Forces on spokes
bicycle_disciple
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
carl...@comcast.net
<1.crazy...@gmail.com> wrote:
Dear Ron,
Forces on a pre-tensioned wheel loaded at the axle:
http://www.astounding.org.uk/ian/wheel/index.html
Cheers,
Carl Fogel
Jeff
An interesting and thorough analysis at that link, and yet I am not
sure that I believe
the final result. He concludes that the load is supported almost
exclusively by the
bottom few spokes (the ones pointing down toward the road) which are
strongly in
compression. However, long slender members such as spokes cannot
support large compressive loads because of their tendency to buckle
(bend). Also, much of the
strength of a wheel comes from the fact that all the spokes contribute
to the load at
all times. I suspect that he has not accounted fully for the
pretensioning of the spokes.
Jeff
carl...@comcast.net
wrote:
Dear Jeff,
Actually, Ian's whole article is about accounting fully for the
pre-tensioning of the spokes.
It's a subject that's been covered repeatedly. That's the nicest
online, detailed explanation that I know of.
You can find pretty much the same engineering analysis and conclusions
in "The Bicycle Wheel" by Jobst Brandt, any edition.
And you can see experimental strain gauge confirmation in figures 10
and 11 Professor Gavin's paper here:
http://www.duke.edu/~hpgavin/papers/HPGavin-Wheel-Paper.pdf
The icicle-shapes on the graphs show the pre-tensioned spoke losing
and then regaining a large amount of tension as it rolls under the
loaded axle.
Until all the pre-tension is used up, even a string will "support" a
compressive load, which is why emergency repair spokes can be made of
kevlar string and why whole wheels can and have been made of them.
Cheers,
Carl Fogel
jobst....@stanfordalumni.org
>>> 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?
>> Forces on a pre-tensioned wheel loaded at the axle:
http://www.astounding.org.uk/ian/wheel/index.html
> An interesting and thorough analysis at that link, and yet I am not
> sure that I believe the final result. He concludes that the load is
> supported almost exclusively by the bottom few spokes (the ones
> pointing down toward the road) which are strongly in compression.
I didn't see that there was any compression in the analysis but rather
a reduction in tension. The only spokes that experience a significant
change in length are the ones at the bottom. This analysis was done
after the publication of "the Bicycle Wheel" in which this matter is
discussed at length to avoid any misunderstanding. Because this is
appears to be such an unusual perspective, no analysis of the wheel
was published before "the Bicycle Wheel".
> However, long slender members such as spokes cannot support large
> compressive loads because of their tendency to buckle (bend). Also,
> much of the strength of a wheel comes from the fact that all the
> spokes contribute to the load at all times. I suspect that he has
> not accounted fully for the pretensioning of the spokes.
I suggest you review what was written and possibly look at the full
analysis in the book.
http://sheldonbrown.com/harris/books.html#brandt
Jobst Brandt
SocSecTr...@earthlink.net
Jeff wrote:
> An interesting and thorough analysis at that link, and yet I am not
> sure that I believe
> the final result. He concludes that the load is supported almost
> exclusively by the
> bottom few spokes (the ones pointing down toward the road) which are
> strongly in
> compression. However, long slender members such as spokes cannot
> support large compressive loads because of their tendency to buckle
> (bend). Also, much of the
> strength of a wheel comes from the fact that all the spokes contribute
> to the load at
> all times. I suspect that he has not accounted fully for the
> pretensioning of the spokes.
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 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, and
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.
carl...@comcast.net
Dear SSTW,
Figure 10 in Professor Gavin's paper shows strain gauge results for a
spoke on an actual wheel as it was being ridden, with 8 revolutions in
2.0 seconds:
http://www.duke.edu/~hpgavin/papers/HPGavin-Wheel-Paper.pdf
The huge icicle spikes show the loss of tension as the spoke rolls
under the loaded axle. They're about ten times the size of the other
spikes.
Like the huge spikes, the tiny spikes vary, reflecting real world
conditions.
Figure 11 shows the averaged spoke strain profile from three road
tests. The huge icicle spike is about ten times the size of the other
variation.
It would be very difficult to argue that any significant changes are
seen in the experimental data except when the spoke rolls under the
axle and its tension drops like a rock.
Experiment seems to confirm theory.
Cheers,
Carl Fogel
SocSecTr...@earthlink.net
carl...@comcast.net wrote:
> 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.
SocSecTr...@earthlink.net
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.
carl...@comcast.net
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
Joe Riel
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
ken...@willets.org
a rope, you can sit on it.
A foolish linearity is the hobgoblin of little minds.
Jeff
> >>
> >> http://www.astounding.org.uk/ian/wheel/index.html
> >>
> >> Cheers,
> >>
> >> Carl Fogel
> >
> >An interesting and thorough analysis at that link, and yet I am not
> >sure that I believe
> >the final result. He concludes that the load is supported almost
> >exclusively by the
> >bottom few spokes (the ones pointing down toward the road) which are
> >strongly in
> >compression. However, long slender members such as spokes cannot
> >support large compressive loads because of their tendency to buckle
> >(bend). Also, much of the
> >strength of a wheel comes from the fact that all the spokes contribute
> >to the load at
> >all times. I suspect that he has not accounted fully for the
> >pretensioning of the spokes.
> >Jeff
>
> Dear Jeff,
>
> Actually, Ian's whole article is about accounting fully for the
> pre-tensioning of the spokes.
True - his problem is not ignoring the pretensioning, sorry.
>
> It's a subject that's been covered repeatedly. That's the nicest
> online, detailed explanation that I know of.
>
> You can find pretty much the same engineering analysis and conclusions
> in "The Bicycle Wheel" by Jobst Brandt, any edition.
I certainly hope not.
>
> And you can see experimental strain gauge confirmation in figures 10
> and 11 Professor Gavin's paper here:
>
> http://www.duke.edu/~hpgavin/papers/HPGavin-Wheel-Paper.pdf
>
> The icicle-shapes on the graphs show the pre-tensioned spoke losing
> and then regaining a large amount of tension as it rolls under the
> loaded axle.
Yes, but this does not indicate that they are supporting the load at
that point, but rather that they are *not* supporting the load at that
point. The "icicles" are the spokes at the bottom getting shorter (a
strain gage measures distance) as they lose their pretensioning. The
load is being supported by all of the other spokes *except* for the few
spokes at the bottom that go slack.
>
> Until all the pre-tension is used up, even a string will "support" a
> compressive load,
I don't know what you mean by that sentence. A spoke that is
underneath the axle can't support the load whether it is pretensioned
or not because to oppose the load would require it to go into
compression.
> which is why emergency repair spokes can be made of
> kevlar string and why whole wheels can and have been made of them.
Spokes can be made out of anything that is strong in tension. The fact
that they can be made out of string nicely illustrates the point that
spokes are never in compression, and shows why the spokes at the bottom
of the wheel don't support any of the load.
Jeff
Jeff
> 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%
>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.
> 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
Jeff
Then his analysis must be wrong. The load must be supported by the
spokes that are not underneath the axle, becuase those spokes are
unable to push upward against the downward force exerted by the axle.
Remember, there are only a few spokes at the bottom, and some 30 spokes
not at the bottom.
Jeff
Jeff
bicycle_disciple wrote:
> Hi all.
>
> Just wanted to clear a little question.
Or a not so little question, as the case seems to be!
> 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
jobst....@stanfordalumni.org
I take it then that you don't recall adding and subtracting negative
and positive numbers in algebra. In this case, compression (-) and
tension (+) are these values, pick your norm.
You may visualize this more easily if you imagine two contestants in
a tug-of-war, one of whom is standing at the edge of a swimming pool.
If I were to push his opponent from behind, I would push the other
person into the water via the tensioned rope.
The only reason we tension spokes is because they are too thin to bear
the load in compression. The analysis of their elastic response is
done without considering either buckling or that they are tensioned.
Finite element analysis (FEA) for the bicycle wheel is performed
without introduction of tension, only external loads. The axle is a
fixed node (0,0) coordinates and the road presses against the rim.
I should mention that the rim of a bicycle wheel responds to loads as
an "elastically supported beam" the most common of these being a
railroad rail sitting on cross-ties. With the point load of a rail
wheel, the rail takes on the shape shown in Fig. 11 of Gavin's paper
and in "the Bicycle wheel". The straight line development of a
circular rim takes on this wavy form when loaded.
Jobst Brandt
Jeff
> The only reason we tension spokes is because they are too thin to bear
> the load in compression. The analysis of their elastic response is
> done without considering either buckling or that they are tensioned.
> Finite element analysis (FEA) for the bicycle wheel is performed
> without introduction of tension, only external loads. The axle is a
> fixed node (0,0) coordinates and the road presses against the rim.
>
> I should mention that the rim of a bicycle wheel responds to loads as
> an "elastically supported beam" the most common of these being a
> railroad rail sitting on cross-ties. With the point load of a rail
> wheel, the rail takes on the shape shown in Fig. 11 of Gavin's paper
> and in "the Bicycle wheel". The straight line development of a
> circular rim takes on this wavy form when loaded.
>
> Jobst Brandt
All very learned and no doubt correct. The specific issue being argued
is whether the few spokes directly under the axle support the load, as
the original link in this thread and Carl Fogel claim, or whether all
the other spokes support the load, as I and another poster claim.
Could you comment directly on that?
Jeff
jobst....@stanfordalumni.org
>>>> 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.
>> 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.
> Then his analysis must be wrong. The load must be supported by the
> spokes that are not underneath the axle, because those spokes are
> unable to push upward against the downward force exerted by the
> axle. Remember, there are only a few spokes at the bottom, and some
> 30 spokes not at the bottom.
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.
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.
Jobst Brandt
jobst....@stanfordalumni.org
I think you are caught in semantics. If you were to look at the
analysis of a die cast moped wheel, as depicted in "the Bicycle Wheel"
your question should answer itself. These spokes are rigid enough to
support the load in compression, yet we do not know if the wheel by
differential cooling leaves these spokes in tension or compression,
both being possible. The FEA of the wheel is unaffected by semantics.
It sees only that under load the bottom spokes are compressed to a
shorter length than the rest and that the others do not experience any
significant load.
As I have pointed out in the past, the minimal increase in tension of
the other spokes for a 36 spoke wheel sums to zero, it being a side
effect of the rim flattening at the load affected zone causing the
remaining rim diameter to increase ever so slightly.
If you were to perform a fatigue test on a bicycle wheel in a non
rotating manner bu loading and unloading the wheel, the three or four
spokes at the bottom would ultimately fail. They being the only ones
affected by the load identical to a wooden wagon wheel.
Jobst Brandt
Jeff
> 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.
>
> 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
carl...@comcast.net
wrote:
Dear Jeff,
Loss of tension is the same as as compression. The spokes are strong
in tension, but weak in compression, so the trick is to make them work
while still in tension. Until a spoke loses all tension, it isn't
going to bend and fail in compression. (And when it does, it just
rattles a bit, since the nipple isn't fixed to the rim.)
It's the reverse of the trick used in pre-stressed concrete. Concrete
is strong in compression, but weak in tension--a concrete pillar
resists squashing nicely, but will pull apart comparatively easily. So
steel rods and other tricks are used to pre-compress a piece of
concrete that will be used in tension. If it's pre-compressed to a
thousand pounds, you have pull on it with a thousand-pound force
before the pre-compression is used up and the concrete begins to act
in its normal, uncompressed, feeble fashion.
The load on the axle is obviously supported by the spokes--nothing
else joins them to the rim.
Theory predicts and experiment confirms that the spokes under the axle
react to the load by losing a large amount of tension. Engineers using
the same tools keep coming up with the same figures--Jobst, Ian, and
others.
The 5 spokes right under the axle in Ian's example lose a large amount
of tension, just as if they were stiff wooden spokes--loss of tension
is the same as compression in the engineering world.
The other 31 spokes all gain some tension.
A common mistake is to think that the all the small tension increases
in other 31 spokes must add up to a large total.
They don't.
The reason is that they gain tension almost all the way around the
clock, so to speak--many of the spokes whose tension increases are
pulling the axle down, not pulling it up. You can only calculate the
lift (pure vertical force) of a 12 newton tension increase if you also
know the angle at which it's pulling:
"The tension is taken from the analysis. Multiplying the axial force
by the total angle factor gives the vertical component of the force.
This is the lift that one particular spoke is contributing to the hub.
If we add them up, we should get 1000, and luckily we do."
"Then, I've split the lift forces into two columns, depending upon
whether the spoke force was tensile or compressive. This is to see if
the hub hangs from tensile spokes, or stands on compressive ones."
"There are 31 tensile spokes. On average they contribute 1.436 N (0.14
kg, just under a third of a pound) each to holding up the hub.
There are 5 compressive spokes. On average they contribute 191.097N
(19 kg, just over 42 lbs) each to holding up the hub."
"Put it another way - the average compressive spoke contributes 133
times as much lift force as the average tensile spoke."
http://www.astounding.org.uk/ian/wheel/index.html
As Ian's table shows, the lift from the 5 bottom spokes is 955.5
newtons, while the 31 other spokes contribute a whopping 44.5 newtons
of lift.
Until you understand that loss of tension and compression are the same
thing, the whole analysis is really, really annoying and ridiculous. I
started out with even stronger feelings than you that the engineers'
analysis was insane.
Cheers,
Carl Fogel
jobst....@stanfordalumni.org
That's where the problem lies. Is "pulling down less" the same as
pushing up more? That's an algebraic sum.
> 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.
Your conclusion is based on that semantic problem and one of statics
(forces). I take it you are not a structural engineer and therefore
have not been involved with superposition of forces. This is such a
case and the net tension in the wheel does not alter its function. It
only absolves the wires of buckling.
"the Bicycle Wheel" has been in print since 1981 and has been reviewed
by many scientists among which we find Karl Wiedemer, professor of
mechanical engineering who published a paper on this item that year.
You are not the first to see it differently but in that, disagree with
experts in the art of structural analysis who agree with the work.
Jobst Brandt
carl...@comcast.net
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
ken...@willets.org
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.
Mike
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
Joe Riel
> 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.
But one may be more useful than the other. Note that these are static
analyses. Consider a buoy anchored to the sea floor via a rope.
Tapping on rope at the bottom transmits a compressional wave through
the rope that vibrates the buoy. It's clear that the rope is
transmitting the force wave, not the ocean.
--
Joe Riel
carl...@comcast.net
wrote:
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
SocSecTr...@earthlink.net
jobst....@stanfordalumni.org wrote:
> Jeff Thomas writes:
>
> >>>> 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.
>
> >> 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.
>
> > Then his analysis must be wrong. The load must be supported by the
> > spokes that are not underneath the axle, because those spokes are
> > unable to push upward against the downward force exerted by the
> > axle. Remember, there are only a few spokes at the bottom, and some
> > 30 spokes not at the bottom.
>
> 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.
I've already done that experiment and reported the results a while back
on this ng, where the results were called "unexpected". The spokes
parallel to the ground had their pich rise significantly.
SocSecTr...@earthlink.net
Joe Riel wrote:
> SocSecTr...@earthlink.net writes:
>
> > carl...@comcast.net wrote:
> >> 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.
> 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.
Ohio Jerry
"Jeff" <jth...@northwestern.edu> wrote in message
news:1156802207....@m79g2000cwm.googlegroups.com...
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
Jeff
I said:
> > 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.
>
> Your conclusion is based on that semantic problem and one of statics
> (forces). > I take it you are not a structural engineer and therefore
> have not been involved with superposition of forces.
Wrong on both counts. I teach statics at a university, so that is why
I am taking such an interest in this thread, which is really quite
interesting.
>
> "the Bicycle Wheel" has been in print since 1981 and has been reviewed
> by many scientists among which we find Karl Wiedemer, professor of
> mechanical engineering who published a paper on this item that year.
> You are not the first to see it differently but in that, disagree with
> experts in the art of structural analysis who agree with the work.
I don't disagree with any of the specific findings as to what the
changes in spoke tension are when the wheel is loaded, only in how
these findings are interpreted. I am certainly not attacking your
book. My issue was with some statements in the original link, and by
Carl Fogel.
You appear to be saying that because the bottom spokes are the ones
whose internal stress state changes, they are the ones supporting the
load. I am saying that from a pure statics point of view the upper
spokes are supporting the load. This is basically semantics, yes.
Depends on what you mean by "supports".
Jeff
Jeff
> 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.
> 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
Jeff
> 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.
>. Neither view is more right or wrong than the other.
But some language is more correct than others.
Jeff
jobst....@stanfordalumni.org
> spokes parallel to the ground had their pitch rise significantly.
You are alone in that finding. This demonstration has been done often
in this regard and the results are not what you seem to have observed.
Summing tension increases for a 36-spoke wheel gives no net upward
force. These tension increases are caused by the rim circumference
increasing from flattening of its curvature in the load affected zone
(at the ground contact). The largest tension increases occur adjacent
to the spokes with tension reduction, are caused bu bending stiffness
of the rim so that its deformation is continuous rather than having a
sudden bend.
Jobst Brandt
Jeff
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.
jta...@nospam.hfx.andara.com
<jer...@brightfreaking.net> wrote:
>
>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.
jobst....@stanfordalumni.org
> I said:
>>> 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.
>> Your conclusion is based on that semantic problem and one of
>> statics (forces). > I take it you are not a structural engineer and
>> therefore have not been involved with superposition of forces.
> Wrong on both counts. I teach statics at a university, so that is
> why I am taking such an interest in this thread, which is really
> quite interesting.
In that event, I think you should re-evaluate your perception of load
superposition in which, in the case of the bicycle wheel, you could
raise and lower tension without affecting the wheel response to loads
as long as no spokes become slack (drop out of the supporting
elements). The only reason that limitation applies is that the spokes
are too thin as columns.
For that reason, "the Bicycle Wheel" shows a wooden wagon wheel, a die
cast aluminum (one piece) wheel and a conventional bicycle wheel.
This underscores the problem as I see it. When do the spokes at the
bottom of the wheel become load bearers? The load distributions being
identical in all three, albeit with obvious pre-stressing in the wire
spoked wheel. The die cast aluminum wheel is doubtful, since it is
unknown what its unloaded spoke tension is, while the wooden wagon
wheel has its spokes prestressed in compression by its steel tire.
>> "the Bicycle Wheel" has been in print since 1981 and has been reviewed
>> by many scientists among which we find Karl Wiedemer, professor of
>> mechanical engineering who published a paper on this item that year.
>> You are not the first to see it differently but in that, disagree with
>> experts in the art of structural analysis who agree with the work.
> I don't disagree with any of the specific findings as to what the
> changes in spoke tension are when the wheel is loaded, only in how
> these findings are interpreted. I am certainly not attacking your
> book. My issue was with some statements in the original link, and by
> Carl Fogel.
> You appear to be saying that because the bottom spokes are the ones
> whose internal stress state changes, they are the ones supporting the
> load. I am saying that from a pure statics point of view the upper
> spokes are supporting the load. This is basically semantics, yes.
> Depends on what you mean by "supports".
Curiously a statics professor with whom I discussed the matter before
publication was also a "hangs from the top" adherent to the extent
that he believed the upper spokes increased in tension roughly as I
knew the bottom spokes to reduce in tension. He said curtly, if you
had a mathematical analysis we might talk about it further. He never
responded to the FEA data and drawings that I subsequently developed
and sent him. His critique was an impetus to performing the analysis
that I originally thought would be beating a dead horse, the matter
being so obvious. As I discovered, the subject is not obvious.
Jobst Brandt
Jeff
> Curiously a statics professor with whom I discussed the matter before
> publication was also a "hangs from the top" adherent to the extent
> that he believed the upper spokes increased in tension roughly as I
> knew the bottom spokes to reduce in tension.
As I said before, I don't disagree with the well-established fact that
the loss of pretension in the bottom spokes is the major change in
spoke tension due to load. I am a "hangs from the top" adherent based
on fact that the top spokes are the ones that exert forces opposite in
direction to the load.
> He said curtly, if you
> had a mathematical analysis we might talk about it further. He never
> responded to the FEA data and drawings that I subsequently developed
> and sent him. His critique was an impetus to performing the analysis
> that I originally thought would be beating a dead horse, the matter
> being so obvious.
He sounds like a jerk, which is something I try hard not to be.
>As I discovered, the subject is not obvious.
No, it is a bit trickier than it appears at first, isn't it? In my
statics class I have to assign a final project that requires the
students to do some detailed analysis and submit a report - maybe I
will do a bicycle wheel next term!
Jeff
>
> Jobst Brandt
mike_o...@yahoo.com
Consider the following for a four spoke wheel:
( Best viewed in monospaced font ).
|
|
|
100
|
|
|
-----100-----O-----100-----
|
|
|
100
|
|
|
Unloaded wheel. Spoke pretension ( 100Lbs ) counteracts each other.
|
|
|
100
|
|
|
-----100-----O-----100-----
|
|
|
0
|
|
|
Wheel loaded with 100Lbs. Only the lower spoke tension changes. The
pretension ( 100Lbs ) of the upper spoke is replaced with wheel load of
100Lbs. In this state, the lower spoke can be removed without any
adverse effects.
Conclusion: The bike does not "stand" on lower spokes.
The above does not take into account any rim flexing.
Jeff
(snip)
> Wheel loaded with 100Lbs. Only the lower spoke tension changes. The
> pretension ( 100Lbs ) of the upper spoke is replaced with wheel load of
> 100Lbs. In this state, the lower spoke can be removed without any
> adverse effects.
>
> Conclusion: The bike does not "stand" on lower spokes.
>
> The above does not take into account any rim flexing.
Nice illustration - thanks!
Jeff
SocSecTr...@earthlink.net
jobst....@stanfordalumni.org wrote:
> >> 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.
>
> > I've already done that experiment and reported the results a while
> > back on this ng, where the results were called "unexpected". The
> > spokes parallel to the ground had their pitch rise significantly.
>
> You are alone in that finding.
Try it yourself: sit on the wheel and pluck the spokes. I'm pretty sure
you will get similar results if you have someone sit on the handlebars
while you pluck the spokes. The difference will be in the tension above
the axle (it will be higher than what you observe if you load the wheel
by sitting on the wheel itself.
> This demonstration has been done often
> in this regard and the results are not what you seem to have observed.
> Summing tension increases for a 36-spoke wheel gives no net upward
> force.
I didn't say they did. I would say that the net force increase is at
90o to the direction of the load applied to the wheel.
> These tension increases are caused by the rim circumference
> increasing from flattening of its curvature in the load affected zone
> (at the ground contact).
If it were merely this, then there would be no increase in tension at
90o, but there is.
> The largest tension increases occur adjacent
> to the spokes with tension reduction,
No they don't. According to Gavin's data, the largest spoke tension
increases come at 90o to the spokes with the tension reduction, an
effect replicated by my literally "seat of the pants" experiment. The
only place where you will see the increase you are talking about is if
you get your measurements from a modeled simulation, instead of
measurements of a real bicycle wheel in real use on a real road.
BTW, Gavin notes that the actual peak at 90o is probably obscured as an
artifact of the measurement process and may be therefore be even higher
than is shown on his chart.
> are caused bu bending stiffness
> of the rim so that its deformation is continuous rather than having a
> sudden bend.
Since those increases don't exist as you described them, discussion of
what causes the increases is pretty pointless.
Michael Press
<1156862860.0...@m79g2000cwm.googlegroups.com>,
"Jeff" <jth...@northwestern.edu> wrote:
[...]
> 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.
Does a wooden wagon wheel hang from the upper spokes or
stand on the lower spokes? Just because you are confused
does not mean I have to be, so I will continue to think
about it productively in the way I choose.
But just for fun, if the hub hangs from the upper spokes
what is supporting the upper rim? Sky hooks?
--
Michael Press
SocSecTr...@earthlink.net
Jeff wrote:
> >
> > Curiously a statics professor with whom I discussed the matter before
> > publication was also a "hangs from the top" adherent to the extent
> > that he believed the upper spokes increased in tension roughly as I
> > knew the bottom spokes to reduce in tension.
>
> As I said before, I don't disagree with the well-established fact that
> the loss of pretension in the bottom spokes is the major change in
> spoke tension due to load. I am a "hangs from the top" adherent based
> on fact that the top spokes are the ones that exert forces opposite in
> direction to the load.
My look at the data, with the greatest spoke tension increase at the
front and trailing edges of the wheel has forced me into the odd
position of "hangs from the side". The wheel ovalizes under load,
raising the tension at +-90o; according to Gavin's data the spokes
above the axle lose some slight tension, which makes it hard to buy
into the theory that the axle/hub hangs from the top (it does, but less
there than anywhere else except for the bottom spokes). It's like a
weight hung between two lengths of tensioned clothesline, and then you
pull back on the tops of each clothesline poll so that the tension
increases in the clotheslines, raising the weight suspended between
them. The hub actually hangs from everywhere except the very bottom,
and hangs more from the 90o spokes than other two pairs of spokes, but
that's not to say that it hangs mostly from them.
Jeff
Michael Press wrote:
> > 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.
>
> Does a wooden wagon wheel hang from the upper spokes or
> stand on the lower spokes?
A wooden wagon wheel has thick spokes that can support some compressive
loads and are obviously not pretensioned. I would guess that the load
mostly "hangs from the upper spokes" but there is probably some
"standing on the lower spokes" as well (unlike a bicycle wheel).
> Just because you are confused
> does not mean I have to be, so I will continue to think
> about it productively in the way I choose.
I'm not confused, and that sort of comment is unproductive.
>
> But just for fun, if the hub hangs from the upper spokes
> what is supporting the upper rim? Sky hooks?
The upper rim is supported by the lower rim, which is supported by the
ground. Not sure where you are trying to go with that one.
Jeff
Jeff
SocSecTr...@earthlink.net wrote:
>
> My look at the data, with the greatest spoke tension increase at the
> front and trailing edges of the wheel has forced me into the odd
> position of "hangs from the side". The wheel ovalizes under load,
> raising the tension at +-90o; according to Gavin's data the spokes
> above the axle lose some slight tension, which makes it hard to buy
> into the theory that the axle/hub hangs from the top (it does, but less
> there than anywhere else except for the bottom spokes). It's like a
> weight hung between two lengths of tensioned clothesline, and then you
> pull back on the tops of each clothesline poll so that the tension
> increases in the clotheslines, raising the weight suspended between
> them. The hub actually hangs from everywhere except the very bottom,
> and hangs more from the 90o spokes than other two pairs of spokes, but
> that's not to say that it hangs mostly from them.
You and Jobst have a disagreement about the tension distribution from
the top to the sides, and I am going to stay out of that one since
neither viewpoint violates basic engineering principles.
As for your "hangs from the side" theory, I would point out that only
the upward component of the tension in any particular spoke is helping
to support the downward load. So a spoke that is at 90 deg cannot
support any of the load, no matter how large its tension. A spoke at
80 deg, even if it has a large tension, only contributes 17% of that
tension in the upward direction. The spokes at the top, even if they
have a lower tension, are aiming all or most of it in the right
direction. (Spokes at the bottom, assuming they maintain some of their
pretension, are pulling the hub downward so they are hurting the cause,
like someone on a tug of war team pulling in the wrong direction on the
rope.)
Jeff
Michael Press
<1156881358....@74g2000cwt.googlegroups.com>,
"Jeff" <jth...@northwestern.edu> wrote:
> Michael Press wrote:
> > > 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.
> >
> > Does a wooden wagon wheel hang from the upper spokes or
> > stand on the lower spokes?
>
> A wooden wagon wheel has thick spokes that can support some compressive
> loads and are obviously not pretensioned. I would guess that the load
> mostly "hangs from the upper spokes" but there is probably some
> "standing on the lower spokes" as well (unlike a bicycle wheel).
>
> > Just because you are confused
> > does not mean I have to be, so I will continue to think
> > about it productively in the way I choose.
>
> I'm not confused, and that sort of comment is unproductive.
You implied that I am not `thinking about this carefully'.
I paraphrased you as saying that I am confused for thinking
about the bicycle wheel as standing on the lower spokes.
I have and am thinking about this carefully.
> > But just for fun, if the hub hangs from the upper spokes
> > what is supporting the upper rim? Sky hooks?
>
> The upper rim is supported by the lower rim, which is supported by the
> ground. Not sure where you are trying to go with that one.
* One rim standing vertically on the ground.
* One spoke from the uppermost spoke hole connected to the hub.
* Apply a 50 kg load at the hub toward the ground.
What happens?
--
Michael Press
Jeff
Michael Press wrote:
> You implied that I am not `thinking about this carefully'.
> I paraphrased you as saying that I am confused for thinking
> about the bicycle wheel as standing on the lower spokes.
> I have and am thinking about this carefully.
OK, fair enough. I was trying to find some common ground, but I can
see why you took it as a negative comment, sorry.
>
> > > But just for fun, if the hub hangs from the upper spokes
> > > what is supporting the upper rim? Sky hooks?
> >
> > The upper rim is supported by the lower rim, which is supported by the
> > ground. Not sure where you are trying to go with that one.
>
> * One rim standing vertically on the ground.
>
> * One spoke from the uppermost spoke hole connected to the hub.
>
> * Apply a 50 kg load at the hub toward the ground.
>
> What happens?
The single spoke goes into tension, supporting the the hub from above,
providing the simplest possible example of what happens in a full
bicycle wheel.
Now let me ask you: The same rim, but now a single spoke from the
bottommost hole connected to the hub. Apply a downward load again and
what happens? (Hint: it won't be pretty!)
Jeff
Cam
Ohio Jerry wrote:
>
> 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.
The wheel does not stand on the lower spokes. It un-hangs off them.
Cam
jobst....@stanfordalumni.org
>>> 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.
>> Does a wooden wagon wheel hang from the upper spokes or stand on
>> the lower spokes?
> A wooden wagon wheel has thick spokes that can support some
> compressive loads and are obviously not pretensioned. I would guess
> that the load mostly "hangs from the upper spokes" but there is
> probably some "standing on the lower spokes" as well (unlike a
> bicycle wheel).
Oops! Wooden wagon wheels have spokes in compression when they are in
good working order. As I asked, when does the wheel begin to hang
from the top when considering the three wheel types (wooden, die cast
aluminum, and wire spoked bicycle wheel)? Your analysis is too narrow
to assess forces in all three types even though the FEA is identical
for them and arrives at the same results. The spoke at the bottom
gets compressed regardless of its precondition.
Let me suggest that you make a class project of a finite element
analysis of a bicycle wheel. Use the plainest 36 spoke wheel, the
values for which (rim and spokes) are shown and listed in "the Bicycle
Wheel" from which you could save time. I think that ought to make the
mechanics of it more clear. I'm sure you have such software at your
school and it would be a good exercise for the class to work on in
teams on such an evaluation.
>> But just for fun, if the hub hangs from the upper spokes
>> what is supporting the upper rim? Sky hooks?
> The upper rim is supported by the lower rim, which is supported by the
> ground. Not sure where you are trying to go with that one.
The four spoke example does nothing for the problem other than make
assumptions of an inflexible rim or maybe a four bar linkage, models
most people have in their minds. A rigid rim, lets say a granite ring
of 6x6" cross section, would give the picture people often visualize.
In that model, the rim is the fixed "node" and the hub displaces
radially giving a membrane type stretch to their complement. You'll
note that the real bicycle wheel the hub is the fixed node and the
contact point rotates to give local deformation.
That a typical bicycle rim can be deflected with the hand when
unspoked as much as it experiences in use, helps get rid of the rigid
rim visualization that usually obscures the effects.
Visualizing the rim as a long 1/8" thick aluminum strip one inch wide
supported on a 1/4" thick foam rubber pad to which it is glued (with
the pad glued to the table), the deflection of that strip when
depressed at its mid point with the thumb is what occurs in the
bicycle rim. It has a dip under the load and a wavy dissipation of
that dip to either side. The support (spoke) directly under the load
becomes shorter while the support is slightly raised (stretched) to
either side of the dip.
No glue would be required if the whole strip could be prestressed so
the pad were in compression. This strip does not hang from the far
ends of the table but gives another example of an elastically
supported beam.
Jobst Brandt
jobst....@stanfordalumni.org
>>>> But just for fun, if the hub hangs from the upper spokes what is
>>>> supporting the upper rim? Sky hooks?
>>> The upper rim is supported by the lower rim, which is supported by
>>> the ground. Not sure where you are trying to go with that one.
>> * One rim standing vertically on the ground.
>>
>> * One spoke from the uppermost spoke hole connected to the hub.
>>
>> * Apply a 50 kg load at the hub toward the ground.
>>
>> What happens?
> The single spoke goes into tension, supporting the the hub from
> above, providing the simplest possible example of what happens in a
> full bicycle wheel.
Whoa! The rim collapses. You don't have a wheel. In a bicycle
wheel, working loads deflect the rim about 0.2mm and operate in the
elastic stretch of spokes. You must be aware that most analytical
models can be distorted so that they are no longer valid. The four
spoke wheel of Spinergy didn't last long on the bicycle and on the
market for that reason. It was in fact a wheel hanging from the top
spokes, there being insufficient stretch in the spokes to carry the
load and they rattled in use.
> Now let me ask you: The same rim, but now a single spoke from the
> bottommost hole connected to the hub. Apply a downward load again
> and what happens? (Hint: it won't be pretty!)
Now you are confused or at least not serious.
Jobst Brandt
MykalCrooks
> 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)
>
>snip<
When you "divide" the spokes into categories the spokes are no longer part
of a wheel. You may as well divide your brain in to various pieces, observe
that no thought is taking place, and then conclude that brain cells are
incapable of supporting thought.
The spokes, when laced into a wheel and properly tensioned, are part of a
whole. As such, spokes as part of a wheel are mechanically different from
spokes that are separate from the wheel. To insist otherwise is to commit a
fallacy of equivocation, and to base your insistence upon the presupposition
that your intuition trumps the conclusive empirical evidence cited in this
thread is to rely upon false authority.
You work in software, I presume.
mC
bicycle_disciple
I cannot open that link you sent me. The message is that the file may
be corrupted. You sure that link is valid?
-B.D
carl...@comcast.net wrote:
> On 28 Aug 2006 10:22:51 -0700, "Jeff" <jth...@northwestern.edu>
> wrote:
>
> >
> >carl...@comcast.net wrote:
> >> On 28 Aug 2006 05:23:47 -0700, "bicycle_disciple"
> >> <1.crazy...@gmail.com> wrote:
> >>
> >> >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
> >
> >An interesting and thorough analysis at that link, and yet I am not
> >sure that I believe
> >the final result. He concludes that the load is supported almost
> >exclusively by the
> >bottom few spokes (the ones pointing down toward the road) which are
> >strongly in
> >compression. However, long slender members such as spokes cannot
> >support large compressive loads because of their tendency to buckle
> >(bend). Also, much of the
> >strength of a wheel comes from the fact that all the spokes contribute
> >to the load at
> >all times. I suspect that he has not accounted fully for the
> >pretensioning of the spokes.
> >Jeff
>
> Dear Jeff,
>
> Actually, Ian's whole article is about accounting fully for the
> pre-tensioning of the spokes.
>
> It's a subject that's been covered repeatedly. That's the nicest
> online, detailed explanation that I know of.
>
> You can find pretty much the same engineering analysis and conclusions
> in "The Bicycle Wheel" by Jobst Brandt, any edition.
>
> And you can see experimental strain gauge confirmation in figures 10
> and 11 Professor Gavin's paper here:
>
> http://www.duke.edu/~hpgavin/papers/HPGavin-Wheel-Paper.pdf
>
> The icicle-shapes on the graphs show the pre-tensioned spoke losing
> and then regaining a large amount of tension as it rolls under the
> loaded axle.
>
> Until all the pre-tension is used up, even a string will "support" a
> compressive load, which is why emergency repair spokes can be made of
> kevlar string and why whole wheels can and have been made of them.
>
> Cheers,
>
> Carl Fogel
Mike O Hannon
More food for thought.
As can be seen in my previous diagram, the tension on the top spoke did
not change from load on the wheel. The only time the tension on the
top spokes change is when the load on the wheel is GREATER than the
pretension. If the wheel load on the lower diagram was increased to
150Lbs, the top spoke tension would increase to 150Lbs. A wheel having
multiple spokes each having only a reasonable amount of pretension,
will carry a large load before overcoming the pretension. This is why
there is no observed increase in tension of top spokes. The pretension
of lower spokes pulling on the top spokes is just replaced by the exact
amount of load on the wheel. Try loosening all the spokes on a wheel,
add a load and then see what spokes have tension.
SocSecTr...@earthlink.net
jobst....@stanfordalumni.org wrote:
> Let me suggest that you make a class project of a finite element
> analysis of a bicycle wheel. Use the plainest 36 spoke wheel, the
> values for which (rim and spokes) are shown and listed in "the Bicycle
> Wheel" from which you could save time. I think that ought to make the
> mechanics of it more clear. I'm sure you have such software at your
> school and it would be a good exercise for the class to work on in
> teams on such an evaluation.
The only problem is that your FEA does not represent the real world.
Look at Gavin's data. The forces predicted by the FEA line are
completely different from the observed data, except for detensioning of
the spokes immediately underneath the axle.
Jeff
MykalCrooks wrote:
> "Jeff" <jth...@northwestern.edu> wrote in message
> news:1156804665....@m79g2000cwm.googlegroups.com...
> > 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)
> >
> >snip<
>
> When you "divide" the spokes into categories the spokes are no longer part
> of a wheel. You may as well divide your brain in to various pieces, observe
> that no thought is taking place, and then conclude that brain cells are
> incapable of supporting thought.
I didn't mean divide them as in remove them from the wheel and make
three piles! The calculation of the stresses and forces in the
individual members that make up a more complex object is one of the
fundamental processes of engineering.
>
> The spokes, when laced into a wheel and properly tensioned, are part of a
> whole.
Very true
>As such, spokes as part of a wheel are mechanically different from
> spokes that are separate from the wheel.
Not true at all, and kind of a strange thing to say.
Jeff
Jeff
jobst....@stanfordalumni.org wrote:
> Jeff Thomas writes:
>
> >>>> But just for fun, if the hub hangs from the upper spokes what is
> >>>> supporting the upper rim? Sky hooks?
>
> >>> The upper rim is supported by the lower rim, which is supported by
> >>> the ground. Not sure where you are trying to go with that one.
>
> >> * One rim standing vertically on the ground.
> >>
> >> * One spoke from the uppermost spoke hole connected to the hub.
> >>
> >> * Apply a 50 kg load at the hub toward the ground.
> >>
> >> What happens?
>
> > The single spoke goes into tension, supporting the the hub from
> > above, providing the simplest possible example of what happens in a
> > full bicycle wheel.
>
> Whoa! The rim collapses. You don't have a wheel.
Hey, now you are not being fair! This was a simple thought experiment
that I was responding to, and I think that both the proposer and I were
assuming that the load was not large enough to break the rim.
>
> > Now let me ask you: The same rim, but now a single spoke from the
> > bottommost hole connected to the hub. Apply a downward load again
> > and what happens? (Hint: it won't be pretty!)
>
> Now you are confused or at least not serious.
I wasn't asking you, I was asking the person who made the other
proposal, who thinks that the wheel is actually standing on the lower
spokes, as in literally.
SocSecTr...@earthlink.net
Mike O Hannon wrote:
> As can be seen in my previous diagram, the tension on the top spoke did
> not change from load on the wheel.
If you look at Gavin's data the tension in the top spokes does change-
it drops.
> The only time the tension on the
> top spokes change is when the load on the wheel is GREATER than the
> pretension.
Experimentally disproved.
> Try loosening all the spokes on a wheel,
> add a load and then see what spokes have tension.
Have you tried that? Rather than a thought experiment where you tell us
what the results are, try it in reality and let's see what happens. I
think that with no force to keep the wheel round it will distort ovally
very significantly, and you will see the greatest rise in tension in
the spokes perpendicular to the load.
bicycle_disciple
professors, writers and engineers arguing among each other.
Whats the final call on this debate? I'm all smiles here, but still
confused as the beginning.
-B.D
Michael Press
<1156884671.2...@i3g2000cwc.googlegroups.com>,
"Jeff" <jth...@northwestern.edu> wrote:
> Michael Press wrote:
> > > In article
> > > <jack-EBC1FA.1...@newsclstr02.news.prodigy.com>,
> > > Michael Press <ja...@abc.net> wrote:
> > > > But just for fun, if the hub hangs from the upper spokes
> > > > what is supporting the upper rim? Sky hooks?
> > >
> > > The upper rim is supported by the lower rim, which is supported by the
> > > ground. Not sure where you are trying to go with that one.
> >
> > * One rim standing vertically on the ground.
> >
> > * One spoke from the uppermost spoke hole connected to the hub.
> >
> > * Apply a 50 kg load at the hub toward the ground.
> >
> > What happens?
>
> The single spoke goes into tension, supporting the the hub from above,
> providing the simplest possible example of what happens in a full
> bicycle wheel.
I said a 50 kg load. The rim collapses. Do the experiment
if you think otherwise.
You say that the load on the hub is supported by the upper
portion of the rim through the upper spokes in tension.
But I still do not know what supports the upper portion of
the rim.
> Now let me ask you: The same rim, but now a single spoke from the
> bottommost hole connected to the hub. Apply a downward load again and
> what happens? (Hint: it won't be pretty!)
Yes as an Euler strut, a bicycle spoke collapses at about
2 kg * g. But in a bicycle wheel the bottom spoke is
pre-stressed.
--
Michael Press
Joe Riel
> As can be seen in my previous diagram, the tension on the top spoke did
> not change from load on the wheel. The only time the tension on the
> top spokes change is when the load on the wheel is GREATER than the
> pretension.
You might want to think that through. Where does the nonlinearity
come from?
--
Joe Riel
Jeff
bicycle_disciple wrote:
> Its funny how a noobish question from me has now ended up in statics
> professors, writers and engineers arguing among each other.
>
> Whats the final call on this debate? I'm all smiles here, but still
> confused as the beginning.
Yes it is funny :) That is the internet at its best/worst
Actually, your original question as to whether the spokes on a bicycle
wheel were in tension or compression has been answered
uncontroversially - they are always in tension, if the wheel is
prooperly adjusted and not overloaded.
The main argument that arose is whether a bicycle wheel is better
described as "hanging from the upper spokes" or "standing on the lower
spokes". I've explained previously why I believe that the first is
sort of true but not very precise, and the latter is incorrect.
There is also a debate raging as to whether the tension in the
"sideways" spokes increases signifciantly on loading.
If you are expecting these issues to be resolved on this thread, you
may have a long wait!
Jeff
Joe Riel
A more productive way to look at this is to consider which spokes
contribute the most to the radial stiffness of the wheel.
--
Joe Riel
Jeff
> > The single spoke goes into tension, supporting the the hub from above,
> > providing the simplest possible example of what happens in a full
> > bicycle wheel.
>
> I said a 50 kg load. The rim collapses. Do the experiment
> if you think otherwise.
OK the rim collapses. What does that prove? If it was a 10 kg load
then it would hold.
>
> You say that the load on the hub is supported by the upper
> portion of the rim through the upper spokes in tension.
> But I still do not know what supports the upper portion of
> the rim.
>
> > Now let me ask you: The same rim, but now a single spoke from the
> > bottommost hole connected to the hub. Apply a downward load again and
> > what happens? (Hint: it won't be pretty!)
>
> Yes as an Euler strut, a bicycle spoke collapses at about
> 2 kg * g. But in a bicycle wheel the bottom spoke is
> pre-stressed.
Right! So the bottom spokes are pulling down on the hub, increasing
the downward load on the hub rather than opposing it. This is why I
think it is wrong to say that the wheel is "standing on the lower
spokes"
Jeff
bicycle_disciple
> If you are expecting these issues to be resolved on this thread, you
> may have a long wait!
>
> Jeff
I agree.
Lets see what my statics professor has to say on this. I'm a university
student, so I can get to do this anytime..well ofcourse, office hours
only.
-B.D
Jeff
Good question, but easily answered. The nonlinearity is due to the
fact that the bottom spokes do not go into compression after they lose
their pretension, they just go slack.
Jeff
jason...@gmail.com
For better or for worse, Jobst et al. are right. I have (yet another!)
way of visualizing this that may help (but probably won't).
For what it's worth, I'm an engineer who does FEA all day long. When I
was in grad school, I, like Jeff, also taught statics to undergrads.
I have a major problem with Ian's model, but it's not a technical
objection. I just wish he added 981N (100 kgf) to each spoke to
represent pre-tension. Then none of the spokes in his solution would
have negative tension numbers, and thus wouldn't appear to be in
compression. Those spokes would simply have smaller tensile (positive)
values. Compression in a spoke would cause it to buckle, as everyone
agrees.
Ian is fairly flippant about this. To wit: "The first issue to address
is that of linear superposition. What this means is that I'm not
analysing all the stresses in the wheel. I know that all the spokes
start out with a uniform tension, and I don't really care about it. For
the purposes of the analysis I simply ignore it, and it goes away!"
What Ian's saying is not technically wrong, but it is confusing for
anyone new to the problem (engineer or not). What's more, there's no
good reason for ignoring the uniform initial tension on the wheel. It
doesn't help the analysis to do so. I can only guess that Ian's FEA
application doesn't allow him to arbitrarily pre-tension beam elements.
As far as I can tell, he doesn't metion which FEA code he's running
(Nastran?)
In my humble opinion, linear superposition has nothing to do with this.
In my further opinion (still humble!) he's misusing the phrase. We
/are/ assuming that this is a linear problem, but we're not
superimposing any loads if I've read the write-up correctly. We're
applying a single load, and since superposition requires the stress
results of two or more loads to be--wait for it--superimposed upon one
another.
In my final harrumph about the article, Ian completely misuses the
phrase "static indeterminacy." In my world, static indeterminacy is
reached when you have more variables than you have equations of
equilibrium (e.g., sum of forces in X, Y and Z, sum of moments about X,
Y and Z, etc). The stiffness of the rim and spokes has nothing (well,
little) to do with the problem, counter to what Ian suggests. Plenty of
statically indeterminate problems assume perfectly rigid components. On
the other hand, Ian's is obviously from the UK and "statically
indeterminate" may mean something slightly different to UK engineers
than it does to US engineers.
Ian's article would be much easier for the average reader to understand
if he simply added 100 kgf (981 N) to each spoke's tension, thus
un-ignoring the initial uniform tension state. Then it would be clear
that no spoke is actually loaded in compression.
(I chose 981N/100kgf because many wheels are built to the spec of ~100
kgf tension in each spoke..it's something of a de facto standard).
And here is my long-promised alternative illustration of the problem:
- Make a 2d free-body diagram of the hub, and nothing but the hub
(basically, a disk with 36 holes in it). I promise that we're not
losing anything or fudging anything by going 2-D on this. If we cared
about the compressive forces in the hub shell between the flanges, a
2-D analysis would NOT be valid.
- Mark points corresponding to the centers of the spoke holes
- Add 981N to each of the spoke tension values on Ian's web page
- Apply these modified vectors to the appropriate spoke holes points.
- Apply a downward force of 500N to the axle
- Sum your vectors and your 500N force (you will, of course, get zero).
If you ignore phrases like "hanging down from" or "standing on" and
just pay attention to the vectors, then this problem works out just
fine. Adding up all those vectors is tedious, but it should make it
clear that reducing the tension vector magnitudes on the "bottom"
spokes creates a net upward force equal to (and opposite) the downward
load. This doesn't violate any of the principles we teach students in
first-year engineering classes, but the terms become confused quite
easily if we let them.
I hope this has helped.
Jason
Joe Riel
In a two spoke wheel with a rigid rim, the top spoke will increase in
tension by the amount that the bottom spoke decreases. Absolute
tension in the bottom spoke doesn't reach zero until 200 lbs is applied
to the hub (assuming a 100 lb initial tension in the spokes).
--
Joe Riel
Jeff
Yep, I agree with everything you say. I also have agreed with just
about everything that Jobst has said, although a lot of it was overly
detailed and off the original topic :)
My main problem with Ian's page is way down at the bottom where he
concludes that the hub is supported by "standing on the lower spokes,"
which I found misleading enough to just call plain wrong. The fact
that the loss of prestress in the bottom spokes is the main response to
loading does not mean that the wheel is standing on the lower spokes.
What do you say about this?
Jeff
carl...@comcast.net
<1.crazy...@gmail.com> wrote:
Dear B.D.,
I just saw your post and checked. Both links work for me.
http://www.astounding.org.uk/ian/wheel/index.html
http://www.duke.edu/~hpgavin/papers/HPGavin-Wheel-Paper.pdf
Neither seems to be long enough to require tinyurl to get around
browser problems.
The Gavin link requires a pdf reader, such as a Adobe or Foxit.
Possibly whichever site failed for you was just down at the time for
maintenance?
Cheers,
Carl Fogel
carl...@comcast.net
>Jeff wrote:
>> ken...@willets.org wrote:
>> > 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.
>
>Consider the following for a four spoke wheel:
>( Best viewed in monospaced font ).
>
> |
> |
> |
> 100
> |
> |
> |
> -----100-----O-----100-----
> |
> |
> |
> 100
> |
> |
> |
>
>Unloaded wheel. Spoke pretension ( 100Lbs ) counteracts each other.
>
>
> |
> |
> |
> 100
> |
> |
> |
> -----100-----O-----100-----
> |
> |
> |
> 0
> |
> |
> |
>
>Wheel loaded with 100Lbs. Only the lower spoke tension changes. The
>pretension ( 100Lbs ) of the upper spoke is replaced with wheel load of
>100Lbs. In this state, the lower spoke can be removed without any
>adverse effects.
>
>Conclusion: The bike does not "stand" on lower spokes.
>
>The above does not take into account any rim flexing.
Dear Mike,
That's a fairly common misunderstanding.
When you try to roll the wheel from which you removed the spoke, it
collapses immediately.
Or take it back another step. Try to build a pre-tensioned wheel using
only 3 spokes at 90-degree angles. You can't, of course.
You've removed the spoke, but added a force equivalent to it to keep
the wheel from falling apart. Roll the wheel, and it collapses.
Cheers,
Carl Fogel
MykalCrooks
>
> MykalCrooks wrote:
> > "Jeff" <jth...@northwestern.edu> wrote in message
> > news:1156804665....@m79g2000cwm.googlegroups.com...
> > > 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)
> > >
> > >snip<
> >
> > When you "divide" the spokes into categories the spokes are no longer
part
> > of a wheel. You may as well divide your brain in to various pieces,
observe
> > that no thought is taking place, and then conclude that brain cells are
> > incapable of supporting thought.
>
> I didn't mean divide them as in remove them from the wheel and make
> three piles! The calculation of the stresses and forces in the
> individual members that make up a more complex object is one of the
> fundamental processes of engineering.
>
>
>Jeff
>
I beg you for this moment to ignore the distraction you've created by your
well-intentioned but obtuse appeal to authority and pay attention to what
you actually stated, quoted as follows:
"Now let me ask you: The same rim, but now a single spoke from the
bottommost hole connected to the hub. Apply a downward load again and what
happens? (Hint: it won't be pretty!)"
Take note that in the model you've detailed you do in fact divide the spokes
"as in remove them from the wheel." Allegorically, you similarly separate
the spokes in your analyses as evidenced by other statements you've made.
Thus, you appear to practice engineering principles because you allude to
the authoritative body of knowledge -- "the fundamental processes of
engineering" -- but in actual practice you continue to rely foremost upon
your own naive intuition as you make your conclusions.
Forgive me for condescending, but when you finally get this principle of the
spoked wheel that is being discussed here, you will consider yourself
enlightened. Until then, you will consider yourself smart.
Been there, did that.
-mC
Michael Press
<1156889656.2...@p79g2000cwp.googlegroups.com>,
"Jeff" <jth...@northwestern.edu> wrote:
> > > The single spoke goes into tension, supporting the the hub from above,
> > > providing the simplest possible example of what happens in a full
> > > bicycle wheel.
> >
> > I said a 50 kg load. The rim collapses. Do the experiment
> > if you think otherwise.
>
> OK the rim collapses. What does that prove? If it was a 10 kg load
> then it would hold.
It proves that you need to do better when you tell me that
the load is carried by the upper spokes. What supports the
top of the rim if the hub hangs from the upper spokes?
> > But in a bicycle wheel the bottom spoke is
> > pre-stressed.
>
> Right! So the bottom spokes are pulling down on the hub, increasing
> the downward load on the hub rather than opposing it. This is why I
> think it is wrong to say that the wheel is "standing on the lower
> spokes"
You will have to fill in the blanks between pre-stressed
spokes and "[not] standing on the lower spokes" for me.
In beginning statics the rigid body simplification is
used. When analyzing a spoked wheel we cannot think in
terms of rigid bodies, but if we do, then indeed the wheel
stands on the lower spokes.
When a spoked wheel is loaded at the hub and set on the
ground, how does it take the load?
--
Michael Press
jason...@gmail.com
> Yep, I agree with everything you say. I also have agreed with just
> about everything that Jobst has said, although a lot of it was overly
> detailed and off the original topic :)
>
> My main problem with Ian's page is way down at the bottom where he
> concludes that the hub is supported by "standing on the lower spokes,"
> which I found misleading enough to just call plain wrong. The fact
> that the loss of prestress in the bottom spokes is the main response to
> loading does not mean that the wheel is standing on the lower spokes.
> What do you say about this?
>
> Jeff
Hi Jeff,
Cool--we're all on the same page as far as the phenomena are concerned.
I agree with you completely that Ian's conclusion that the hub stands
on the lower spokes is dangerously misleading, but I have a hard time
calling it wrong.
I'm reminded of a bon mot attributed to physicist Wolfgang Pauli,
something to the effect of, "That's not right. That's not even wrong."
We can tell ourselves whatever story we like about how a bicycle wheel
supports itself, but in the end the vector sum is all that matters.
Wheels are deceptively complex tensioned structures, and any
non-mathematical description of how they work will be inexact. That
said, I find a number of Ian's assertions to be especially inexact.*
I'm afraid my attempt to explain this to a layperson would be
unsatisfyingly vague; it might be something along these lines:
"The stiffness of the rim and the tension in the spokes work together
to make a very stiff assembly. The rim and the spokes work together to
stiffen the assembly, and it's dangerous to treat them as discrete
entities. Under load, spoke tension decreases markedly near the contact
patch, indicating a radial displacement of the rim at that point. The
rest of the structure responds to this displacement and tension changes
throughout the wheel, but mostly near the contact patch."
I told you it would be unsatisfying ;)
Jason
* I may be frustrated with Ian's account of his FEA model, but that
doesn't mean I don't like the model itself. Everything seems kosher to
me, and although I'd like to know more about which FEA application
Ian's using, which beam elements and number/type of degrees of freedom,
the model itself looks just fine. I certainly don't object to Ian's
model on an FEA basis, and as I haven't constructed my own model, I
really can't complain. I'd bet dollars to doughnuts that Ian's model
corresponds quite well with reality.
Mike
> On Tue, 29 Aug 2006 16:09:19 +1200, Mike <m.fee@iirrll..ccrrii..nnzz>
> wrote:
>
> >In article <5697f2tnf3ni4eotp...@4ax.com>, carl...@comcast.net says...
> >> On 28 Aug 2006 13:50:54 -0700, ken...@willets.org wrote:
> >>
> >> >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.
>
Note that I am not talking about cutting a tensioned spoke or rubber band, I am talking about cutting the spoke/band in
a situation where the tension is precisely zero. Doing so simply illuistrates that in that particular loading situation
the spoke in question is not transmitting forces of any kind so, _as an individual structural element_, it cannot be
considered as carrying a load of any form.
> The response of the pre-tensioned spokes on a bicycle wheel to a load
> on the axle is predictable and measurable by experiment.
>
If you re-read what I wrote above you will see that I do not dispute that.
> The spokes directly under the axle account for 95% of the change from
> an unloaded state.
>
i don't dispute this.
> 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.
>
And I don't dispute that the load is equal to the algebraic sum of the vertical tensile forces in all the spokes - of
which the change in tension of the bottom spoke is the greatest absolute change.
> 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.
>
I don't object to Jobst's and other's _model_. The model predicts the observed behaviour of a loaded wheel, which is
all that a model has to do. But you must accept that it is just a model, and like all models it has its limitations.
For example: to a close approximation the tension in the bottom spoke reduces approximately linearly as the load on the
wheel increases, while there is a small redistribution of tensile forces on the other spokes. The 'compressive load
model' interprets this as a compressive load on the bottom spoke and accurately predicts the behaviour of the wheel. It
even correctly predicts (from the materials properties of the spoke and its dimensions) the reduction in length of the
bottom spoke as it is 'compressed'. However, if the load is increased until it is approximately equal to the pre-loaded
tension in the bottom spoke the model fails to predict behaviour. For now, the bottom spoke starts to bend a little as
it is 'compressed' below its un-tensioned equilibrium length, and the neighbouring spokes to either side start to show
a significant reduction in tension. The model can be rescued by assuming that the bottom spoke has reached some sort of
'buckling point' and can no longer respond to the increase in compression from the load so the neighbouring spokes are
now responding compressively to take the load. Once again the model will accurately predict the wheels behaviour -
possibly right to the point that the wheel buckles.
But now stand back and consider the spoke in isolation. Take a real spoke, just like the spoke you might buy from your
local bike shop, mount it in a press and start to compress it longitudinally without any other constraint. You will
initially get a nice linear stress/strain relationship with a slope that can be predicted from the elastic modulus of
steel and the dimensions of the spoke, but eventually the spoke will begin to buckle, the stress/strain slope will kink
and then flatten off as the spoke bends. The exact stress required to buckle the spoke cannot be accurately predicted,
but can be very roughly approximated from the materials and dimensions of the spoke, and will certainly be within the
first few tens of Newtons for any real spoke.
If we now look at the behaviour of the spokes in the 'compressive load' model, their behaviour is quite different.
These spokes show exactly the same stress/strain relationship initially, but now this can be extended up to many
hundreds of Newtons before the spoke starts to kink. What's more - the load required to cause the kink and loss in
linearity in the stress/strain curve is no longer a function of the materials and dimensions of the spoke but can
instead, now be accurately predicted from the initial pre-tensioning of the wheel. In fact, ( within obvious limits) by
increasing the tension in all the spokes, you can tune the kink point at will.
Thus - although the compressive load model accurately predicts the static and dynamic behaviour of the wheel within
most practical limits, it relies on the presence of compressive spokes which exhibit materials properties not actually
demonstrable in the real world. So as a model, it is perfectly valid and reasonable, but as a description of the
underlying reality of the situation it is no more valid than is the fluid dynamicists assumption that water is an
incompressible fluid.
Regards,
Mike
jobst....@stanfordalumni.org
I think you will, like those who don't believe in radar accuracy, stop
traveling with any motor vehicle, all of which are designed using FEA
and upon which we all rely. That Gavin's report might be amiss is not
beyond my imagination, he having copied my work and failed to list it
in his bibliography may be an indication that he is not fully aware of
what he writes.
Let's rather stay with what I have written here and in "the Bicycle
Wheel". I began all this by building a tensiometer which became a
product at Avocet, DT, and FSA with which I verified what I had
discovered while building wheels. My measurements were then verified
by FEA as well as in Prof. Wiedemer's publication which I list in the
book.
I don't know where you get the "are completely different from the
observed data" because I and others have compared the computed results
with measurements and found them to be correct. How did you determine
that FEA is an invalid method?
Jobst Brandt
jobst....@stanfordalumni.org
> Experimentally disproved.
I think this ought to be easily done and I have observed it with
wheels that had essentially no tension. The wheel remains as round as
spoke adjustment allows with a long flat section on the ground and has
five or more rattling loose spokes at the bottom. With luck, if there
are no side loads, the wheel will survive.
This is not a working bicycle wheel, it not having a full complement
of active spokes.
Jobst Brandt
SocSecTr...@earthlink.net
Joe Riel wrote:
> In a two spoke wheel with a rigid rim, the top spoke will increase in
> tension by the amount that the bottom spoke decreases. Absolute
> tension in the bottom spoke doesn't reach zero until 200 lbs is applied
> to the hub (assuming a 100 lb initial tension in the spokes).
Rims aren't rigid and they don't have only two spokes. Consider a real,
non-rigid rim with four spokes.
SocSecTr...@earthlink.net
jobst....@stanfordalumni.org wrote:
> anonymous snipes:
>
> >> Let me suggest that you make a class project of a finite element
> >> analysis of a bicycle wheel. Use the plainest 36 spoke wheel, the
> >> values for which (rim and spokes) are shown and listed in "the
> >> Bicycle Wheel" from which you could save time. I think that ought
> >> to make the mechanics of it more clear. I'm sure you have such
> >> software at your school and it would be a good exercise for the
> >> class to work on in teams on such an evaluation.
>
> > The only problem is that your FEA does not represent the real world.
> > Look at Gavin's data. The forces predicted by the FEA line are
> > completely different from the observed data, except for detensioning
> > of the spokes immediately underneath the axle.
>
> I think you will, like those who don't believe in radar accuracy, stop
> traveling with any motor vehicle, all of which are designed using FEA
> and upon which we all rely. That Gavin's report might be amiss is not
> beyond my imagination, he having copied my work and failed to list it
> in his bibliography may be an indication that he is not fully aware of
> what he writes.
I don't have any problem with FEAs, but if they don't model reality
they're wrong, it's that simple. Your FEA doesn't appear to model
reality. The fact that you reference an apparently inaccurate FEA to
support your argument makes it difficult for me to give any credence to
your theory.
Gavin's work may or may not be wrong. but to insist that it is wrong
because his measurements of reality do not match an FEA is absurd.
Prima facie, the FEA is wrong.
Cut the crap about motor vehicles, FEAs and implied luddism. It's
nothing but a thinly veiled ad hominem, and it again reflects poorly on
whatever argument you are trying to make.
SocSecTr...@earthlink.net
jobst....@stanfordalumni.org wrote:
> anonymous snipes:
>
> >> As can be seen in my previous diagram, the tension on the top spoke
> >> did not change from load on the wheel.
>
> > If you look at Gavin's data the tension in the top spokes does
> > change- it drops.
>
> >> The only time the tension on the top spokes change is when the load
> >> on the wheel is GREATER than the pretension.
>
> > Experimentally disproved.
>
> >> Try loosening all the spokes on a wheel, add a load and then see
> >> what spokes have tension.
>
> > Have you tried that? Rather than a thought experiment where you tell
> > us what the results are, try it in reality and let's see what
> > happens. I think that with no force to keep the wheel round it will
> > distort ovally very significantly, and you will see the greatest
> > rise in tension in the spokes perpendicular to the load.
>
> I think this ought to be easily done and I have observed it with
> wheels that had essentially no tension. The wheel remains as round as
> spoke adjustment allows with a long flat section on the ground and has
> five or more rattling loose spokes at the bottom.
Nonsense. A wheel with all slack spokes is the same as no spokes at
all. If you are claiming that you can put a load on an unlaced rim
without the rim distending ovally, I don't really have any response,
except to say I don't think most of us believe that to be true.
> This is not a working bicycle wheel, it not having a full complement
> of active spokes.
True. And it's not my though experiment. But I think it does represent
a limit, assuming that the spokes are loosened the minimum amount
necessary to measure zero tension.
Johnny Sunset aka Tom Sherman
bicycle_disciple TOP POSTED:
> Its funny how a noobish question from me has now ended up in statics
> professors, writers and engineers arguing among each other.
>
> Whats the final call on this debate? I'm all smiles here, but still
> confused as the beginning.
Google "Trevor Jeffrey". ;)
--
Tom Sherman - Behind the Cheddar Curtain
Johnny Sunset aka Tom Sherman
ken...@willets.org used indefinite pronouns without context:
> 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.
As Michael Press might write, "What are you talking about?"
Phil Holman
"bicycle_disciple" <1.crazy...@gmail.com> wrote in message
news:1156888335.7...@h48g2000cwc.googlegroups.com...
> Its funny how a noobish question from me has now ended up in statics
> professors, writers and engineers arguing among each other.
>
> Whats the final call on this debate? I'm all smiles here, but still
> confused as the beginning.
>
> -B.D
This has been discussed and beaten to death several times on RBT but it
has never been satisfactorily resolved to everyone's liking. Time for
another round, I guess.
It would make a good Standardized Test question:
Given three wheels, (1) wooden with the spokes in compression, (2) cast
aluminum with zero stress in the spokes and (3) a normal bicycle wheel
with tensioned spokes. A 50lb load is applied downward to the axle ends
(total 100lb) and is reacted at the rim by contact with the ground.
Which sentence best provides a universal description of the how the
wheel hubs are supported?
(a) The hubs are hanging from the top spokes (top spoke load changes)
(b) The hubs are standing on the bottom spokes (bottom spoke load
changes)
(c) Wheels (1) and (2): the hub is standing on the bottom spokes and
wheel (3): the hub is hanging form the top spokes even though the
spoke loading change is identical to all three wheels.
(d) The hub is supported by the horizontal spokes (hint: don't pick this
one).
Phil H
Michael Press
<JtidnURWFb5jbGnZ...@comcast.com>,
"Phil Holman" <piholmanc@yourservice> wrote:
> "bicycle_disciple" <1.crazy...@gmail.com> wrote in message
> news:1156888335.7...@h48g2000cwc.googlegroups.com...
> > Its funny how a noobish question from me has now ended up in statics
> > professors, writers and engineers arguing among each other.
> >
> > Whats the final call on this debate? I'm all smiles here, but still
> > confused as the beginning.
>
> This has been discussed and beaten to death several times on RBT but it
> has never been satisfactorily resolved to everyone's liking. Time for
> another round, I guess.
New usenet appellation: zombie thread.
> It would make a good Standardized Test question:
>
> Given three wheels, (1) wooden with the spokes in compression, (2) cast
> aluminum with zero stress in the spokes and (3) a normal bicycle wheel
> with tensioned spokes. A 50lb load is applied downward to the axle ends
> (total 100lb) and is reacted at the rim by contact with the ground.
> Which sentence best provides a universal description of the how the
> wheel hubs are supported?
>
> (a) The hubs are hanging from the top spokes (top spoke load changes)
> (b) The hubs are standing on the bottom spokes (bottom spoke load
> changes)
> (c) Wheels (1) and (2): the hub is standing on the bottom spokes and
> wheel (3): the hub is hanging form the top spokes even though the
> spoke loading change is identical to all three wheels.
> (d) The hub is supported by the horizontal spokes (hint: don't pick this
> one).
Thanks for this.
--
Michael Press
jobst....@stanfordalumni.org
>> Its funny how a noobish question from me has now ended up in
>> statics professors, writers and engineers arguing among each other.
>> Whats the final call on this debate? I'm all smiles here, but still
>> confused as the beginning.
> This has been discussed and beaten to death several times on RBT but
> it has never been satisfactorily resolved to everyone's liking. Time
> for another round, I guess.
> It would make a good Standardized Test question:
> Given three wheels, (1) wooden with the spokes in compression, (2)
> cast aluminum with zero stress in the spokes and (3) a normal
> bicycle wheel with tensioned spokes. A 50lb load is applied downward
> to the axle ends (total 100lb) and is reacted at the rim by contact
> with the ground. Which sentence best provides a universal
> description of the how the wheel hubs are supported?
> (a) The hubs are hanging from the top spokes (top spoke load
> changes)
> (b) The hubs are standing on the bottom spokes (bottom spoke load
> changes)
> (c) Wheels (1) and (2): the hub is standing on the bottom spokes and
> wheel (3): the hub is hanging form the top spokes even though
> the spoke loading change is identical to all three wheels.
> (d) The hub is supported by the horizontal spokes (hint: don't pick
> this one).
I think that's a concise summation of the technical assessment of
what supports the hub. Nice work!
Jobst Brandt
carl...@comcast.net
Dear Phil,
Can we add a few more wheels? Wheels with pre-compressed "spokes" are
woefully neglected on this narrow-minded newsgroup.
(4) A wheel whose hub is supported by 36 stiff coil springs, each with
200 pounds of pre-compression.
(5) A wheel whose hub is supported 18 bicycle spokes with 200 lbs of
pre-tension, alternating with 18 stiff coil springs with 200 lbs of
pre-compression.
6) A wheel whose hub is supported by 9 loose wooden spokes, mixed with
9 zero-stress aluminum struts, interleaved with 9 bicycle spokes at
200 lbs pre-tension, topped off with 9 coil springs at 200 lbs
pre-compression.
Idealized radial spoking or an increase to 48 spokes may be necessary
to make these wheels fly, if you'll pardon a mixed metaphor.
Cheers,
Carl Fogel
41
Jeff wrote:
> >
> > Curiously a statics professor with whom I discussed the matter before
> > publication was also a "hangs from the top" adherent to the extent
> > that he believed the upper spokes increased in tension roughly as I
> > knew the bottom s pokes to reduce in tension.
>
> As I said before, I don't disagree with the well-established fact that
> the loss of pretension in the bottom spokes is the major change in
> spoke tension due to load. I am a "hangs from the top" adherent based
> on fact that the top spokes are the ones that exert forces opposite in
> direction to the load.
>
>
> > He said curtly, if you
> > had a mathematical analysis we might talk about it further. He never
> > responded to the FEA data and drawings that I subsequen tly developed
> > and sent him. His critique was an impetus to performing the analysis
> > that I originally thought would be beating a dead horse, the matter
> > being so obvious.
>
> He sounds like a jerk, which is something I try hard not to be.
>
> >As I discovered, the subject is not obvious.
>
> No, it is a bit trickier than it appears at first, isn't it? In my
> statics class I have to assign a final project that requires the
> students to do some detailed analysis and submit a report - maybe I
> will do a bicycle wheel next term!
As a class project, I think that if confined to the issue of whether
the rim ovalizes, or else flattens at the contact point, whether the
tension (mostly) increases at the top spokes or side spokes, or
(mostly) decreases at the bottom spokes, with some guidance that which
of the latter occurs depends on the relative stiffness of rim and
spokes, and some illustration that the strength of the wheel comes from
the lacing, etc., then this would be a very worthwhile excercise,
assuming the class is at a level where it can calculate such things.
However, with the goal of determining whether the wheel stands on its
bottom spokes or hangs from the top, I expect it would be a waste of
time if not a disaster. The questions in the above paragraph are real
engineering questions, which Jobst did a great job analyzing and others
did not. The questions beginning this paragraph are somewhat undefined
and morewhat literary questions, and in my capacity as an editor I
would have suggested something different.
How about:
-the applied load leaks out the bottom
-the applied load is absorbed by the bottom spokes
-loading the hub unhangs it from the bottom, if humour is the goal...
Neither standing nor hanging seems apropos to the situation to me. When
something hangs it is not supposed to be pulled to the ground as well
and when something stands it is not supposed to be pulled to the
ceiling as well. Extending the words to these situations is not a
matter of deduction, it is a matter of allusion and of audience rating.
I have hangers in my cupboard and if I roped them up from the bottom as
well I would not say they were hanging any longer, regardless of the
behaviour of the attachments upon external loads or deformation of the
floor or ceiling. If I were standing with a noose around my neck and
pulling up while someone else pulled me down to compress my legs
nevertheless, I would not say I was standing any longer- even if, were
the floor bumped up, my knees had to bend instead of the noose getting
looser.
†
Joe Riel
> (4) A wheel whose hub is supported by 36 stiff coil springs, each with
> 200 pounds of pre-compression.
>
> (5) A wheel whose hub is supported 18 bicycle spokes with 200 lbs of
> pre-tension, alternating with 18 stiff coil springs with 200 lbs of
> pre-compression.
>
> 6) A wheel whose hub is supported by 9 loose wooden spokes, mixed with
> 9 zero-stress aluminum struts, interleaved with 9 bicycle spokes at
> 200 lbs pre-tension, topped off with 9 coil springs at 200 lbs
> pre-compression.
>
> Idealized radial spoking or an increase to 48 spokes may be necessary
> to make these wheels fly, if you'll pardon a mixed metaphor.
I've already submitted patents for 4-6.
--
Joe Riel
Jeff
jason...@gmail.com wrote:
> Hi Jeff,
>
> Cool--we're all on the same page as far as the phenomena are concerned.
>
> I agree with you completely that Ian's conclusion that the hub stands
> on the lower spokes is dangerously misleading, but I have a hard time
> calling it wrong.
That's close enough to my own opinion to make me happy. I certainly
don't think that "hanging from the top spokes" is a particulary apt
description, just the best of the overly simple statements.
>
> I'm reminded of a bon mot attributed to physicist Wolfgang Pauli,
> something to the effect of, "That's not right. That's not even wrong."
> We can tell ourselves whatever story we like about how a bicycle wheel
> supports itself, but in the end the vector sum is all that matters.
> Wheels are deceptively complex tensioned structures, and any
> non-mathematical description of how they work will be inexact. That
> said, I find a number of Ian's assertions to be especially inexact.*
>
> I'm afraid my attempt to explain this to a layperson would be
> unsatisfyingly vague; it might be something along these lines:
>
> "The stiffness of the rim and the tension in the spokes work together
> to make a very stiff assembly. The rim and the spokes work together to
> stiffen the assembly, and it's dangerous to treat them as discrete
> entities. Under load, spoke tension decreases markedly near the contact
> patch, indicating a radial displacement of the rim at that point. The
> rest of the structure responds to this displacement and tension changes
> throughout the wheel, but mostly near the contact patch."
>
> I told you it would be unsatisfying ;)
Actually, I find it quite satisfying and accurate :)
>
> * I may be frustrated with Ian's account of his FEA model, but that
> doesn't mean I don't like the model itself. Everything seems kosher to
> me, and although I'd like to know more about which FEA application
> Ian's using, which beam elements and number/type of degrees of freedom,
> the model itself looks just fine. I certainly don't object to Ian's
> model on an FEA basis, and as I haven't constructed my own model, I
> really can't complain. I'd bet dollars to doughnuts that Ian's model
> corresponds quite well with reality.
I also got the impression that he did a good job with the model itself,
but then stumbled badly at the end when he summed up his findings,
because he apparently forgot that he had "normalized" his values to the
pretensioned state. In the followng text from his page he treats the
values as the absolute values. This leads to mistakes. For example,
he concludes that the top spokes provide only a tiny amount of lift
force, when in fact they still provide lots of lift due to their
pretensioning:
"Then, I've split the lift forces into two columns, depending upon
whether the spoke force was tensile or compressive. This is to see if
the hub hangs from tensile spokes, or stands on compressive ones.
- There are 31 tensile spokes. On average they contribute 1.436 N
(0.14 kg, just under a third of a pound) each to holding up the hub.
- There are 5 compressive spokes. On average they contribute 191.097N
(19 kg, just over 42 lbs) each to holding up the hub."
Anyone reading that in isolation would assume that the bottom spokes
were heavily in compression so that the wheel really was standing on
them. As an engineer, if you do the calculations correctly but then
summarize the calculations incorrectly to the public or your client,
you have failed at your job.
This is of course a bit unfair to Ian, who I should point out is not
here to defend himself and published his analysis for amusement
purpose.
So in summary, Jason, I would say that we are in agreement on the
facts, but I am just a bit harder on Ian than you are.
Jeff
Jeff
Michael Press wrote:
> It proves that you need to do better when you tell me that
> the load is carried by the upper spokes. What supports the
> top of the rim if the hub hangs from the upper spokes?
The force applied to the hub is tranferred to the spokes, and then from
the spokes to the rim, and then from the rim to the ground. Obviously
that is not the answer you are looking for. You are trying to make a
point with this question, but I don't know what it is. Why don't you
just make the point.
>
> > > But in a bicycle wheel the bottom spoke is
> > > pre-stressed.
> >
> > Right! So the bottom spokes are pulling down on the hub, increasing
> > the downward load on the hub rather than opposing it. This is why I
> > think it is wrong to say that the wheel is "standing on the lower
> > spokes"
>
> You will have to fill in the blanks between pre-stressed
> spokes and "[not] standing on the lower spokes" for me.
>
OK:
1. All spokes are prestressed in tension, so they are all trying to
pull the hub toward the rim along their own axis.
2. This means that the bottom spokes on a loaded wheel are pulling
downward on the hub with their remaining pretension. Since the load is
also trying to push the hub down toward the ground, the bottom spokes
are not supporting (opposing) the load, but rather are working in the
same direction as the load.
3. The phase "X is standing on Y" is commonly understood to mean that
X is on top of Y, pushing down on Y, and Y is pushing back up on X,
supporting X from falling downward, in an analogy to a person standing
on a chair.
4. Comparing 2 and 3, you see that the situations are different,
indeed opposite, and so therefore the wheel does not "stand on the
bottom spokes"
Jeff
Jeff
carl...@comcast.net wrote:
> That's a fairly common misunderstanding.
>
> When you try to roll the wheel from which you removed the spoke, it
> collapses immediately.
That is so willfully obtuse that it almost qualifies as a troll. It is
a thought experiment, not a working wheel.
Jeff
Jeff
> the rim ovalizes, or else flattens at the contact point, whether the
> tension (mostly) increases at the top spokes or side spokes, or
> (mostly) decreases at the bottom spokes, with some guidance that which
> of the latter occurs depends on the relative stiffness of rim and
> spokes, and some illustration that the strength of the wheel comes from
> the lacing, etc., then this would be a very worthwhile excercise,
> assuming the class is at a level where it can calculate such things.
No, it is an introductory class and we would have to focus on the
vector analysis and find a simple way to calculate the approximate
changes in the internal spoke tensions.
>
> However, with the goal of determining whether the wheel stands on its
> bottom spokes or hangs from the top, I expect it would be a waste of
> time if not a disaster. The questions in the above paragraph are real
> engineering questions, which Jobst did a great job analyzing and others
> did not. The questions beginning this paragraph are somewhat undefined
> and morewhat literary questions,
Agreed. I wish everyone on this thread realized that.
and in my capacity as an editor I
> would have suggested something different.
>
> How about:
> -the applied load leaks out the bottom
> -the applied load is absorbed by the bottom spokes
> -loading the hub unhangs it from the bottom, if humour is the goal...
>
> Neither standing nor hanging seems apropos to the situation to me. When
> something hangs it is not supposed to be pulled to the ground as well
> and when something stands it is not supposed to be pulled to the
> ceiling as well.
I would add that when something stands, something else is pushing up on
it from below.
Jeff
Joe Riel
> I also got the impression that he did a good job with the model itself,
> but then stumbled badly at the end when he summed up his findings,
> because he apparently forgot that he had "normalized" his values to the
> pretensioned state. In the followng text from his page he treats the
> values as the absolute values. This leads to mistakes. For example,
> he concludes that the top spokes provide only a tiny amount of lift
> force, when in fact they still provide lots of lift due to their
> pretensioning:
But the bottom spokes provide precisely the same amount of "fall" (opposite
of "lift") due to their pretensioning.
--
Joe Riel
SocSecTr...@earthlink.net
Jeff wrote:
> > * I may be frustrated with Ian's account of his FEA model, but that
> > doesn't mean I don't like the model itself. Everything seems kosher to
> > me, and although I'd like to know more about which FEA application
> > Ian's using, which beam elements and number/type of degrees of freedom,
> > the model itself looks just fine. I certainly don't object to Ian's
> > model on an FEA basis, and as I haven't constructed my own model, I
> > really can't complain. I'd bet dollars to doughnuts that Ian's model
> > corresponds quite well with reality.
Define "well".
This is the thing that I find most annoying about this entire thread
and the others that preceded it. The only measurements that exist of
spoke tension of a wheel in use do not agree with the models. Gavin's
data is very clear about that. How can you possibly dismiss it? The
spokes next to those directly under the axle so _not_ show the greatest
increase in tension, and those over the axle lose tension. Both of
these significant _facts_ are unrepresented in the model.
For the record, I believe that the hub is suspended from all the spokes
that retain + tension under load. It just happens that the horizontal
spokes have the highest tension in a loaded wheel, and that's a fact.
Mike O Hannon
> Mike O Hannon wrote:
>
> > As can be seen in my previous diagram, the tension on the top spoke did
> > not change from load on the wheel.
>
> If you look at Gavin's data the tension in the top spokes does change-
> it drops.
Incorrect, relook at figure 11. Angles 0 and 360 ( top of wheel ) have
a reading of ZERO. That is no change. "Negative strain indicates a
pretress loss".
And if you reread my first post you would see that my analysis did NOT
include flexing of the rim. Flexing of the rim is what causes the
increased tension of spokes 90 degrees to the load. But tension of
spokes 90 degrees to the load carry very little load.
> > The only time the tension on the
> > top spokes change is when the load on the wheel is GREATER than the
> > pretension.
>
> Experimentally disproved.
Where?
Figure 11 shows the bottom spokes losing >250 microstrains. If the
bottom spokes lose tension why doesn't the hub move up ( caused by the
tension of the upper spokes )? Could it be because of the load on the
hub pulling down on the upper spokes?
All forces within the wheel have to ballance out or the hub will move
in the direction of where the greatest tension until all the forces are
equal. If the lower spokes lose tension, and the tension on the upper
spokes remain the same, there is an imbalance which can only be
accounted for by adding the load seen at the hub. This is how the
lower spokes can lose tension while the upper spokes remain at the same
tension.
> > Try loosening all the spokes on a wheel,
> > add a load and then see what spokes have tension.
>
> Have you tried that? Rather than a thought experiment where you tell us
> what the results are, try it in reality and let's see what happens. I
> think that with no force to keep the wheel round it will distort ovally
> very significantly, and you will see the greatest rise in tension in
> the spokes perpendicular to the load.
That would be correct depending on stiffness of the rim and loseness of
the spokes.
Joe Riel
Those, like myself, who prefer to describe the wheel as standing on
its bottom spokes do so because we see the unloaded but tensioned
wheel as the useful reference frame. Those who insist that the hub
hangs from the top spokes do so because they believe, implicitly, that
the significant frame of reference is the completely detensioned
wheel. But why stop there? Why not start with the aluminum rim stock
and undrawn wire spoke stock as the "initial state"? For all we know,
now that rims are frequently welded, they could have a huge residual
bending moment that needs to be accounted for in the static analysis.
--
Joe Riel
ken...@willets.org
That's linear elasticity - the force that the member exerts is
proportional to its elongation. To increase tension, a member has to
elongate a certain amount. To decrease tension by the same amount, it
has to shorten by the same amount (by the linearity assumption). If an
upward-pulling and downward-pulling member are connected rigidly in the
middle, then one member cannot increase tension without moving the
connection point and decreasing tension in the other.
This is high school physics. Nothing is perfectly rigid, or else we'd
have some very strange collisions.
Jeff
Joe Riel wrote:
> Those, like myself, who prefer to describe the wheel as standing on
> its bottom spokes do so because we see the unloaded but tensioned
> wheel as the useful reference frame.
That frame can be useful, for example to see how spoke tensions change
on loading. But it is not useful for describing what parts of the
wheel are supporting the hub, because the hub itself is not prestressed
and thus not part of that frame. You need to go back to the
untensioned frame of reference to do that. Otherwise you are not
accounting for the prestressing because you have "normalized it out".
This leads to absurdities like the following situation: a heavy rider
does a trackstand on a bike, causing the bottom spoke in the rear wheel
to become completely detensioned. You tell me the hub is "standing on
the bottom spokes". I pluck out the bottom spoke, hold it up, and say
"no its not!"
>Those who insist that the hub
> hangs from the top spokes do so because they believe, implicitly, that
> the significant frame of reference is the completely detensioned
> wheel.
Correct, though I would call it the frame of reference of the hub,
since that is the focal point of the analysis (the "free body" as we
say in statics.).
> But why stop there? Why not start with the aluminum rim stock
> and undrawn wire spoke stock as the "initial state"? For all we know,
> now that rims are frequently welded, they could have a huge residual
> bending moment that needs to be accounted for in the static analysis.
Those residual stresses from manufacturing are all internal to the
individual members. One of the cardinal rules of static analysis is
that you ignore internal forces, because they cancel themselves out.
Or to put it another way, the residual stresses in the spokes never
cause a net force to be applied to the hub or the rim (unlike the
pretensioning).
Jeff
carl...@comcast.net
wrote:
Dear Jeff,
When thought experiments drift off into non-working wheels, it's a
hint that they're non-working experiments.
Even practical experiments make the same kind of mistake.
Here's a video and page that illustrates the problem:
http://www.biketechreview.com/misc/hangin_hub.htm
By sawing out a section of one spoke of a heavy 3-strut wheel, the
author felt that he had proved something or other.
But all that it really does is show that the rim is so stiff that it
supports the rider without any pre-tension and that the struts are so
strong that they can function in both tension and compression,
depending on whether they're above or below the axle.
It's fun, but it's not a pre-tensioned wheel, so it doesn't say much
about a pre-tensioned wheel.
You cannot build a pre-tensioned wheel with only 3 spokes at 90
degrees to each other.
Cheers,
Carl Fogel
carl...@comcast.net
Dear SSTW,
Please spend about $60 on a Park spoke tension gauge and see if it
confirms your theory about horizontal spokes having the highest
tension of those that gain tension.
If it does, post the data.
Cheers,
Carl Fogel