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spoke tension changes under load

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13 September 2007
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  1. 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

  2. Carl Fogel said:

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

    Quoted message said:

    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

    Quoted message said:

    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

    Quoted message said:

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

    Quoted message said:

    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

    Quoted message said:

    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.

    Quoted message said:

    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

    Quoted message said:

    Oops!

    Quoted message said:

    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.

    Quoted message said:

    What's the explanation?

    Quoted message said:

    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.

    Quoted message said:

    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.

    Quoted message said:

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

    Quoted message said:

    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.

    Quoted message said:

    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.

    Quoted message said:

    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.

    Quoted message said:

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

    Quoted message said:

    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.

    Quoted message said:

    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

    Quoted message said:

    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

    Quoted message said:

    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

    Quoted message said:

    A few conclusions...

    Quoted message said:

    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.

    Quoted message said:

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

    Quoted message said:

    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.

    Quoted message said:

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

    Quoted message said:

    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.

    Quoted message said:

    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

  3. Quoted message said:
    Carl Fogel said:

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

    Quoted message said:

    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

    Quoted message said:

    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

    Quoted message said:

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

    Quoted message said:

    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

    Quoted message said:

    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.

    Quoted message said:

    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

    Quoted message said:

    Oops!

    Quoted message said:

    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.

    Quoted message said:

    What's the explanation?

    Quoted message said:

    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.

    Quoted message said:

    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.

    Quoted message said:

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

    Quoted message said:

    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.

    Quoted message said:

    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.

    Quoted message said:

    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.

    Quoted message said:

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

    Quoted message said:

    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.

    Quoted message said:

    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

    Quoted message said:

    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

    Quoted message said:

    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

    Quoted message said:

    A few conclusions...

    Quoted message said:

    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.

    Quoted message said:

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

    Quoted message said:

    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.

    Quoted message said:

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

    Quoted message said:

    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.

    Quoted message said:

    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

  4. On 2007-09-13, [email hidden] <[email hidden]> wrote:
    [...]

    Quoted message said:

    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.

  5. Quoted message said:
    Quoted message said:
    Carl Fogel said:

    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

    Quoted message said:

    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-

    Quoted message said:
    Quoted message said:
    Quoted message said:

    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-

    Quoted message said:
    Quoted message said:
    Quoted message said:

    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?

    Quoted message said:
    Quoted message said:

    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.

    Quoted message said:

    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-

    Quoted message said:

    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

  6. On Thu, 13 Sep 2007 16:18:43 -0500, A Muzi <[email hidden]>

    Quoted message said:
    Quoted message said:
    Quoted message said:

    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-

    Quoted message said:
    Quoted message said:

    > 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-

    Quoted message said:
    Quoted message said:

    > 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?

    Quoted message said:
    Quoted message said:

    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.

    Quoted message said:

    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-

    Quoted message said:

    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

  7. Quoted message said:
    Quoted message said:

    Carl Fogel writes:

    Quoted message said:
    Quoted message said:

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

    Quoted message said:
    Quoted message said:

    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:

    Quoted message said:

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

    Quoted message said:
    Quoted message said:

    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:

    Quoted message said:

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

    Quoted message said:
    Quoted message said:

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

    Quoted message said:
    Quoted message said:

    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:

    Quoted message said:

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

    Quoted message said:
    Quoted message said:

    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.

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    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:

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

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    Oops!

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    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.

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    What's the explanation?

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    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.

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    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.

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

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    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.

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    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.

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    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.

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

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    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.

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    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:

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

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    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:

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

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    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:

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

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

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

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    A few conclusions...

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    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.

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

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    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.

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

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    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.

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    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?

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    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.

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    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.

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    Thanks for the effort.

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    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.

  8. email hidden said:

    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

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