and starts rolling, any single spoke
> should start to behave as predictably as Professor Gavin's
> measurements showed, whether the initial tension was even or
> not. Any single spoke should lose considerable tension as it rolls
> under the wheel for about 50 degrees and then return to its "normal"
> level for the rest of the cycle.

Why do you cite Gavin's work when he did his study in response to "the
Bicycle Wheel" that predates his work? You could cite results from
the book where all those values are given.

> The evidence for this is Professor Gavin's real-world test with a
> strain gauge on a bicycle ridden around a course. He didn't measure
> the change in tension in many spokes as the wheel was loaded. In
> figures 9 & 10, he measured what happened to a single spoke _after_
> the wheel was loaded and began rolling around the course:

http://www.duke.edu/~hpgavin/papers/HPGavin-Wheel-Paper.pdf

> I think that the test that you suggest will just duplicate Gavin's
> results, which are better done with a strain gauge in real time,
> while the motionless wheel test for unevenly tensioned spokes is
> probably easier to do at my crude level.

In Gavin's test "obstacles, such as potholes, were not avoided." and
included instrumentation and road noise, obscuring essential data.
Just the same, the significant strain occurred the same as in the
computed analysis. You may understand Gavin's Graph 10 but the person
who is not technically inclined may see it merely as a noisy
oscillograph trace, the hash having, literally, little significance.

That road shock affects the level of spoke strain should be obvious.
My intent in the analysis is to show the characteristic of spoke
strain versus position caused by wheel load. In my estimation, that
is best shown in computed graphs that are not distorted by road
irregularities. Effects of road roughness, over miles, can be summed
and added to the computed curves, but in the long term, they merely
increase the magnitude of the computed curves.

Jobst Brandt

[A Muzi]

>> Carl Fogel writes:
>>> What happens to spoke tension on a motionless wheel when a normal
>>> load is placed on the axle?
>>> This page uses FEA to calculate spoke tension changes in newtons for
>>> a 36-spoke cross-3 symmetrical (front) wheel with a very heavy 1,000
>>> newton (225 lb) load:
>> http://www.astounding.org.uk/ian/wheel/index.html
>>
>>> Here's an extrapolated graph of the spoke tension changes that Ian
>>> predicts, in pounds rather than newtons and for a more reasonable 95
>>> pound load, with the spokes re-numbered from 1 at the bottom at 6
>>> o'clock:
>> http://i16.tinypic.com/47ca8fm
-snip-
>>> And here are graphs showing how even the initial spoke tension was,
>>> with a level line showing Ian's idealized wheel set to the average
>>> for the two real wheels:
>> http://i11.tinypic.com/4lp55cl.gif
>> http://i15.tinypic.com/4zxw03t.gif
>> http://i6.tinypic.com/4u1lesl.gif
-snip-
>>> D) Real testing often produces curious results. I wonder what spokes
>>> do on rear wheels, which have inherently uneven tension? Maybe
>>> someone will email me about testing a really beautifully tensioned
>>> rear wheel?

> jobst.brandt@stanfordalumni.org wrote:
>> Nice work. May I suggest measuring the same spoke as it is moved from
>> one position to the next, 10° at a time, with the graph going from 12:00
>> to 12:00 so that the "load affected zone" lies in the center of the plot.
>>
>> Using the same spoke will avoid effects of varying initial spoke
>> tension that may confuse the diagram. It will show the continuity of
>> the salient feature in the center of the plot.

carlfogel@comcast.net wrote:
> I think that might miss the point of loading and testing a motionless
> wheel (the familiar plucking test fails for uneven tension) versus
> what happens to any single spoke once the wheel has been loaded and
> starts rolling.
>
> Given a motionless and unloaded wheel, we can't predict what the
> tension changes will be when we load the wheel _if_ the initial spoke
> tension varies significantly.
-snip-
> I think that the test that you suggest will just duplicate Gavin's
> results, which are better done with a strain gauge in real time, while
> the motionless wheel test for unevenly tensioned spokes is probably
> easier to do at my crude level.

Did I misread this or did you? I thought Jobst meant to mark each spoke,
measure one and then lift the apparatus to index the wheel 1/36
revolution, repeat measure, repeat index, etc
--
Andrew Muzi
www.yellowjersey.org
Open every day since 1 April, 1971

[mike.a.schwab@gmail.com]

On Sep 13, 2:48 am, carlfo...@comcast.net wrote:
> On 13 Sep 2007 06:20:37 GMT, jobst.bra...@stanfordalumni.org wrote:
>
>
>
> >Carl Fogel writes:
>
> >> What happens to spoke tension on a motionless wheel when a normal
> >> load is placed on the axle?
>
> >> This page uses FEA to calculate spoke tension changes in newtons for
> >> a 36-spoke cross-3 symmetrical (front) wheel with a very heavy 1,000
> >> newton (225 lb) load:
>
> >http://www.astounding.org.uk/ian/wheel/index.html
>
> >> Here's an extrapolated graph of the spoke tension changes that Ian
> >> predicts, in pounds rather than newtons and for a more reasonable 95
> >> pound load, with the spokes re-numbered from 1 at the bottom at 6
> >> o'clock:
>
> >http://i16.tinypic.com/47ca8fm
>
> >> How well does Ian's theoretical wheel match a real wheel?
>
> >> Here's a rig to load a front wheel with 95 pounds on a bathroom
> >> scale, just an old frame with its seat post trapped in a bench vise
> >> and a pole and board attached to the top tube to hold weights over
> >> the axle:
>
> >http://i9.tinypic.com/4p97ur7.jpg
>
> >> First, I measured the tension changes in 36-spoke cross-3 aero rim
> >> from a bike used by visitors. The wheel came nicely trued from the
> >> factory.
>
> >> Here's the graph of how spoke tension changed from that real wheel
> >> with a tire inflated to 110 psi, first in the air and then standing
> >> on a scale showing 95 pounds:
>
> >http://i8.tinypic.com/52at279.gif
>
> >> Oops!
>
> >> Obviously, twanging spokes on that wheel would not confirm the
> >> theory that only the lowermost spokes change tension significantly
> >> when the axle is loaded. It doesn't match Ian's predicted graph very
> >> well. Instead of staying at about 3 pounds of increased tension,
> >> spokes are jumping up and down between 30 pound gains and 20 pound
> >> losses.
>
> >> What's the explanation?
>
> >> A) Gross incompetence at Fogel Labs must account for some of the
> >> wild variation--the pay is scandalously low and attracts only
> >> workers unable to find more rewarding jobs.
>
> >> But if the discrepancy was just the result of inaccurate
> >> measurements, then the bottom spokes probably wouldn't match Ian's
> >> FEA prediction. And a 50-pound variation where the graph is
> >> supposed to be nearly level at a 3 pound gain would be amazingly
> >> inaccurate.
>
> >> B) Theoretical wheel models don't include inflated tires
> >> constricting the rim and lowering the spoke tension about 10% to
> >> 15%.
>
> >> But I'm damned if I can see how that would change things. I just put
> >> tires on the wheels to make them as real as possible.
>
> >> C) Theoretical wheel models do not include one effect of
> >> cross-lacing, namely that lowering the tension in any spoke must
> >> lower the tension in the other spoke around which the first spoke
> >> bends at the crossing.
>
> >> But this effect, however large it might be, should be fairly even
> >> and diminishing, without one spoke gaining and the next spoke losing
> >> lots of tension.
>
> >> D) Theoretical wheel models assume absolutely uniform initial spoke
> >> tension that real wheels never achieve.
>
> >> In fact, many real wheels show very uneven tension. Significant
> >> random variations in initial spoke tension on a true rim might lead
> >> to significant random variations in spoke tension changes under
> >> load.
>
> >> So I tested another 36-spoke cross-3 wheel, one that had more evenly
> >> tensioned spokes than the first wheel, though nothing to boast
> >> about:
>
> >http://i12.tinypic.com/67n6o1c.gif
>
> >> Aha! The more even the initial spoke tension, the more the spoke
> >> tension changes resemble the idealized FEA prediction on Ian's page.
> >> Here's a graph with all three spoke-tension changes:
>
> >http://i13.tinypic.com/4qro8qx.gif
>
> >> And here are graphs showing how even the initial spoke tension was,
> >> with a level line showing Ian's idealized wheel set to the average
> >> for the two real wheels:
>
> >http://i11.tinypic.com/4lp55cl.gif
>
> >http://i15.tinypic.com/4zxw03t.gif
>
> >http://i6.tinypic.com/4u1lesl.gif
>
> >> A few conclusions...
>
> >> A) Pay cuts may not be necessary at Fogel Labs, but workers should
> >> still strive to improve accuracy. Marginal employees may be given
> >> more suitable tasks, such as cleaning up after the guard dog.
>
> >> B) On real wheels, spokes with uneven initial spoke tension may
> >> indeed twang in very unexpected ways, even though the wheels are
> >> true.
>
> >> Anyone sinfully proud of his evenly tensioned spokes can arrange to
> >> have his wheel tested--you pay to ship it, I'll pay to ship it back.
>
> >> C) Uneven initial tension may be a bigger problem than expected.
>
> >> A real spoke that gains or loses more tension than expected as soon
> >> as you sit on the bike may lead a very exciting secret life when the
> >> wheel starts rolling, with more or larger tension changes per
> >> revolution than an idealized spoke.
>
> >> D) Real testing often produces curious results. I wonder what spokes
> >> do on rear wheels, which have inherently uneven tension? Maybe
> >> someone will email me about testing a really beautifully tensioned
> >> rear wheel?
>
> >Nice work. May I suggest measuring the same spoke as it is moved from
> >one position to the next, 10° at a time, with the graph going from 12:00
> >to 12:00 so that the "load affected zone" lies in the center of the plot.
>
> >Using the same spoke will avoid effects of varying initial spoke
> >tension that may confuse the diagram. It will show the continuity of
> >the salient feature in the center of the plot.
>
> >Thanks for the effort.
>
> >Jobst Brandt
>
> Dear Jobst,
>
> I think that might miss the point of loading and testing a motionless
> wheel (the familiar plucking test fails for uneven tension) versus
> what happens to any single spoke once the wheel has been loaded and
> starts rolling.
>
> Given a motionless and unloaded wheel, we can't predict what the
> tension changes will be when we load the wheel _if_ the initial spoke
> tension varies significantly.
>
> The 31 spokes not under the axle, which would show only a tiny ~3-lb
> rise in tension and tone on an evenly tensioned wheel, may gain or
> lose 20 to 30 lbs in tension when the wheel is unevenly tensioned.
>
> This may be why some posters are unconvinced by the motionless
> plucking test--it really doesn't work if the wheel isn't tensioned
> evenly, even though the wheel may be as true as anyone could wish.
>
> But once a wheel is loaded and starts rolling, any single spoke should
> start to behave as predictably as Professor Gavin's measurements
> showed, whether the initial tension was even or not. Any single spoke
> should lose considerable tension as it rolls under the wheel for about
> 50 degrees and then return to its "normal" level for the rest of the
> cycle.
>
> The evidence for this is Professor Gavin's real-world test with a
> strain gauge on a bicycle ridden around a course. He didn't measure
> the change in tension in many spokes as the wheel was loaded. In
> figures 9 & 10, he measured what happened to a single spoke _after_
> the wheel was loaded and began rolling around the course:
>
> http://www.duke.edu/~hpgavin/papers/HPGavin-Wheel-Paper.pdf
>
> I think that the test that you suggest will just duplicate Gavin's
> results, which are better done with a strain gauge in real time, while
> the motionless wheel test for unevenly tensioned spokes is probably
> easier to do at my crude level.
>
> Cheers,
>
> Carl Fogel

For the purposes of this test, why not take the wheel(s) off and set
all spokes to the same tension. Leave the brakes unconnected, remount
the wheel, put a load on (passenger / cargo hanging from the seat, and
make your measurements. After the test retrue the wheel.

[carlfogel@comcast.net]

On Thu, 13 Sep 2007 16:18:43 -0500, A Muzi <am@yellowjersey.org>
wrote:

>>> Carl Fogel writes:
>>>> What happens to spoke tension on a motionless wheel when a normal
>>>> load is placed on the axle?
>>>> This page uses FEA to calculate spoke tension changes in newtons for
>>>> a 36-spoke cross-3 symmetrical (front) wheel with a very heavy 1,000
>>>> newton (225 lb) load:
>>> http://www.astounding.org.uk/ian/wheel/index.html
>>>
>>>> Here's an extrapolated graph of the spoke tension changes that Ian
>>>> predicts, in pounds rather than newtons and for a more reasonable 95
>>>> pound load, with the spokes re-numbered from 1 at the bottom at 6
>>>> o'clock:
>>> http://i16.tinypic.com/47ca8fm
>-snip-
>>>> And here are graphs showing how even the initial spoke tension was,
>>>> with a level line showing Ian's idealized wheel set to the average
>>>> for the two real wheels:
>>> http://i11.tinypic.com/4lp55cl.gif
>>> http://i15.tinypic.com/4zxw03t.gif
>>> http://i6.tinypic.com/4u1lesl.gif
>-snip-
>>>> D) Real testing often produces curious results. I wonder what spokes
>>>> do on rear wheels, which have inherently uneven tension? Maybe
>>>> someone will email me about testing a really beautifully tensioned
>>>> rear wheel?
>
>> jobst.brandt@stanfordalumni.org wrote:
>>> Nice work. May I suggest measuring the same spoke as it is moved from
>>> one position to the next, 10° at a time, with the graph going from 12:00
>>> to 12:00 so that the "load affected zone" lies in the center of the plot.
>>>
>>> Using the same spoke will avoid effects of varying initial spoke
>>> tension that may confuse the diagram. It will show the continuity of
>>> the salient feature in the center of the plot.
>
>carlfogel@comcast.net wrote:
>> I think that might miss the point of loading and testing a motionless
>> wheel (the familiar plucking test fails for uneven tension) versus
>> what happens to any single spoke once the wheel has been loaded and
>> starts rolling.
>>
>> Given a motionless and unloaded wheel, we can't predict what the
>> tension changes will be when we load the wheel _if_ the initial spoke
>> tension varies significantly.
>-snip-
>> I think that the test that you suggest will just duplicate Gavin's
>> results, which are better done with a strain gauge in real time, while
>> the motionless wheel test for unevenly tensioned spokes is probably
>> easier to do at my crude level.
>
>Did I misread this or did you? I thought Jobst meant to mark each spoke,
>measure one and then lift the apparatus to index the wheel 1/36
>revolution, repeat measure, repeat index, etc

Dear Andrew,

Let's assume that I misread it, not you.

In any case, it involves either an awful lot of heavy lifting on
someone else's part, followed by groveling on the floor to measure the
most awkward spoke a few dozen times, or else a considerably improved
test rig.

My point, again, is that plucking spokes on a motionless wheel before
and after loading will not produce the idealized results that many
posters have been told to expect _if_ the spokes are unevenly
tensioned.

That was what prompted the whole test--SSTW wrote that he didn't hear
the predicted tone change when plucking motionless spokes and that a
much earlier test that I did showed weird tension changes in a
motionless wheel.

Once the wheel has been loaded and starts rolling, any single spoke
will likely show the expected dramatic tension drop as it rolls under
the axle.

Possibly a single spoke on an unevenly tensioned wheel will also
behave weirdly after it starts rolling, but there are 36 possible
suspects, an infinite variety of uneven tension levels, and each spoke
would have to be tested for a full revolution. The weirdness might
take the form of a narrower (or wider) span where tension drops (say
only 20 or 80 degrees instead of 50), a greater (or lesser) range of
tension drop under the axle (say half or twice as much as the next
spoke), or even strange spots where a particular spoke gains (or
loses) a lot of tension in the other 310 degrees.

The test does suggest how uneven tension may cause a greater range of
tension change for an oddball spoke and cause it to fail sooner, even
though it never loses all tension, which is the usual explanation.

Back to burning slits in the plastic U-skeleton of my seat bag with a
hot ice-pick to repair the failed strap.

Cheers,

Carl Fogel

[carlfogel@comcast.net]

On Fri, 14 Sep 2007 05:41:14 -0000, "mike.a.schwab@gmail.com"
<mike.a.schwab@gmail.com> wrote:

>For the purposes of this test, why not take the wheel(s) off and set
>all spokes to the same tension. Leave the brakes unconnected, remount
>the wheel, put a load on (passenger / cargo hanging from the seat, and
>make your measurements. After the test retrue the wheel.

Dear Mike,

Well, it's much less fuss and trouble to undo the quick releases on
two real wheels that have been ridden and stayed true and pop them in
a modifed test rig than to adjust 36 spokes before and after testing
with a surprisingly awkward unmodified bicycle.

Plus I'm interested in real wheels.

If you have a 700c front wheel that you can spare that's true enough
to suit you, email me about shipping it without any tuning up.

Cheers,

Carl Fogel