Forces on spokes

The tension will increase at the top, and decrease at the bottom.
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.

On 30 Aug 2006 08:00:04 -0700, "Jeff" <[email hidden]>

Quoted message said:

Quoted message said:

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

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

Quoted message said:

Jeff said:

Quoted message said:

* 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.

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

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

Quoted message said:

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.

Well said, and without the help of Shakespeare. ;-)

Rick

Quoted message said:

Jeff said:

Quoted message said:

* I may be frustrated with Ian's account of his FEA model, but that

Actually that was Jason's text.
Jeff

Carl,

Quoted message said:

When thought experiments drift off into non-working wheels, it's a
hint that they're non-working experiments.

The correct questions to ask about a thought experiment are:

1. Does it work the way the author says it does?
2. Does it show anything useful?"

Since it was specified as a static situation, you can't attack it by
saying it won't hold up when it starts rolling. I would say that this
experiment clearly passes question 1. In other words, you should
attack it based on question 2 rather than question 1 (if you want to
attack it at all).

Jeff

anonymous snipes:

Quoted message said:

Quoted message said:

Quoted message said:

* 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.

Quoted message said:

Define "well".

Quoted message said:

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.

Quoted message said:

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.

You are alone in that "fact", tension distribution upon loading having
been measured by tensiometer, tone and FEA. Your belief doesn't land
well with so many readers having a bicycle at hand to verify that it
isn't so. Besides, you failed to append the word "period" at the end
of your claim, to give it absolute credibility.

Jobst Brandt

On 30 Aug 2006 11:04:42 -0700, "Jeff" <[email hidden]>

Quoted message said:

Carl,

Quoted message said:

When thought experiments drift off into non-working wheels, it's a
hint that they're non-working experiments.

The correct questions to ask about a thought experiment are:

1. Does it work the way the author says it does?
2. Does it show anything useful?"

Since it was specified as a static situation, you can't attack it by
saying it won't hold up when it starts rolling. I would say that this
experiment clearly passes question 1. In other words, you should
attack it based on question 2 rather than question 1 (if you want to
attack it at all).

Jeff

Dear Jeff,

In logic, it is usually considered a fallacy to start with a false
premise.

A non-working wheel is arguably a false premise.

Cheers,

Carl Fogel

c> >For the record, I believe that the hub is suspended from all the
spokes

Quoted message said:

Quoted message said:

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.

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

I agree with Carl (for once). I have stayed out of this so far because
I don't have an opinion yet, but I am interested in what the answer is.

Jeff

In article
<[email hidden]>,

Quoted message said:

The tension will increase at the top, and decrease at the bottom.
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.

This is a hand waving argument that may or may not apply
in any particular configuration. It does not apply to a
loaded spoked bicycle wheel. The deformation of that
configuration has been measured and the measurements do
not conform to your thesis.

--
Michael Press

Quoted message said:

Quoted message said:

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.

Therefore the hub plunges all the way to the ground
because this is not a static situation.

Only if you have removed the upper spokes.
I'm not sure if you are deeply confused or a troll, but I am not going
to explain anything else to you unless you pay me a consulting fee.

Jeff

Quoted message said:

Jeff said:

Quoted message said:

* 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.

Dear SSTW,

Here's the kind of data from a Park gauge that my other post asks for.

I quickly measured tension around a 32-spoke MA3 from Performance
Bike, nicely true, with the wheel in the air, not even the weight of
the bike on it, no tire.

Then I put 80 lbs of weights on a barbell laid like a bridge from one
bench to another. The bike's handlebars are just high enough that the
bar sits on them and tips slightly to one side or the other.

Sit on the floor and quickly re-measure the tension.

The spoke tension obviously varies around the wheel, with the two
spokes on either side of the valve hole being noticeably higher. When
loads are applied to unevenly pre-tensioned wheels, the unevenness
seems to be leveled out before we see the results predicted by
theoretical calculations for idealized wheels with perfectly even
initial tension.

I saw nothing that indicated unusual behavior by the horizontal
spokes. Repeated testing with more careful measurements might show
something unexpected, but I suspect that real wheels with real initial
tension variation between spokes behave about like this.

Considerable experience with this tedious and awkward business of
measuring spoke tensions leads me to expect that this single run may
well contain errors and anomalies. That is, if I re-measured several
times, I might well find a spoke where the next 3 measurements hint
that I mis-measured it or mistook a 17 for an 18.

I didn't, for example, bother to squeeze all the spokes together
gently at the crossings to make sure that no spoke was hanging up due
to friction and about to release a little extra tension.

Notes and data are below.

Cheers,

Carl Fogel

wheel untouched, from performance bike, nicely true

quick park tension gauge measurements wheel in air
quick park tension gauge measurements, 80 lb weight over axle

view bike from rider's left
spokes numbered 1..36 counter-clockwise

spoke #1 roughly at bottom (cross-3 makes this tricky)

valve hole between spokes 17 & 18 at roughly top of wheel
kind of interesting
those two spokes have noticeably higher initial tension
notice the tension drop, too

14.5 and 13 are off the bottom of the park scale
kgf estimated from curve

quick and dirty
suggests real wheel's varying tension affects results
suggests coarse measurement also affects results
models with idealized tension get around this

horizontal spokes are roughly 8 & 9, 25 & 26

80 lbs 80 lbs
over axle over axle
wheel in wheel on wheel in wheel on tension
spoke air ground air ground change
position
park park kgf kgf

bot 1 17 13 65 47 -18
bot 2 17 14.5 65 52 -13
3 17.5 15.5 69 57 -12
4 18 16 72 59 -13
5 17 18 65 72 7
6 17 17.5 65 69 4
7 17 16.5 65 62 -3
8 18 16.5 72 62 -10
hz 9 16.5 16 62 59 -3
hz 10 17 17 65 65 0
11 16.5 16.5 62 62 0
12 17 17.5 65 69 4
13 16.5 17.5 62 69 7
14 16 16.5 59 62 3
15 17 17.5 65 69 4
16 16 16.5 59 62 3
top17 19 17 80 65 -15
top18 19.5 18 85 72 -13
19 17 15 65 54 -11
20 16 16 59 59 0
21 16.5 16.5 62 62 0
22 19 17 80 65 -15
23 16.5 16.5 62 62 0
24 17 17 65 65 0
hz 25 16.5 16.5 62 62 0
hz 26 16 17 59 65 6
27 16.5 17 62 65 3
28 17 16.5 65 62 -3
29 16 17.5 59 69 10
30 16 17 59 65 6
31 16 16.5 59 62 3
32 17 16 65 59 -6

*** end of data

On 30 Aug 2006 13:11:04 -0700, "Jeff" <[email hidden]>

Quoted message said:

Quoted message said:

Quoted message said:

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.

Therefore the hub plunges all the way to the ground
because this is not a static situation.

Only if you have removed the upper spokes.
I'm not sure if you are deeply confused or a troll, but I am not going
to explain anything else to you unless you pay me a consulting fee.

Jeff

Dear Jeff,

Accusing people who disagree with you of being a troll, which you've
done elsewhere, is a weak argument.

Claiming that you could explain something but won't is even weaker.

Cheers,

Carl Fogel

Jeff said:

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.

Of course it can. I gave the example of an object hung between two
lengths of tensioned clothesline. If you raise the tension higher, the
clothesline will support more of the weight of the object. (Raising the
tension would require that the clothesline pole be heavily reinforced.)
Yes, it will sag, but the higher the tension of the horizontal
clothesline, the less force that would be required to be supplied from
a crane above the object to eliminate the sag. So the bottom spokes
become unloaded, the horizontal spokes increase their tension, and the
top spokes continue to "support" the hub without an increase in
tension. So I say that it is the horizontal spokes that support the
load as an oversimplification of what really is taking place.

Removing the support from underneath the object on the clothesline
causes a concurent rise in the tension of the clothesline itself
(through the ovalizing of the rim), allowing the object on the
clothesline to maintain its height (approximately) from the ground
without increasing the force applied from the overhead crane.

Quoted message said:

(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.)

But spokes at the bottom even slightly offset from the spokes directly
underneath the axle will add to the lifting effect on the hub. The
determinant is, is the distance from the center of the axle to the
rim-nipple interface longer or shorter than it is for an unloaded
wheel?

The thing is, in a pretensioned wheel, the load that would deform the
rim in a non-tensioned wheel is transmitted through the rim itself to
the horizontalish spokes. Their resulting rise in tension is what
resists the deformation of the wheel, and, therefore supports the load.
Supporting the load is, afterall, nothing more than keeping the wheel
from collapsing.

The tension in the horizontal spokes does not rise because of the load
pulling from the axle, it is because of the distension of the rim
ovally along the horizontal axis. This rise in tension supports the
hub.

Carl Fogel said:

Here's the kind of data from a Park gauge that my other post asks
for.

Quoted message said:

I quickly measured tension around a 32-spoke MA3 from Performance
Bike, nicely true, with the wheel in the air, not even the weight of
the bike on it, no tire.

Quoted message said:

Then I put 80 lbs of weights on a barbell laid like a bridge from
one bench to another. The bike's handlebars are just high enough
that the bar sits on them and tips slightly to one side or the
other.

Quoted message said:

Sit on the floor and quickly re-measure the tension.

Quoted message said:

The spoke tension obviously varies around the wheel, with the two
spokes on either side of the valve hole being noticeably
higher. When loads are applied to unevenly pre-tensioned wheels, the
unevenness seems to be leveled out before we see the results
predicted by theoretical calculations for idealized wheels with
perfectly even initial tension.

Carl,

Rather than entering all those numbers in a table of varying initial
tensions, please repeat the experiment using one spoke with the wheel
repositioned so that one spoke after another is successively pointing
straight down. I don't know how your tensiometer works, but not
zeroing the instrument on each spoke to be measured can cause spurious
values. Therefore, reading the same spoke 32 times is more accurate
and avoids deriving tension changes from differing initial and final
values to derive results.

I have done this and found the result to be nearly as consistent as
the computed values. Applying the load purely vertically (no side
loading) is also a major cause of inaccuracy.

Jobst Brandt

anonymous snipes:

Quoted message said:

Quoted message said:

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.

Quoted message said:

Of course it can. I gave the example of an object hung between two
lengths of tensioned clothesline. If you raise the tension higher,
the clothesline will support more of the weight of the
object. (Raising the tension would require that the clothesline pole
be heavily reinforced.) Yes, it will sag, but the higher the
tension of the horizontal clothesline, the less force that would be
required to be supplied from a crane above the object to eliminate
the sag. So the bottom spokes become unloaded, the horizontal spokes
increase their tension, and the top spokes continue to "support" the
hub without an increase in tension. So I say that it is the
horizontal spokes that support the load as an oversimplification of
what really is taking place.

Oh! So how tight does the power company stretch its power lines to
make them not sag (in a catenary curve)? I think you are putting us
on or do not understand force vectors. Horizontal spokes can support
no vertical force, especially being hinged at the hub and free at the
rim.

Quoted message said:

Removing the support from underneath the object on the clothesline
causes a concurent rise in the tension of the clothesline itself
(through the ovalizing of the rim), allowing the object on the
clothesline to maintain its height (approximately) from the ground
without increasing the force applied from the overhead crane.

I think you don't understand the model being discussed, that of a
wheel with the hub fixed in space and a road pushing up on it. If you
have no fixed reference, you can make all sorts of claims that are
difficult to track down.

Quoted message said:

The tension in the horizontal spokes does not rise because of the
load pulling from the axle, it is because of the distension of the
rim ovally along the horizontal axis. This rise in tension supports
the hub.

The rim doe not deform into an oval. You are making this up of pure
air!

Jobst Brandt

Jeff said:

Not quite. The pretensioning is a byproduct of external forces exerted
on the spoke by the hub and the rim, and those can't be ignored.
Manufacturing stresses exist without any external forces on the spoke.
So from the point of view of the hub, the pretensioning matters but the
residual stress does not.

Suppose, after building a wheel, all the joints (rim to nipple, nipple
to spoke, spoke to hub) were welded together. Now you have a solid
structure. Is the tension in the spokes ignorable? How is it different
from any other manufacturing induced residual stress?

Or consider a cast wheel (something Jobst suggested earlier in the
thread), one with spokes thick enough to handle a compressive load
without buckling. Because you choose to ignore any residual stresses,
you must conclude that the hub primarily stands on its bottom spoke.
But, depending on how the material set, the spoke could be in
tension or compression.

Basically we need to decide which point of view is more useful.
I find that looking at which members are primarly affected by
the applied load to be the more useful.

Either way there will be some confusion. I have to live with the
oddity that a spoke with no tension is providing support. You have to
live the paradox above, as well as the converse of mine. That is, the
spokes that (you claim) provide support may show essentially no change
in stress when a load is applied.

--
Joe Riel

Quoted message said:

Carl Fogel said:

Here's the kind of data from a Park gauge that my other post asks
for.

Quoted message said:

I quickly measured tension around a 32-spoke MA3 from Performance
Bike, nicely true, with the wheel in the air, not even the weight of
the bike on it, no tire.

Quoted message said:

Then I put 80 lbs of weights on a barbell laid like a bridge from
one bench to another. The bike's handlebars are just high enough
that the bar sits on them and tips slightly to one side or the
other.

Quoted message said:

Sit on the floor and quickly re-measure the tension.

Quoted message said:

The spoke tension obviously varies around the wheel, with the two
spokes on either side of the valve hole being noticeably
higher. When loads are applied to unevenly pre-tensioned wheels, the
unevenness seems to be leveled out before we see the results
predicted by theoretical calculations for idealized wheels with
perfectly even initial tension.

Carl,

Rather than entering all those numbers in a table of varying initial
tensions, please repeat the experiment using one spoke with the wheel
repositioned so that one spoke after another is successively pointing
straight down. I don't know how your tensiometer works, but not
zeroing the instrument on each spoke to be measured can cause spurious
values. Therefore, reading the same spoke 32 times is more accurate
and avoids deriving tension changes from differing initial and final
values to derive results.

I have done this and found the result to be nearly as consistent as
the computed values. Applying the load purely vertically (no side
loading) is also a major cause of inaccuracy.

Jobst Brandt

Dear Jobst,

I'm baffled by the idea that reading one spoke in 32 positions can be
more "accurate" than reading each spoke in its actual position.

The ultimate question is what all the spokes are doing at that
instant. In a computer simulation, all spokes have identical initial
tensions. On a real wheel, the initial tensions vary, and that causes
the results to vary--but that's reality.

I'm not trying to make the wheel match my pre-conceptions. Indeed, I
suspect that a lot of the "tone" measurements are well-nigh worthless
because of the pre-conceptions involved.

I measured a pair of noticeably higher-tension top spokes losing
tension when the axle was loaded. It's a little puzzling, but not if
you've measured a lot of changing tensions and noticed that varying
tensions between adjacent spokes seem to even out before they climb.
This would seem to be a similar behavior. If it's just a quirk or a
wild mistake, no one will repeat it.

Along the same lines, until I actually tested a number of real wheels,
I expected to find that mmild spoke squeezing would produce the
outlandish tension increases bandied about here on RBT.

But extensive testing showed that on typical 32 and 36 spoke wheels,
the peculiar stress of two-handed spoke-squeezing simply deformed the
rims in a faint S-curve to either side and raised the tension only
about as much as the squeeze force--a 60 pound squeeze force on each
pair of spokes, one with each hand, would raise the tension only about
60 pounds.

I'm certainly not arguing that the spoke tensions that I checked
quickly today are marvels of accuracy, but I suspect that they're in
the ballpark.

If they're not, someone with a wheel, some weights, and a tension
gauge can spend a little time and produce better data.

I suggest testing several wheels, front and rear, with different spoke
counts, just as I tested--measure the initial tensions of all spokes,
then load the wheel, re-measure each spoke with the wheel in the same
position, and look at the data.

Another approach would be to re-measure the same wheel several times,
with the wheel turned a quarter turn each time (or 32 times, but you
can imagine the work involved). This would show what goes on with the
other spokes as the lowest (and highest) tension spokes move to
different positions.

I doubt that the data would be as pretty as some people want and
others expect, but it would be real data, not an effort to make real
wheels behave in a purely theoretical fashion.

Cheers,

Carl Fogel

Quoted message said:

Jeff said:

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.

Of course it can. I gave the example of an object hung between two
lengths of tensioned clothesline. If you raise the tension higher, the
clothesline will support more of the weight of the object. (Raising the
tension would require that the clothesline pole be heavily reinforced.)
Yes, it will sag, but the higher the tension of the horizontal
clothesline, the less force that would be required to be supplied from
a crane above the object to eliminate the sag.

Right you are. But what you say doesn't change my point which is that
even if the side spokes have larger absolute tensions, their upward
component remains relatively small compared to those of the top spokes.

Quoted message said:

So the bottom spokes
become unloaded, the horizontal spokes increase their tension, and the
top spokes continue to "support" the hub without an increase in
tension.

Ok, so we are just a pair of quotes away from agreement 🙂

Quoted message said:

So I say that it is the horizontal spokes that support the
load as an oversimplification of what really is taking place.

My definition of how much of the load is supported by a particular
spoke is the amount of that spoke's tension that is in the opposite
direction as the load - that is, upwards. To me this is just logical,
but I now see that there are other points of view:

By my logic, the upper spokes support the load, since they contribute
the most upward force

Some people think that the bottom spokes support the load because they
undergo the greatest change in tension on loading (a decrease in
tension)

You think the side spokes support the load because you believe that
they have the largest absolute tension (some disagree but that is
beside the point here)

Jeff

Jeff said:

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.

You are assuming that in order for a spoke to support a load by
compressing that the spoke has no tension in it. That is not
necessarily the case. If a spoke has a tension of 10 units and you
then compress it with a load of 5 units, the spoke is being compressed
but will still have a tension of 5 units. That is exactly how a
bicycle wheel works. Keep the compressive load above the initial
tension of the spoke and the wheel will support the load.
------------------
Alex