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radial drive wind-up

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Cycling Equipment
Published
10 September 2006
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13 September 2006
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steve
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  1. I would like to question the theory that a radial drive rear wheel
    increases spoke tension significantly assuming the non-drive is laced
    in a 2x or 3x pattern and your hub body is reasonably stiff. In fact I
    would argue that given these conditions the non-drive spokes see a
    greater tension change than the drive spokes during tortional loads. I
    have done tests with shimano 7800 dura-ace and ksrium ssc sl wheels
    both which use radial drive. Using a dt tension meter I had a large
    person apply the rim brake to the rear wheel and crank down as hard as
    they could on the pedal to induce a large tortional load. When they
    did this I measured the change in spoke tension of drive and non-drive
    pull spokes. The change in the drive was so small it could have easily
    been error due to hand pressure. On the non-drive pull spokes I found
    tensions varying 20-30kg. To me this seems to be a large difference and
    it makes me think that there must be some other reason besides large
    tension changes for premature spoke fatigue on a radial drive.
    I also think that since the tensions of the spokes are so high hub
    rotation will not cause the bedded spoke to rotate in the hub flange.
    There for it seems that the only cause of premature failure would be
    the constant bending and unbending of the spoke right after it leaves
    the hub flange from hub rotation. This is obviously very amatuer
    thinking and would appreciate any words of wisdom that you might have
    to set me straight.

  2. steve said:

    I would like to question the theory that a radial drive rear wheel
    increases spoke tension significantly assuming the non-drive is laced
    in a 2x or 3x pattern and your hub body is reasonably stiff. In fact I
    would argue that given these conditions the non-drive spokes see a
    greater tension change than the drive spokes during tortional loads. I
    have done tests with shimano 7800 dura-ace and ksrium ssc sl wheels
    both which use radial drive. Using a dt tension meter I had a large
    person apply the rim brake to the rear wheel and crank down as hard as
    they could on the pedal to induce a large tortional load. When they
    did this I measured the change in spoke tension of drive and non-drive
    pull spokes. The change in the drive was so small it could have easily
    been error due to hand pressure. On the non-drive pull spokes I found
    tensions varying 20-30kg. To me this seems to be a large difference and
    it makes me think that there must be some other reason besides large
    tension changes for premature spoke fatigue on a radial drive.
    I also think that since the tensions of the spokes are so high hub
    rotation will not cause the bedded spoke to rotate in the hub flange.
    There for it seems that the only cause of premature failure would be
    the constant bending and unbending of the spoke right after it leaves
    the hub flange from hub rotation. This is obviously very amatuer
    thinking and would appreciate any words of wisdom that you might have
    to set me straight.

    Great idea to actually measure the tension; thanks for posting your
    observations!

    As you theorize, certainly a stiff hub shell helps transfer the torque
    to the crossed left side spokes. The existence of wheels like the ones
    you checked shows they "work". In wheels like that, the "left side"
    spokes *are* the "drive side" spokes -- they do the driving, not the
    right side spokes.

    Do such wheels even suffer premature spoke failure? I don't know -- I'm
    asking because I haven't heard of any premature spoke failures in
    factory wheels that have radial right-side spokes.

  3. Quoted message said:
    steve said:

    I would like to question the theory that a radial drive rear wheel
    increases spoke tension significantly assuming the non-drive is laced
    in a 2x or 3x pattern and your hub body is reasonably stiff. In fact I
    would argue that given these conditions the non-drive spokes see a
    greater tension change than the drive spokes during tortional loads. I
    have done tests with shimano 7800 dura-ace and ksrium ssc sl wheels
    both which use radial drive. Using a dt tension meter I had a large
    person apply the rim brake to the rear wheel and crank down as hard as
    they could on the pedal to induce a large tortional load. When they
    did this I measured the change in spoke tension of drive and non-drive
    pull spokes. The change in the drive was so small it could have easily
    been error due to hand pressure. On the non-drive pull spokes I found
    tensions varying 20-30kg. To me this seems to be a large difference and
    it makes me think that there must be some other reason besides large
    tension changes for premature spoke fatigue on a radial drive.
    I also think that since the tensions of the spokes are so high hub
    rotation will not cause the bedded spoke to rotate in the hub flange.
    There for it seems that the only cause of premature failure would be
    the constant bending and unbending of the spoke right after it leaves
    the hub flange from hub rotation. This is obviously very amatuer
    thinking and would appreciate any words of wisdom that you might have
    to set me straight.

    Great idea to actually measure the tension; thanks for posting your
    observations!

    As you theorize, certainly a stiff hub shell helps transfer the torque
    to the crossed left side spokes. The existence of wheels like the ones
    you checked shows they "work". In wheels like that, the "left side"
    spokes *are* the "drive side" spokes -- they do the driving, not the
    right side spokes.

    Do such wheels even suffer premature spoke failure? I don't know -- I'm
    asking because I haven't heard of any premature spoke failures in
    factory wheels that have radial right-side spokes.


    Steve and Di -

    Interesting topic, somewhat near and dear to my heart.

    I have some experience with the Shimano wheels - the RD5XX variety.

    These I bought as an experiment because they were uniquely enough
    constructed to pique my curiosity. I fully expected them to fail on me,
    as I'm relatively large and have a reputation for exerting considerable
    forces on stuff. I nick-named them the "bumble-bee" wheels, because
    there was no way they could actually work - like bumble-bees can't fly.

    These wheels are radially laced on the right side and crossed on the
    left (due to my experience with these wheels I have abandoned the
    terminology of "drive side" and "non-drive side"😉.

    They also have the spoke heads at the rim, and are reduced spoke count
    wheels. There were times when they felt a bit soft, which I attribute to
    the reduced spoke count.

    The placement of the spoke head at the rim seems like a Good Idea. Most
    of the movement that a spoke sees is at the hub/head junction. Putting a
    large nipple there in a good seat certainly seems like a stronger
    engineering solution, as the weakest portion of the spoke is in a place
    where it doesn't see as much flex or movement. The spokes are
    conventional (but extremely long and bladed), but require a special
    washer at the rim. Obviously the rims are non-standard, having the spoke
    hole in the side of the semi-aero rim as are the hubs. These are not
    wheels one can really rebuild, with the exception of spoke replacement.

    I rode these wheels for about 6000 miles with absolutely no issues with
    spoke breakage. In fact, the wheels stayed true the entire time. They
    were among the best wheels I have ever had over the past 35 years. The
    took a lickin' and kept on tickin'.

    I wish I could continue the experiment with the wheels, but the bike was
    stolen last weekend.

    Based upon my experiences with these wheels I decided to build a new set
    of wheels for my commuter bike. These are 36 spoke wheels, but the right
    side is laced radially and the left side is three cross.

    My commute is fairly rough, as I have occasion to ride down stairs, down
    the middle of railroad tracks (it's easier at speed!) and through
    unpaved areas. I usually have the panniers loaded pretty well, as well
    as my 200+ pound lard ass on board. I run a Continental 700X37 tire. I
    have had some problems with spoke breakage in the past on this bike in
    this usage.

    So far they have a thousand miles or so on them and have worked well.
    They have remained true and there has been no spoke damage (which I
    would not expect in any wheel with only 1000 mile son it).

    Part of the thought process that lead me to do this is that, with
    today's drive trains, rear wheels have a severe dish. If the right side
    is the drive side, then those spokes need to provide most of the motive
    torque as well as holding the dish. If they are radially laced, then
    they cannot really transmit any torque and they are left with the job of
    holding the dish, while the left side spokes provide the driving torque.

    Admittedly, I'm running on intuition and not FEA....

    For now I will say that in my usage, on my bike, with me riding it, they
    work fine. Let's get together in a couple of years and I'll tell you how
    they have fared over 10,000 miles ;^) .

    Cheers,

    Tom

  4. Tom Schmitz said:

    I have some experience with the Shimano wheels - the RD5XX variety.
    There were times when they felt a bit soft, which I attribute to
    the reduced spoke count.

    They are about the flexiest wheels ever made. The fact that you had no
    trouble shows how little flex matters...

    Quoted message said:

    Part of the thought process that lead me to do this is that, with
    today's drive trains, rear wheels have a severe dish. If the right side
    is the drive side, then those spokes need to provide most of the motive
    torque as well as holding the dish. If they are radially laced, then
    they cannot really transmit any torque and they are left with the job of
    holding the dish, while the left side spokes provide the driving torque.

    This is a solution to a "problem" that doesn't exist though, for a
    wheel that is well built. The increased tension from driving torque is
    small and will still not exceed the spoke's capabilities.

    There are some issues with using radial spokes on the right. The right
    hub flange needs to be quite strong to take radial spokes with such
    high tension... especially with 36 spokes. Also your hub needs to
    relatively beefy in the center to transfer the torque without yielding.
    And the crossed spokes will be more likely to go slack during torque +
    bumps because they are already rather loose (on a normal hub anyway).
    This will result in fatigue and failure of the spokes eventually. If
    the left flange is moved in to balance the tension better, this isn't
    an issue... but of course that increases lateral flex, too.

    One thing that radial on the drive side (of the bike, not the hub) can
    give you is a better bracing angle to the rim... if you lace heads in.
    You may not have enough derailleur clearance though. Because of this
    one advantage, it is an ok idea for a manufacturer to design and build
    a wheel this way... but be careful when you do it yourself and use
    parts that *weren't* designed for it.

  5. Ron Ruff said:
    Tom Schmitz said:

    I have some experience with the Shimano wheels - the RD5XX variety.
    There were times when they felt a bit soft, which I attribute to
    the reduced spoke count.

    They are about the flexiest wheels ever made. The fact that you had no
    trouble shows how little flex matters...

    My sentiments as well. I noticed it, but was not bothered by it.

    Quoted message said:
    Quoted message said:

    Part of the thought process that lead me to do this is that, with
    today's drive trains, rear wheels have a severe dish. If the right side
    is the drive side, then those spokes need to provide most of the motive
    torque as well as holding the dish. If they are radially laced, then
    they cannot really transmit any torque and they are left with the job of
    holding the dish, while the left side spokes provide the driving torque.

    This is a solution to a "problem" that doesn't exist though, for a
    wheel that is well built. The increased tension from driving torque is
    small and will still not exceed the spoke's capabilities.

    Hmmm.. Not sure I agree 100% with that. "A wheel that is well built" is
    somewhat nebulous, and I might argue that a well built wheel is a bit at
    the ragged edge of performance with severely dished designs. Relieving
    the right side of some duty creates an additional margin of strength. Of
    course, lacing the right side radially places the strain vector through
    a smaller section on the hub. It all could be [censored]-for-tat.

    Alas, this is a bit of an argument similar to how many angels can dance
    on the head of a pin. There are so many variables and intended usages to
    cope with. You are correct in that currently designed conventional
    wheels are strong enough as-is.

    Quoted message said:


    There are some issues with using radial spokes on the right. The right
    hub flange needs to be quite strong to take radial spokes with such
    high tension... especially with 36 spokes. Also your hub needs to
    relatively beefy in the center to transfer the torque without yielding.

    Yes to all of that. The hub I'm using is similar in design to a Shimano
    Parallax, which has a rather beefy center. I'm not aware of any
    conventional rear hub, however, that is designed for radial build and
    this one is no different in that respect. Whether or not it will
    withstand such treatment only time will tell. This is, after all, an
    experiment (I'm easily amused).

    Quoted message said:

    And the crossed spokes will be more likely to go slack during torque +
    bumps because they are already rather loose (on a normal hub anyway).
    This will result in fatigue and failure of the spokes eventually. If
    the left flange is moved in to balance the tension better, this isn't
    an issue... but of course that increases lateral flex, too.

    I have not noticed any strain-induced slackness; time will tell on the
    fatigue aspect.

    Quoted message said:


    One thing that radial on the drive side (of the bike, not the hub) can
    give you is a better bracing angle to the rim... if you lace heads in.
    You may not have enough derailleur clearance though. Because of this
    one advantage, it is an ok idea for a manufacturer to design and build
    a wheel this way... but be careful when you do it yourself and use
    parts that *weren't* designed for it.


    I did build "heads in" for that very reason. I didn't do the math, but
    it must be at least .005% better than real life.... :^)

    Cheers,

    Tom

  6. Ron Ruff said:
    Quoted message said:

    This is a solution to a "problem" that doesn't exist though, for a


    wheel that is well built. The increased tension from driving torque is
    small and will still not exceed the spoke's capabilities.

    There are some issues with using radial spokes on the right. The right
    hub flange needs to be quite strong to take radial spokes with such
    high tension... especially with 36 spokes. Also your hub needs to
    relatively beefy in the center to transfer the torque without yielding.
    And the crossed spokes will be more likely to go slack during torque +
    bumps because they are already rather loose (on a normal hub anyway).
    This will result in fatigue and failure of the spokes eventually. If
    the left flange is moved in to balance the tension better, this isn't
    an issue... but of course that increases lateral flex, too.

    One thing that radial on the drive side (of the bike, not the hub) can
    give you is a better bracing angle to the rim... if you lace heads in.
    You may not have enough derailleur clearance though. Because of this
    one advantage, it is an ok idea for a manufacturer to design and build
    a wheel this way... but be careful when you do it yourself and use
    parts that *weren't* designed for it.

    So from what I understand you are saying the largest issues with radial
    lacing on the drive side is hub body and flange strength as well as
    higher fatigue rates for "push" spokes on the non-drive side. Lets say
    we lace a wheel up to a philwood hub which does allow radial lacing and
    has a large diameter hub body. If the drive side was radially laced
    and the non-drive was 3x would you be more concerned with the non-drive
    spokes failing prematurely or the drive side? As you said earlier, we
    must consider that tensions are more even between drive and non-drive
    since heads in radial lacing gives a greater bracing angle.
    Steve

  7. steve said:

    Lets say
    we lace a wheel up to a philwood hub which does allow radial lacing and
    has a large diameter hub body. If the drive side was radially laced
    and the non-drive was 3x would you be more concerned with the non-drive
    spokes failing prematurely or the drive side? As you said earlier, we
    must consider that tensions are more even between drive and non-drive
    since heads in radial lacing gives a greater bracing angle.

    Sheldon Brown postulates that in a normal wheel (3x both sides) it is
    not uncommon for "pushing" spokes on the NDS to go slack and fatigue.
    He recommends radial lacing on the NDS for this reason. By making the
    DS radial so the NDS has to transfer all the torque, it will be even
    more likely that the "pushing" spokes go slack. So... I'd be more
    concerned about the NDS... the radial spokes on the DS should be
    fine... so long as the hub is ok.

    If you are curious you might look at the bracing angles and what the
    resulting ratios in spoke tensions would be for the two cases. An
    offset rim (like an Aerohead OC) would also help.

  8. BTW steve, when you found tensions varying 20-30kg, that was between
    the lowest and highest... yes? So a single spoke would see a 10-15kg
    tension change from it's unloaded state?

  9. On 10 Sep 2006 21:27:06 -0700, "Ron Ruff" <[email hidden]>

    Quoted message said:


    steve said:

    Lets say
    we lace a wheel up to a philwood hub which does allow radial lacing and
    has a large diameter hub body. If the drive side was radially laced
    and the non-drive was 3x would you be more concerned with the non-drive
    spokes failing prematurely or the drive side? As you said earlier, we
    must consider that tensions are more even between drive and non-drive
    since heads in radial lacing gives a greater bracing angle.

    Sheldon Brown postulates that in a normal wheel (3x both sides) it is
    not uncommon for "pushing" spokes on the NDS to go slack and fatigue.
    He recommends radial lacing on the NDS for this reason. By making the
    DS radial so the NDS has to transfer all the torque, it will be even
    more likely that the "pushing" spokes go slack. So... I'd be more
    concerned about the NDS... the radial spokes on the DS should be
    fine... so long as the hub is ok.

    If you are curious you might look at the bracing angles and what the
    resulting ratios in spoke tensions would be for the two cases. An
    offset rim (like an Aerohead OC) would also help.

    Dear Steve and Ron,

    Browse down to "Half-radial Spoking" and then "Wrong-way Half Radial":

    http://sheldonbrown.com/wheelbuild.html#radial

    Cheers,

    Carl Fogel

  10. Ron Ruff said:

    BTW steve, when you found tensions varying 20-30kg, that was between
    the lowest and highest... yes? So a single spoke would see a 10-15kg
    tension change from it's unloaded state?

    Yes, a single pull spoke would increase 10-15kg after a torque was
    applied. I understand that this might not be a huge amount but it is
    still a huge difference compared to the drive side tension changes
    according to this test. So my question still stands as to why most
    people think that radial drive will cause drive side spokes to
    prematurely fail.

  11. Quoted message said:

    On 10 Sep 2006 21:27:06 -0700, "Ron Ruff" <[email hidden]>
    wrote:

    Dear Steve and Ron,

    Browse down to "Half-radial Spoking" and then "Wrong-way Half Radial":

    http://sheldonbrown.com/wheelbuild.html#radial

    Cheers,

    Carl Fogel

    Carl,
    I did browse "Half-radial Spoking" and the "Wrong-way Half Radial" but
    it doesn't seem to explain anything new. I think that some companies
    might have laced the drive side radially for the reasons Sheldon brown
    states but, I think it is quite clear that heads in radial lacing on
    the drive side does provide a better bracing angle. This being the
    case I find most people disaprove of radial drive lacing not because of
    the fatigue of non-drive spokes but because of premature fatigue on the
    drive side. In fact I believe even Joe Brandt stated in his book that
    a radial dive lacing would cause substantial increase in tension on the
    drive side from tortional loads causing excellerated fatigue, though
    please correct me if I am wrong since I do not have the text in front
    of me and could be mis-interpreting what he wrote. This is what I am
    arguing, that the drive side of a radial laced spoke experiences very
    little tension change through tortional loads. So, if we were able to
    tension the non-drive crossed spokes to the point were the "push"
    spokes would not completly detension what would be the problem in
    biulding a wheel like this assuming the hub is capable of handling this
    lacing pattern.

    Steve

  12. steve said:


    Quoted message said:

    On 10 Sep 2006 21:27:06 -0700, "Ron Ruff" <[email hidden]>
    wrote:

    Dear Steve and Ron,

    Browse down to "Half-radial Spoking" and then "Wrong-way Half Radial":

    http://sheldonbrown.com/wheelbuild.html#radial

    Cheers,

    Carl Fogel

    Carl,
    I did browse "Half-radial Spoking" and the "Wrong-way Half Radial" but
    it doesn't seem to explain anything new. I think that some companies
    might have laced the drive side radially for the reasons Sheldon brown
    states but, I think it is quite clear that heads in radial lacing on
    the drive side does provide a better bracing angle. This being the
    case I find most people disaprove of radial drive lacing not because of
    the fatigue of non-drive spokes but because of premature fatigue on the
    drive side. In fact I believe even Joe Brandt stated in his book that
    a radial dive lacing would cause substantial increase in tension on the
    drive side from tortional loads causing excellerated fatigue, though
    please correct me if I am wrong since I do not have the text in front
    of me and could be mis-interpreting what he wrote. This is what I am
    arguing, that the drive side of a radial laced spoke experiences very
    little tension change through tortional loads. So, if we were able to
    tension the non-drive crossed spokes to the point were the "push"
    spokes would not completly detension what would be the problem in
    biulding a wheel like this assuming the hub is capable of handling this
    lacing pattern.

    Steve

    Dear Steve,

    Here are Jobst's comments on radial spoking:

    Radial spokes carry loads just as well as crossed spokes, but they
    cannot transmit torque. They transmit torque only after the hub
    rotates ahead of the rim, making the spokes no longer truly radial.
    This rotation produces a small tangential offset, or lever, on which
    spoke tension can act to produce torque. This lever is the distance
    between the as of the hub and the extended as of the no-longer-radial
    spokes. The driving torque is the product of this small offset and the
    tension of all the spokes.

    In a radial rear wheel the windup that occurs while riding is small
    (less than two degrees). However, this motion increases spoke fatigue,
    and spoke rotation in the flange causes wear. As radial spokes wind up
    under torque, they become appreciably tighter causing high rim stress
    and, in some instances, flange or rim failure. Looser spoking would
    reduce windup induced tension, but it would also reduce wheel
    strength.

    Even though they transmit no torque, front wheels should not be spoked
    radially because high radial stress can cause fatigue failure of their
    flanges. The spoke holes of aluminum alloy hubs can break out causing
    wheel collapse. Flange fatigue takes time, so these failures do not
    occur immediately. Some lightweight hubs carry specific warnings
    against radial spoking.

    --"The Bicycle Wheel," 3rd edition, p. 67

    I'm not sure that I follow which spokes you plan to tension how much,
    but I suspect that any scheme that relies on radically changing the
    tension on one side without affecting the other will fail.

    Cheers,

    Carl Fogel

  13. Ron Ruff said:
    Quoted message said:

    Lets say we lace a wheel up to a Phil Wood hub which does allow
    radial lacing and has a large diameter hub body. If the drive side
    was radially laced and the non-drive was 3x would you be more
    concerned with the non-drive spokes failing prematurely or the
    drive side? As you said earlier, we must consider that tensions
    are more even between drive and non-drive since heads in radial
    lacing gives a greater bracing angle.

    Quoted message said:

    Sheldon Brown postulates that in a normal wheel (3x both sides) it
    is not uncommon for "pushing" spokes on the NDS to go slack and
    fatigue. He recommends radial lacing on the NDS for this reason. By
    making the DS radial so the NDS has to transfer all the torque, it
    will be even more likely that the "pushing" spokes go
    slack. So... I'd be more concerned about the NDS... the radial
    spokes on the DS should be fine... so long as the hub is OK.

    Quoted message said:

    If you are curious you might look at the bracing angles and what the
    resulting ratios in spoke tensions would be for the two cases. An
    offset rim (like an Aerohead OC) would also help.

    If you look at the graphs in "the Bicycle Wheel" you can assure
    yourself that this will not occur, the torque load shown there is the
    same as the radial load and the braking load, just to make the
    relative effects more comparable. In effect, the wheel shown is
    climbing a vertical wall.

    Jobst Brandt

  14. Quoted message said:

    Here are Jobst's comments on radial spoking:
    Even though they transmit no torque, front wheels should not be spoked
    radially because high radial stress can cause fatigue failure of their
    flanges. The spoke holes of aluminum alloy hubs can break out causing
    wheel collapse. Flange fatigue takes time, so these failures do not
    occur immediately. Some lightweight hubs carry specific warnings
    against radial spoking.

    --"The Bicycle Wheel," 3rd edition, p. 67

    Don't the spokes on a front wheel transmit torque under braking?

    Cam

  15. Cam said:


    Quoted message said:

    Here are Jobst's comments on radial spoking:
    Even though they transmit no torque, front wheels should not be spoked
    radially because high radial stress can cause fatigue failure of their
    flanges. The spoke holes of aluminum alloy hubs can break out causing
    wheel collapse. Flange fatigue takes time, so these failures do not
    occur immediately. Some lightweight hubs carry specific warnings
    against radial spoking.

    --"The Bicycle Wheel," 3rd edition, p. 67

    Don't the spokes on a front wheel transmit torque under braking?

    This depends on where the braking surface is located relative to the
    hub.

  16. Cam said:

    Don't the spokes on a front wheel transmit torque under braking?

    No, since the brake acts directly on the rim rather than the hub.

  17. Quoted message said:

    If you look at the graphs in "the Bicycle Wheel"

    Gotta get that book someday...

  18. steve said:

    Joe Brandt stated in his book that
    a radial dive lacing would cause substantial increase in tension on the
    drive side from tortional loads causing excellerated fatigue

    He is refering to having an entire rear wheel radial laced. In that
    case the hub/rim would wind up and increase fatigue. In a half radial
    wheel the crossed spokes carry the torque with very little
    displacement, so the radial spokes are fine.

  19. Quoted message said:
    Quoted message said:


    If you look at the graphs in "the Bicycle Wheel" you can assure
    yourself that this will not occur, the torque load shown there is the
    same as the radial load and the braking load, just to make the
    relative effects more comparable. In effect, the wheel shown is
    climbing a vertical wall.

    Jobst Brandt

    Jobst,
    If you don't mind, I would like to comment on your statement that a
    rear wheel, which is radially laced, increases spoke tensions
    significantly when a tortional load is applied. Using my amateur math,
    it seems that spoke tensions would not change a significant amount. As
    I understand it, when a tortional load is applied to a wheel the
    tension changes in the spoke as a result of the hub flange rotating a
    certain amount there for increasing the distance between the flange
    hole and the rim which stretches the spoke and causes it to increase in
    tension. In your book I believe you stated that the wind-up of a rear
    wheel that is radially laced would be less than two degrees. If this
    is the case it seems to me that the distance between the flange hole
    and the rim would change very little which should result in a
    relatively small tension increase.

    Thank you for your time and comments

    Steve

  20. Steve Sauter said:
    Quoted message said:

    If you look at the graphs in "the Bicycle Wheel" you can assure
    yourself that this will not occur, the torque load shown there is
    the same as the radial load and the braking load, just to make the
    relative effects more comparable. In effect, the wheel shown is
    climbing a vertical wall.

    Quoted message said:

    If you don't mind, I would like to comment on your statement that a
    rear wheel, which is radially laced, increases spoke tensions
    significantly when a tortional load is applied. Using my amateur
    math, it seems that spoke tensions would not change a significant
    amount. As I understand it, when a tortional load is applied to a
    wheel the tension changes in the spoke as a result of the hub flange
    rotating a certain amount there for increasing the distance between
    the flange hole and the rim which stretches the spoke and causes it
    to increase in tension. In your book I believe you stated that the
    wind-up of a rear wheel that is radially laced would be less than
    two degrees. If this is the case it seems to me that the distance
    between the flange hole and the rim would change very little which
    should result in a relatively small tension increase.

    Quoted message said:

    Thank you for your time and comments

    Torsional windup of two degrees has a cosine effect of 0.1, and that
    times a flange radius of 22mm gives 2.2mm elongation over the initial
    stress of spoke tension. That is more than double the tension and
    cyclically would rip the spoke out of the flange radially in a short
    time. Even at x3 spokes tear out of rear hubs. Beyond this, the
    spokes and nipples would also be under a greater cyclic stress than
    cross laced spoking causes.

    As you see, broken spokes are discussed here off and on, showing that
    they occur under apparently far better conditions than on radially
    spoked drive wheels. You can spoke your wheels any way you like but
    don't encourage others do choose your method.

    Jobst Brandt

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