Forces on spokes

bicycle_disciple said:

Hi all.

Just wanted to clear a little question. Thinking of a wheel spoke as a
prismatic member, what is the nature of normal forces acting on it. Is
it all in tension, all in compression or a mix of both?

Thanks.

Ron

Dear Ron,

Forces on a pre-tensioned wheel loaded at the axle:

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

Cheers,

Carl Fogel

Quoted message said:

Until all the pre-tension is used up, even a string will "support" a
compressive load

A string may support a compressive load if it is pretensioned but if
there is nothing to support the string it doesn't matter. There is no
way for a spoke under compressive load to support anything except by
its nipple's friction with the spoke hole. Any compressive load will
try to push the spoke out the outside of the rim.

Quoted message said:

Experiment seems to confirm theory.

The experiment confirms that the spokes do indeed go slack as they pass
under the hub. It doesn't in anyway prove that they are supporting the
wheel through compressive loading before they go slack.

Quoted message said:

Quoted message said:

Experiment seems to confirm theory.

The experiment confirms that the spokes do indeed go slack as they pass
under the hub. It doesn't in anyway prove that they are supporting the
wheel through compressive loading before they go slack.

Dear SSTW,

All the spokes are accounted for in both theory and experiment.

What else besides the spokes connects the wheel to the loaded axle?

If the forces don't show up anywhere else, what supports the load?

Ian's page goes through this in patient detail--the increase in
tension in the other spokes isn't anywhere near enough to support the
load.

Cheers,

Carl Fogel

Quoted message said:

Quoted message said:

Until all the pre-tension is used up, even a string will "support" a
compressive load

A string may support a compressive load if it is pretensioned but if
there is nothing to support the string it doesn't matter. There is no
way for a spoke under compressive load to support anything except by
its nipple's friction with the spoke hole. Any compressive load will
try to push the spoke out the outside of the rim.

What would you say if the string were replaced with a chain that was
welded to the rim? How is the link to link interface of the chain any
different from the nipple to rim interface?

The point being, the pretension in the spoke acts on the nipple to rim
interface just as it does on the links (or string or spoke).

--
Joe Riel

That article makes the simplifying assumption that if you can hang from
a rope, you can sit on it.

A foolish linearity is the hobgoblin of little minds.

Quoted message said:

Someone did a test of a bicycle with a tensiometer providing constant
telemetry of spoke tension and found that the spokes under the axle
lost tension, the spokes above the axle stayed relatively close, and
the spokes at +-90o from those under the axle increased. My ignorant
conclusion based on this data was that all the spokes except those
directly under the axle contributed to sharing the load, and that the
load was shared (this part is even more controversial) by the tendencey
of the rim to distort ovally. Others on this ng will now proceed to
dismiss this data as insignificant

Not me - I agree 100%

Quoted message said:

and insist that because the spokes
under the axle are tensioned, they are able to support the weight of
the bike until the load becomes great enough that they go slack,

By being pretensioned the spokes at the bottom are trying to pull the
axle downward, not to push it back up. The pretensioning in the
bottome spokes actually increases the load that the other spokes must
support.

Quoted message said:

they don't really bother to explain convincingly (for me) why the
greatest tension rise is seen in the spokes that are _parallel_ to the
road surface.

For me personally, the tensioned spoke theory would be plausible if the
spoke nipple were somehow fixed in the rim, but because the nipple is
not fixed, there is no way for the spoke (tensioned or not) to
significantly act acgainst the rim to provide support of the weight of
the bicycle when the spoke is directly under the axle/hub.

And a spoke would be woefully inadequate to support any compressive
loads anyway.

Jeff

bicycle_disciple said:

Hi all.

Just wanted to clear a little question.

Or a not so little question, as the case seems to be!

Quoted message said:

Thinking of a wheel spoke as a
prismatic member, what is the nature of normal forces acting on it. Is
it all in tension, all in compression or a mix of both?

Spokes are always in tension. A thin wire cannot go into compression
without buckling. Spokes are pretensioned when the wheel is built, and
the tension in any spoke increases or decreases as the wheel rotates,
with the lowest tension when the spoke is beneath the axle.
This much is uncontroversial, I think.

Jeff

Quoted message said:

Maybe you should pluck spokes at various locations around the wheel
and nor which ones (by change in tone) are affected by placing a load
on the wheel. Let me tell you in advance what you will find (for pure
vertical loading). The only spokes affected by the load will be the
three or four spokes at the bottom directed at the road from the hub.

Those spokes are affected much more than the others by the load, I
agree. They undergo a dramatic loss of pretensioning.

Quoted message said:

If the spokes at the top are supporting the wheel, as you propose,
then they would be affected by the load, but they are not. I think
you are, as many others, not visualizing these things algebraically.
The problem is much like adding debits and credits to a bank account.

Here is my best explanation: The downward force on the axle due to the
weight of the rider must must be countered by an upward force of equal
magnitude exerted by the spokes on the hub. Thats just elementary
statics, what I think you are calling "debits and credits"

Lets divide the spokes into three somewhat imprecise categories:
1. Spokes at the bottom, underneath the axle.
2. Spokes to the side of the axle (mostly horizontal)
3. Spokes above the axle (mostly vertical)

How spokes in each category help to exert an upward force on the axle?

Category 1 would have to "push" upward on the axle from below. This
would put them in compression, which cannot, and does not, happen.

Category 2 cannot push up or down on the axle very much because they
are oriented mostly sideways to it.

Category 3 would have to pull upward on the axle, requiring them to be
in tension, which is what spokes are designed to do.

Conclusion, the load is supported by the spokes above the wheel. This
does not mean that their natural pretension has to increase very much,
or at all, when the weight is applied, since they no longer have to
support the pretensioning of the bottom spokes. But they are the ones
supporting the wheel by keeping the hub from dropping toward the
ground. You could remove the spokes at the bottom and at the sides
from a loaded wheel at rest and the wheel would not collapse.

Jeff

Quoted message said:

That article makes the simplifying assumption that if you can hang from
a rope, you can sit on it.

A foolish linearity is the hobgoblin of little minds.

Dear Kendall,

Cut a rubber band, tie it to something that weighs a few pounds, and
take it to the post office.

Note the weight on the digital scale.

Use one finger to pull up on the rubber band until half the weight
disappears from the scale.

Push your finger down a bit with your other hand.

The digital scale will indicate that you are pushing down on it
through the stretched rubber band.

The scale will keep showing how hard you push until all the rubber
band's pre-tension is used up.

A string will do the same thing, but its range of elasticity is so
small that we can't see what happens--and the range of elasticity of
steel spokes is even smaller.

I agree that the ability of a pre-tensioned member to function in
compression is a very annoying principle.

Cheers,

Carl Fogel

Unfortunately, I missed this sentence which redefines the variables:

"This is a change from the unloaded state, so compression doesn't
actually mean compression, it means reduction in tension."

This is a perturbation in force.

In article <[email hidden]>, [email hidden] says...

Quoted message said:

Quoted message said:

That article makes the simplifying assumption that if you can hang from
a rope, you can sit on it.

A foolish linearity is the hobgoblin of little minds.

Dear Kendall,

Cut a rubber band, tie it to something that weighs a few pounds, and
take it to the post office.

Note the weight on the digital scale.

Use one finger to pull up on the rubber band until half the weight
disappears from the scale.

Push your finger down a bit with your other hand.

The digital scale will indicate that you are pushing down on it
through the stretched rubber band.

The scale will keep showing how hard you push until all the rubber
band's pre-tension is used up.

A string will do the same thing, but its range of elasticity is so
small that we can't see what happens--and the range of elasticity of
steel spokes is even smaller.

I agree that the ability of a pre-tensioned member to function in
compression is a very annoying principle.

Cheers,

Carl Fogel

I think the issue here is more in the semantics of the term "function in compression" than in any mis-understanding of
the underlying physics.

The problem comes as follows. Assume the parcel has weight W, and you stretch the rubber band until the scale registers
a weight of W/2. Note that the band now has tension W/2, but as this is your equilibrium starting point you ignore it.
Now you press down on your hand with a force f < W/2 and the weight registers by the scale increases by precisely the
same amount f. In effect, the force of your hand on your finger appears to be transferred through the rubber band and,
as you are pressing down on it, this must be a compressive force. At this point it is reasonable to claim that the
rubber band is "function[ing] in compression" . But now, increase the force until f = W/2. According to the "function
in compression" arguement the rubber band is now passing a compressive load of W/2 to the parcel to increase the scale
reading from the initial W/2 equilibrium to W. But if your helpful postmaster now leans across the bench wielding a
pair of scissors, he/she can now cut the rubber band and the weight registered by the scales remains unchanged. So now
where does this mysterious extra W/2 on the scales come from. It can no longer be considered as a compressive force
acting through the rubber band because the band is no longer in the picture.

So in a statically loaded bicycle wheel the question of which spokes are responding to the force applied by the rider
depends on the starting point. Considering a tensioned wheel as the starting point it is reasonable to claim that the
bottom spoke acts in compression. Considering the individual untensioned spokes and rim as the starting point it is
reasonable to claim that the spokes act in concert to relieve the load - with the bottom spoke under the least tension
and the lateral spokes under the greatest tension. Neither view is more right or wrong than the other.

Regards,
Mike

On Tue, 29 Aug 2006 16:09:19 +1200, Mike <[email protected]>

Quoted message said:

In article <[email hidden]>, [email hidden] says...

Quoted message said:

Quoted message said:

That article makes the simplifying assumption that if you can hang from
a rope, you can sit on it.

A foolish linearity is the hobgoblin of little minds.

Dear Kendall,

Cut a rubber band, tie it to something that weighs a few pounds, and
take it to the post office.

Note the weight on the digital scale.

Use one finger to pull up on the rubber band until half the weight
disappears from the scale.

Push your finger down a bit with your other hand.

The digital scale will indicate that you are pushing down on it
through the stretched rubber band.

The scale will keep showing how hard you push until all the rubber
band's pre-tension is used up.

A string will do the same thing, but its range of elasticity is so
small that we can't see what happens--and the range of elasticity of
steel spokes is even smaller.

I agree that the ability of a pre-tensioned member to function in
compression is a very annoying principle.

Cheers,

Carl Fogel

I think the issue here is more in the semantics of the term "function in compression" than in any mis-understanding of
the underlying physics.

The problem comes as follows. Assume the parcel has weight W, and you stretch the rubber band until the scale registers
a weight of W/2. Note that the band now has tension W/2, but as this is your equilibrium starting point you ignore it.
Now you press down on your hand with a force f < W/2 and the weight registers by the scale increases by precisely the
same amount f. In effect, the force of your hand on your finger appears to be transferred through the rubber band and,
as you are pressing down on it, this must be a compressive force. At this point it is reasonable to claim that the
rubber band is "function[ing] in compression" . But now, increase the force until f = W/2. According to the "function
in compression" arguement the rubber band is now passing a compressive load of W/2 to the parcel to increase the scale
reading from the initial W/2 equilibrium to W. But if your helpful postmaster now leans across the bench wielding a
pair of scissors, he/she can now cut the rubber band and the weight registered by the scales remains unchanged. So now
where does this mysterious extra W/2 on the scales come from. It can no longer be considered as a compressive force
acting through the rubber band because the band is no longer in the picture.

So in a statically loaded bicycle wheel the question of which spokes are responding to the force applied by the rider
depends on the starting point. Considering a tensioned wheel as the starting point it is reasonable to claim that the
bottom spoke acts in compression. Considering the individual untensioned spokes and rim as the starting point it is
reasonable to claim that the spokes act in concert to relieve the load - with the bottom spoke under the least tension
and the lateral spokes under the greatest tension. Neither view is more right or wrong than the other.

Regards,
Mike

Dear Mike,

If you cut a spoke or a rubber band that's in tension, it's no longer
a pre-tensioned structure. This is a common mistake in discussions of
the wheel's behavior.

The response of the pre-tensioned spokes on a bicycle wheel to a load
on the axle is predictable and measurable by experiment.

The spokes directly under the axle account for 95% of the change from
an unloaded state.

The other spokes gain a little tension, but their measured vertical
force (the result of the tension gain and its angle) supports only
about 5% of the load.

The behavior is not obvious, which leads to attempts to prove that
something else must happen, but no usable theory has ever replaced the
one that Jobst and Ian worked out. In engineering circles, it's about
as controversial as calculating the area of a circle.

The pre-tensioned spokes must somehow tranfer the load from the axle
to the ground. Their tension changes can be predicted, and the changes
are confirmed by strain gauge testing.

Objections to the model used by Jobst, Ian, and other engineers always
involve spoke strains that cannot be calculated and never show up in
tests.

Incidentally, the lateral spokes don't show significantly different
tension changes than the rest of the non-bottom spokes. Check Ian's
tables again:

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

Nor does testing show significant differences for the lateral spokes.
See Professor Gavin's test result graphs again, figures 10 and 11:

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

Cheers,

Carl Fogel

Joe Riel said:

Quoted message said:

Quoted message said:

Until all the pre-tension is used up, even a string will "support" a
compressive load

A string may support a compressive load if it is pretensioned but if
there is nothing to support the string it doesn't matter. There is no
way for a spoke under compressive load to support anything except by
its nipple's friction with the spoke hole. Any compressive load will
try to push the spoke out the outside of the rim.

What would you say if the string were replaced with a chain that was
welded to the rim? How is the link to link interface of the chain any
different from the nipple to rim interface?

There is a major difference: the nipple to rim interface is essentially
nonexistent when the compressive force is applied perpendicular to it;
compressive force applied to a chain in the same direction is
perpendicular to the direction of force that would tend to buckle the
chain. Tensioning counteracts the tendency of the chain to buckle at
the links, as it counteracts the tendency of the spoke to buckle, but
the problem is not the spoke buckling, it's the spoke telescoping into
the spoke hole.

Quoted message said:

The point being, the pretension in the spoke acts on the nipple to rim
interface just as it does on the links (or string or spoke).

No, it doesn't.

"Jeff" <[email hidden]> wrote in message
news:[email hidden]...

Quoted message said:

bicycle_disciple said:

Hi all.

Just wanted to clear a little question.

Or a not so little question, as the case seems to be!

Quoted message said:

Thinking of a wheel spoke as a
prismatic member, what is the nature of normal forces acting on it. Is
it all in tension, all in compression or a mix of both?

Spokes are always in tension. A thin wire cannot go into compression
without buckling. Spokes are pretensioned when the wheel is built, and
the tension in any spoke increases or decreases as the wheel rotates,
with the lowest tension when the spoke is beneath the axle.
This much is uncontroversial, I think.

Jeff

Jeff, I agree with you.

I'm no engineer, but I think I see two reasons for all the controversy.

1. Apparently in engineer-speak "reduction of tension" = "compression" to
make it easier to visualize/explain the transmission of forces between/among
two or more objects.

2. Maybe I'm reading this wrong but it looks like sometimes people are
equating "change in tension" to "total tension". Huge difference.

The idea of figuring the distribution of vector sums on the hub and rim
while allowing for rim and spoke distortion boggles *my* mind.

Jerry

Quoted message said:

Cut a rubber band, tie it to something that weighs a few pounds, and
take it to the post office.

Note the weight on the digital scale.

Use one finger to pull up on the rubber band until half the weight
disappears from the scale.

Push your finger down a bit with your other hand.

The digital scale will indicate that you are pushing down on it
through the stretched rubber band.

Wrong - you are not pushing down with the rubber band, you are pulling
upward less strongly with the rubber band. You can call this siz of
one and half dozen of the other, or just semantics, but I think that
the phrase "pushing down through the rubber band" is dangerously
misleading, since a rubber band can't push anything. At the very least
it could potentially lead to a heated newsgroup discussion.

Quoted message said:

I agree that the ability of a pre-tensioned member to function in
compression is a very annoying principle.

Loss of pretension is *not* functioning in compression. The rubber
band (or spoke) is still functioning in tension, the tension is just
less. We both have a firm grasp of what is happening, but you are just
using some loose langauge.

Jeff

Quoted message said:

I think the issue here is more in the semantics of the term "function in compression" than in any mis-understanding of
the underlying physics.

Yes, I agree.

Quoted message said:

. Neither view is more right or wrong than the other.

But some language is more correct than others.
Jeff

Quoted message said:

Unfortunately, I missed this sentence which redefines the variables:

"This is a change from the unloaded state, so compression doesn't
actually mean compression, it means reduction in tension."

This is a perturbation in force.

This quote from the original link is critical. The author normalizes
all of the changes to the pretensioned state, so that a loss of
pretension is reported in his table as compression. In my view this is
counterproductive to understanding what is going on, but is OK as long
as you keep it in mind. Unfortunately, he doesn't. After making the
correct caveat above, he forgets all about it and bases all of his
final conclusions as if the table values are the absolute values, i.e.
in relation to their unloaded state. Thus he assumes that some of the
spokes are really in compression. This leads to his unfortunate
conclusion:

"From these figures, I conclude that it is perfectly reasonable to say
that the hub stands on the lower spokes, and that it does not hang from
the upper spokes."

It is much more correct to say that the wheel hangs from the upper
spokes, although it is an awkward and oversimplified way to think about
it. It is completely incorrect to say that is "standing on the lower
spokes" as I hope all of us who are thinking about this carefully can
agree.

Ohio Jerry said:

The idea of figuring the distribution of vector sums on the hub and rim
while allowing for rim and spoke distortion boggles *my* mind.

Why?

It's all just maths, afterall.

Take you a while with paper and pencil, but people have done things
like work out trig and log tables - a cycle wheel is trivial by
comparison.

Perhaps it's just a sign of present-day innumeracy and the
dumbing-down of educational standards. In my first year of upper
school we were taught to extract square roots longhand - people today
prefer to ignore numbers and rely on their "common sense", and they
get legislators (who are no more numerate) making foolish decisions
for them, and so they get the laws they deserve.