Yet another broken spoke

Tom Keats said:

Quoted message said:

Waving the long term fatigue flag does not answer the question of
how low spoke tension causes spoke failure; a claim that appears in
this newsgroup often. I believe the example of rim deflection
under riding loads (which is the amount by which spoke preload is
reduced) is the appropriate parameter for stress change and it
shows that compression buckling is not possible in that respect as
I pointed out.

Quoted message said:

So, would a newly-installed, brand-new spoke that's too loose,
immediately break due to rim deflection, or break before its
adjacent brethren (that have hitherto held-up so well) do?

If the spoke was initially not loose, as spokes are on a new wheel, It
would only be deemed too loose if load deflection of the rim at the
load affected zone (where the tire meets the road) is greater than
elastic elongation of spokes from tensioning. That is the problem
with many wheels these days where rims crack if tightened to a
reliable tension that will mot slacken under load. That is
exacerbated by using fewer spokes so that the preload of one or two
spokes alone support the load.

Quoted message said:

What exactly /is/ rim deflection, and how does it happen? What
makes it happen? Are we talking about the momentary bottom of the
rim tending to squash flat on the surface it runs on and thereby
compressing spokes, (I guess not, since you above rule-out
compression buckling,) or are we talking about putting lateral 'S'
curves in the rim, and thereby bending spokes? Or maybe it's about
torque in a hard-driven wheel, between the rim and hub, where the
hub tends to rotate faster than the rim can keep up with, and the
spokes in-between bear the brunt, and the rim is deflected from the
POV of the hub (and the connecting spokes?)

When a wheel bears a load applied to its axle, that force is
transmitted to the road by compressing the spokes in roughly the tire
contact patch so that they lose preload equivalent to the axle load.
All other spokes remain essentially unchanged in tension (especially
the top ones that have been believed to get tighter).

You can check this by plucking spokes with and without loading the
wheel and note the tone. A lower tone indicates lower tension, a
higher tone indicated higher tension then initially when the wheel was
not loaded.

Quoted message said:

I don't know about these things, but I am curious, and I'd truly
like to understand.

You can get a better picture of this in "the Bicycle Wheel" in which
this is described in detail with computed graphs of wheel deformation.
This subject comes up often enough that this book on the shelves of
most bicycle shops. It is also available from Amazon and ABE, among
others.

http://sheldonbrown.com/harris/books.html#brandt
http://www.amazon.com/exec/obidos/ISBN=0960723668/1361-7743389-379578
http://tinyurl.com/3d7a49

Jobst Brandt

On 2007-09-04, [email hidden] <[email hidden]> wrote:
[...]

Quoted message said:

With a tighter spoke the stress variation can have a larger excursion
than that of a looser spoke.

Why?

Just to clarify: suppose I plot a graph of stress against time for a
spoke on a wheel on a bicycle that's being ridden down the road. I
expect the graph would be some kind of wave, going up and down as the
spoke passes over the contact patch.

By "larger excursion" do you mean that this wave would have a greater
amplitude?

Perhaps I'm being stupid but I don't see why you would get a larger
amplitude for a tighter spoke.

Ben C said:

On 2007-09-04, [email hidden] <[email hidden]> wrote:
[...]

Quoted message said:

With a tighter spoke the stress variation can have a larger excursion
than that of a looser spoke.

Why?

Just to clarify: suppose I plot a graph of stress against time for a
spoke on a wheel on a bicycle that's being ridden down the road. I
expect the graph would be some kind of wave, going up and down as the
spoke passes over the contact patch.

By "larger excursion" do you mean that this wave would have a greater
amplitude?

Perhaps I'm being stupid but I don't see why you would get a larger
amplitude for a tighter spoke.

Because you would not. If tensioned to, say 200 lbs, and 200 lbs is
suspended from roughly8 of the 28 spokes, you might end up with
something like 250 lbs tension on any one spoke. That tension would
only change something like 60 lbs in use, and at all times the spoke
would be under a minimum of something like 140 lbs. With a 15 or 14
guage spoke,that tension would keep the spoke from fatigue.

Think of the spoke as a bolt, and read the following from
Writetool.com:

Tension Joints
The shear joint does not rely on tension in the bolt to hold parts
together. The tension joint, however, relies on the tension of the
bolt to hold two joined parts together. The greater the tension on the
bolt, the more force holding them together. Steel and most metals have
a property known as fatigue, which means that they lose strength upon
repeated loads. For example, a bolt with an ultimate strength of 1,000
lbs. will carry a load of 1,000 lbs. once. It will carry a load of 500
lbs. millions of times. It will carry a load between 500 lbs. and
1,000 lbs. for a limited number of times between 1 and 1 million,
depending on whether the load is closer to the 1,000-lbs.-value or the
500-lbs.-value. It doesn't matter how long the heavy load is carried;
it can carry 1,000 lbs. forever, as long as it is only one cycle. Most
joints are subject to variations in load that either adds or decreases
the tension in the bolt.

How can we get all of the strength we pay for, or do we assume the
bolt strength is only 500 lbs. and use twice as many bolts in the
joint? If the joint has been properly designed, the clamping surfaces
around the bolt will take almost all of the variation if the bolt is
properly tightened. In this scenario, a load of close to 1,000 lbs.
can be used because the load will not fluctuate very much. But if the
joint is not properly tightened, the joined parts will separate and
the full increase on the load will be on the fastener, which will
overload it. Or, the load could go to zero, which means it is in a
fatigue condition and the bolt will fail because of the repeated
application of a load that it could have easily carried except for the
fatigue factor. Therefore, a bolt in a tension joint will fail from
fatigue if it is not tightened enough, and it will fail from fatigue
and overload, if it is tightened beyond its ultimate strength.

In our example the bolt's ultimate strength is 1,000 lbs.; in actual
practice there is a safety factor that extends the range beyond the
1,000 lbs., before the bolt actually breaks from simple overload.
Therefore, it is extremely important that we achieve the proper
tension on the bolt-not too much and not too little.

--
Posted via a free Usenet account from http://www.teranews.com

clare at snyder.on.ca said:

Ben C said:

On 2007-09-04, [email hidden] <[email hidden]> wrote:
[...]

Quoted message said:

With a tighter spoke the stress variation can have a larger excursion
than that of a looser spoke.

Why?

Just to clarify: suppose I plot a graph of stress against time for a
spoke on a wheel on a bicycle that's being ridden down the road. I
expect the graph would be some kind of wave, going up and down as the
spoke passes over the contact patch.

By "larger excursion" do you mean that this wave would have a greater
amplitude?

Perhaps I'm being stupid but I don't see why you would get a larger
amplitude for a tighter spoke.

Because you would not. If tensioned to, say 200 lbs, and 200 lbs is
suspended from roughly8 of the 28 spokes, you might end up with
something like 250 lbs tension on any one spoke.

Are we still talking about riding on the wheel here? You say "suspended"
and I'm not sure.

If you had 200lbf spoke tension (which is a bit high, usually it's more
like 100lbf I think), about 28 spokes, and you put a weight of 250lbs on
the bike, so acting at the hub, you'd expect to see some of the spokes
in the bottom part of the wheel lose a bit of tension, and little or no
tension change in the spokes in the top half. No spoke would go up to
250lbf tension.

Quoted message said:

That tension would only change something like 60 lbs in use, and at
all times the spoke would be under a minimum of something like 140
lbs. With a 15 or 14 guage spoke,that tension would keep the spoke
from fatigue.

Think of the spoke as a bolt, and read the following from
Writetool.com:

[...]

Quoted message said:

How can we get all of the strength we pay for, or do we assume the
bolt strength is only 500 lbs. and use twice as many bolts in the
joint? If the joint has been properly designed, the clamping surfaces
around the bolt will take almost all of the variation if the bolt is
properly tightened.

This is an interesting theory, but I'm not sure it's correct to think of
the spoke as a bolt this way. The equivalent of "the clamping surfaces
around the bolt" is the rest of the wheel, i.e. the rim basically. The
rim is quite stiff, and so I don't think we can build the wheel tight
enough so that the rim flexes but the spokes don't.

But in the bolt example the idea is that the bolt doesn't get a stress
cycle at all (or not much of a one).

The spokes are always going to have a stress cycle. We don't care about
the axial stress cycle (stretching the spoke along its length and
letting it relax again), because the size of the stress in that cycle is
very small compared to the yield strength of the spoke in that
direction, which means fatigue life in that direction is very long and
not a problem.

The key thing is the elbow. If the spoke goes loose, does the elbow bend
and unbend? Bending and unbending means leverage, and therefore much
higher stresses on parts of the spoke. Not enough stress to break it in
one go, but enough to reduce the number of cycles to failure to only a
few hundred miles of riding.

So does it bend and unbend? Jobst says no, jim beam says yes, although
it's not unusual for those guys to disagree with each other.

I think it's very hard to say because how much leverage there is depends
on the details of how the spoke is supported at the elbow and just how
things move around (and don't forget about the interleaving) when the
rim deforms at the contact patch.

It doesn't take much force to bend a spoke (i.e. bring it right up to
yield) when one end of it is anchored in a hub and you're pulling on the
long end. We do it all the time when building wheels often without
thinking about it or doing it deliberately. So I can easily believe that
a slack spoke does receive a cycle that involves stresses close to yield
at the elbow that therefore lead it to premature fatigue failure.

But one cannot rule out the opinion of Jobst easily, and he has a much
better quantitative idea of things like how much the rim does move by
and how much clearance is present in the hub hole than I do.

Ben C said:

clare at snyder.on.ca said:

Ben C said:

On 2007-09-04, [email hidden] <[email hidden]> wrote:
[...]
> With a tighter spoke the stress variation can have a larger excursion
> than that of a looser spoke.

Why?

Just to clarify: suppose I plot a graph of stress against time for a
spoke on a wheel on a bicycle that's being ridden down the road. I
expect the graph would be some kind of wave, going up and down as the
spoke passes over the contact patch.

By "larger excursion" do you mean that this wave would have a greater
amplitude?

Perhaps I'm being stupid but I don't see why you would get a larger
amplitude for a tighter spoke.

Because you would not. If tensioned to, say 200 lbs, and 200 lbs is
suspended from roughly8 of the 28 spokes, you might end up with
something like 250 lbs tension on any one spoke.

Are we still talking about riding on the wheel here? You say "suspended"
and I'm not sure.

If you had 200lbf spoke tension (which is a bit high, usually it's more
like 100lbf I think), about 28 spokes, and you put a weight of 250lbs on
the bike, so acting at the hub, you'd expect to see some of the spokes
in the bottom part of the wheel lose a bit of tension, and little or no
tension change in the spokes in the top half. No spoke would go up to
250lbf tension.

Quoted message said:

That tension would only change something like 60 lbs in use, and at
all times the spoke would be under a minimum of something like 140
lbs. With a 15 or 14 guage spoke,that tension would keep the spoke
from fatigue.

Think of the spoke as a bolt, and read the following from
Writetool.com:

[...]

Quoted message said:

How can we get all of the strength we pay for, or do we assume the
bolt strength is only 500 lbs. and use twice as many bolts in the
joint? If the joint has been properly designed, the clamping surfaces
around the bolt will take almost all of the variation if the bolt is
properly tightened.

This is an interesting theory, but I'm not sure it's correct to think of
the spoke as a bolt this way. The equivalent of "the clamping surfaces
around the bolt" is the rest of the wheel, i.e. the rim basically. The
rim is quite stiff, and so I don't think we can build the wheel tight
enough so that the rim flexes but the spokes don't.

But in the bolt example the idea is that the bolt doesn't get a stress
cycle at all (or not much of a one).

The spokes are always going to have a stress cycle. We don't care about
the axial stress cycle (stretching the spoke along its length and
letting it relax again), because the size of the stress in that cycle is
very small compared to the yield strength of the spoke in that
direction, which means fatigue life in that direction is very long and
not a problem.

The key thing is the elbow. If the spoke goes loose, does the elbow bend
and unbend? Bending and unbending means leverage, and therefore much
higher stresses on parts of the spoke. Not enough stress to break it in
one go, but enough to reduce the number of cycles to failure to only a
few hundred miles of riding.

So does it bend and unbend? Jobst says no, jim beam says yes, although
it's not unusual for those guys to disagree with each other.

I think it's very hard to say because how much leverage there is depends
on the details of how the spoke is supported at the elbow and just how
things move around (and don't forget about the interleaving) when the
rim deforms at the contact patch.

It doesn't take much force to bend a spoke (i.e. bring it right up to
yield) when one end of it is anchored in a hub and you're pulling on the
long end. We do it all the time when building wheels often without
thinking about it or doing it deliberately. So I can easily believe that
a slack spoke does receive a cycle that involves stresses close to yield
at the elbow that therefore lead it to premature fatigue failure.

But one cannot rule out the opinion of Jobst easily, and he has a much
better quantitative idea of things like how much the rim does move by
and how much clearance is present in the hub hole than I do.

Like a said, my numbers were picked from thin air - but the tension
and related bending at the elbow are real. I've never had a properly
tensioned spoke break, and I've had some pretty crappy wheels over the
years. I've had lots of loose spokes break.

Today when I work on a bike with a broken spoke, invariably I find a
generally sloppy wheel.(loose spokes)

--
Posted via a free Usenet account from http://www.teranews.com

Ben C said:

On 2007-09-04, [email hidden] <[email hidden]> wrote:
[...]

Quoted message said:

With a tighter spoke the stress variation can have a larger excursion
than that of a looser spoke.

Why?

Just to clarify: suppose I plot a graph of stress against time for a
spoke on a wheel on a bicycle that's being ridden down the road. I
expect the graph would be some kind of wave, going up and down as the
spoke passes over the contact patch.

By "larger excursion" do you mean that this wave would have a greater
amplitude?

Perhaps I'm being stupid but I don't see why you would get a larger
amplitude for a tighter spoke.

Dear Ben,

A spoke cannot lose more than its pre-tension, so the pre-tension is
the limit of how much its tension can vary. The higher the initial
tension, the greater the possible range of tension change.

First, consider two spokes, one tensioned to 200 pounds, one to only
100 pounds, on a bicycle where rolling under the axle causes a maxium
loss of 50 pounds of tension.

The excursion, or tension loss, will be the same, with one varying
from 200 down to 150 pounds, the other from 100 down to 50 pounds.

Technically, neither spoke is ever loose--both spokes are always under
tension, so both experience the same 50 pound tension change.

But now let the bike hit some bumps at speed, hard enough to cause a
maximum 120 pound loss of tension.

The first spoke, pre-tensioned to 200 pounds, can still lose 120
pounds of pre-tension, dropping from 200 down to 80.

But the other spoke can only drop from 100 pounds of pre-tension down
to 0. After it loses only 100 pounds of tension, it just rattles.

Cheers,

Carl Fogel

On Tue, 04 Sep 2007 17:10:49 -0400, clare at snyder.on.ca wrote:

[snip]

Quoted message said:

Because you would not. If tensioned to, say 200 lbs, and 200 lbs is
suspended from roughly 8 of the 28 spokes, you might end up with
something like 250 lbs tension on any one spoke.

[snip]

Dear Clare,

This may explain some of the misunderstanding. Like just about any
sensible person, you've made the mistake of thinking that the load on
an axle will cause a large increase in tension in the uppermost
spokes.

But despite what you'd think (and I thought until it was explained to
me), pre-tensioned bicycle wheels do not act as if they hang from the
upper spokes.

It's extremely annoying and counter-intuitive, but both theory and
measurement show that the tension does _not_ increase to any
significant degree on the spokes when we load the axle by sitting on
the bicycle.

Almost all the action consists of _losing_ pre-tension in the spokes
under the axle as the rim flattens ever-so-slightly.

Here's a page devoted to the theoretical side of things, with all the
tension changes considered as vectors that sum to zero:

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

A really annoying point made on that page is that yes, all the other
spokes show a slight tension increase, but because of their angle,
many of them are actually pulling the damned axle _downward_ or
sideways, instead of upward as almost everyone expects. (Think which
way a spoke at 4 or 8 o'clock moves the axle if you increase its
tension.)

That's why you want to look at the last three columns of the table in
the middle of the page. After calculating the tension _change_ for
each spoke, Ian then uses the _angle_ of each spoke to calculate the
vertical force that will be produced.

The five spokes that lose tension under the theoretical 1000 newton
load account for 955 newtons of support.

The other 31 spokes all increase in tension. But due to their angle,
14 of the spokes that gain tension are actually pulling the axle
downward. When their forces are calculated, the 31 spokes that gain
tension account for only 45 newtons of support, about 5% as much as
the handful of spokes under the axle.

A really, really annoying point is that the greatest tension increase
isn't even in the uppermost spokes. The greatest tension increase is
in the spokes at roughly 5 and 7 o'clock, on either side of the five
spokes under the axle that lose tension.

Jobst made similar calculations in "The Bicycle Wheel."

By attaching an electronic strain gauge to a single spoke, Professor
Gavin demonstrated the huge loss of pre-tension as spokes roll under
the axle. The massive downward spikes in figures 10 and 11, like
icicles hanging from a roof, shows how the spoke loses tension under
load:

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

Jobst points out that you can test this yourself, with a little help,
by listening to the tone as you pluck spokes before and after someone
sits on a bicycle. The huge loss of tension in the spokes under the
axle will be revealed by the tone dropping.

To summarize, a few spokes under the axle lose impressive amounts of
tension when we load the axle. The other spokes do gain a little
tension, but none of them gain more than 10% of the amount of tension
lost by the spoke directly under the axle--and almost half of them
pull the axle _downward_ because they're angled downward.

As for the loose spoke question, a spoke with more initial tension can
lose more tension before it goes slack. A spoke pre-tensioned to 200
pounds can lose up to 200 pounds of tension as it rolls under the axle
before it rattles loose, but a spoke tensioned to only 100 pounds can
lose only 100 pounds of tension as the rim squashes flat under the
axle.

Again, don't feel bad for making the mistake that everyone makes when
they look at a bicycle wheel. It seems ridiculous that the loading the
axle doesn't put the load on the uppermost spokes, but it doesn't. You
have to work through things and understand that the loss of tension is
the same as a gain in compression.

As Jobst points out in "The Bicycle Wheel," it doesn't matter whether
a wheel has solid wooden spokes with no pre-tension or thin wire
spokes with lots of pre-tension--measurements will show that action
takes place in the spokes under the axle.

The solid wooden spokes under the axle will show a straightforward
gain in compression, which makes sense.

The thin wire pre-tensioned spokes under the axle will show a loss of
tension, which is the same thing, but confusing at first.

In both cases, the spokes under the axle shorten. A gain in
compression is the same as a loss of tension.

Cheers,

Carl Fogel

Quoted message said:

Tom Keats said:

Quoted message said:

Waving the long term fatigue flag does not answer the question of
how low spoke tension causes spoke failure; a claim that appears in
this newsgroup often. I believe the example of rim deflection
under riding loads (which is the amount by which spoke preload is
reduced) is the appropriate parameter for stress change and it
shows that compression buckling is not possible in that respect as
I pointed out.

So, would a newly-installed, brand-new spoke that's too loose,
immediately break due to rim deflection, or break before its
adjacent brethren (that have hitherto held-up so well) do?

If the spoke was initially not loose, as spokes are on a new wheel, It
would only be deemed too loose if load deflection of the rim at the
load affected zone (where the tire meets the road) is greater than
elastic elongation of spokes from tensioning. That is the problem
with many wheels these days where rims crack if tightened to a
reliable tension that will mot slacken under load. That is
exacerbated by using fewer spokes so that the preload of one or two
spokes alone support the load.

Quoted message said:

What exactly /is/ rim deflection, and how does it happen? What
makes it happen? Are we talking about the momentary bottom of the
rim tending to squash flat on the surface it runs on and thereby
compressing spokes, (I guess not, since you above rule-out
compression buckling,) or are we talking about putting lateral 'S'
curves in the rim, and thereby bending spokes? Or maybe it's about
torque in a hard-driven wheel, between the rim and hub, where the
hub tends to rotate faster than the rim can keep up with, and the
spokes in-between bear the brunt, and the rim is deflected from the
POV of the hub (and the connecting spokes?)

When a wheel bears a load applied to its axle, that force is
transmitted to the road n=by compressing the spokes in roughly the
tire contact patch so that they lose preload equivalent to the axle
load. All other spokes remain essentially unchanged in tension
(especially the top ones that have been believed to get tighter).

You can check this by plucking spokes with and without loading the
wheel and not the tone. A lower tone indicates lower tension, a
higher tone indicated higher tension then initially when the wheel was
not loaded.

I did this test and the other spokes did not by any stretch of my
aural imagination "remain essentially unchanged in tension", nor did
they when Fogel attempted to measure the change. I suggest that
everyone who reads this follow Brandt's advice and then report back
here. If you are not tone deaf you will note that the spokes
horizontal to the ground rise in tension enough that the change in
tone (going higher) is easily discerned.

(Tom Keats) said:

In article <[email hidden]>,

Quoted message said:

Waving the long term fatigue flag does not answer the question of how
low spoke tension causes spoke failure; a claim that appears in this
newsgroup often. I believe the example of rim deflection under riding
loads (which is the amount by which spoke preload is reduced) is the
appropriate parameter for stress change and it shows that compression
buckling is not possible in that respect as I pointed out.

So, would a newly-installed, brand-new spoke that's too loose,
immediately break due to rim deflection, or break before its
adjacent brethren (that have hitherto held-up so well) do?

What exactly /is/ rim deflection, and how does it happen?
What makes it happen? Are we talking about the momentary
bottom of the rim tending to squash flat on the surface it
runs on and thereby compressing spokes, (I guess not, since
you above rule-out compression buckling,) or are we talking
about putting lateral 'S' curves in the rim, and thereby
bending spokes? Or maybe it's about torque in a hard-driven
wheel, between the rim and hub, where the hub tends to rotate
faster than the rim can keep up with, and the spokes in-between
bear the brunt, and the rim is deflected from the POV of
the hub (and the connecting spokes?)

I don't know about these things, but I am curious,
and I'd truly like to understand.

It seems obvious to me that there are two types of rim deflection. One
is the deflection of the rim in the immediate area of where force is
applied and where the rim is closest to the pavement; it is a function
of how pliable the rim material is. This deflection is essentially
independent of spoke tension. The other type of deflection is a
function of spoke tension and the force applied to the wheel- how much
the spoke tension allows the wheel hoop to deform from its shape as a
circle. I happen to believe that it is this latter deflection that is
important to understanding the forces at work in a bicycle wheel, but
my views are very controversial because they are at variance with the
"FEAs" if not the experimental evidence.

I don't have time to argue the discussion that is probably
forthcoming, but do the experiment that Brandt suggests, and decide
for yourself how to integrate the results with Brandt's claims. It's
kinda hard.

On Tue, 04 Sep 2007 17:19:47 -0700, [email hidden]

Quoted message said:

Quoted message said:

Tom Keats said:

> Waving the long term fatigue flag does not answer the question of
> how low spoke tension causes spoke failure; a claim that appears in
> this newsgroup often. I believe the example of rim deflection
> under riding loads (which is the amount by which spoke preload is
> reduced) is the appropriate parameter for stress change and it
> shows that compression buckling is not possible in that respect as
> I pointed out.
So, would a newly-installed, brand-new spoke that's too loose,
immediately break due to rim deflection, or break before its
adjacent brethren (that have hitherto held-up so well) do?

If the spoke was initially not loose, as spokes are on a new wheel, It
would only be deemed too loose if load deflection of the rim at the
load affected zone (where the tire meets the road) is greater than
elastic elongation of spokes from tensioning. That is the problem
with many wheels these days where rims crack if tightened to a
reliable tension that will mot slacken under load. That is
exacerbated by using fewer spokes so that the preload of one or two
spokes alone support the load.

Quoted message said:

What exactly /is/ rim deflection, and how does it happen? What
makes it happen? Are we talking about the momentary bottom of the
rim tending to squash flat on the surface it runs on and thereby
compressing spokes, (I guess not, since you above rule-out
compression buckling,) or are we talking about putting lateral 'S'
curves in the rim, and thereby bending spokes? Or maybe it's about
torque in a hard-driven wheel, between the rim and hub, where the
hub tends to rotate faster than the rim can keep up with, and the
spokes in-between bear the brunt, and the rim is deflected from the
POV of the hub (and the connecting spokes?)

When a wheel bears a load applied to its axle, that force is
transmitted to the road n=by compressing the spokes in roughly the
tire contact patch so that they lose preload equivalent to the axle
load. All other spokes remain essentially unchanged in tension
(especially the top ones that have been believed to get tighter).

You can check this by plucking spokes with and without loading the
wheel and not the tone. A lower tone indicates lower tension, a
higher tone indicated higher tension then initially when the wheel was
not loaded.

I did this test and the other spokes did not by any stretch of my
aural imagination "remain essentially unchanged in tension", nor did
they when Fogel attempted to measure the change. I suggest that
everyone who reads this follow Brandt's advice and then report back
here. If you are not tone deaf you will note that the spokes
horizontal to the ground rise in tension enough that the change in
tone (going higher) is easily discerned.

Dear SSTW,

I am unaware that I made any such conclusions.

My experience agrees with Jobst's experience, with Professor Gavin's
strain gauge measurements, and with Ian's theoretical calculations.

The spokes lose huge amounts of pre-tension as they roll under the
wheel. The individual the spokes all the way around the wheel show an
increase of only up to 10% in tension, compared to the spoke directly
under the axle's loss of tension.

Here are Ian's calculations:

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

Note that the greatest increase in tension in Ian's example is the
_lower_ spoke at roughly 5 'o'clock, which gains 40 newtons, about 10%
of the compression lost by the spoke under the axle, 350 newtons.

Here are Professor Gavin's measurements of an actual spoke while the
bicycle was being ridden in figures 10 & 11:

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

The massive loss of tension in the lowermost spokes is obvious.

Possibly you're confusing the results of my tests of spoke tension
change when two spokes are squeezed together on an unloaded wheel,
which is an entirely different situation.

Cheers,

Carl Fogel

Ben C? writes surreptitiously:

Quoted message said:

Quoted message said:

With a tighter spoke the stress variation can have a larger excursion
than that of a looser spoke.

Quoted message said:

Why?

Because the loose spoke can only go from its insufficient tension to
zero while the more highly tensioned one can vary from its full
tension to the reduction caused by the load. This is greater than the
loose spoke stress cycle and at a higher average stress.

Quoted message said:

Just to clarify: suppose I plot a graph of stress against time for a
spoke on a wheel on a bicycle that's being ridden down the road. I
expect the graph would be some kind of wave, going up and down as
the spoke passes over the contact patch.

It is not a wave. It is a straight line with a once-around dip in it
for a short duration while the spoke is pointing (straight down) into
the tire-to-road contact patch and a bit more.

Quoted message said:

By "larger excursion" do you mean that this wave would have a
greater amplitude?

Quoted message said:

Perhaps I'm being stupid but I don't see why you would get a larger
amplitude for a tighter spoke.

Jobst Brandt

Clare who? said:

Quoted message said:

Quoted message said:

With a tighter spoke the stress variation can have a larger excursion
than that of a looser spoke.

Quoted message said:

Quoted message said:

Why?

Quoted message said:

Quoted message said:

Just to clarify: suppose I plot a graph of stress against time for
a spoke on a wheel on a bicycle that's being ridden down the
road. I expect the graph would be some kind of wave, going up and
down as the spoke passes over the contact patch.

Quoted message said:

Quoted message said:

By "larger excursion" do you mean that this wave would have a
greater amplitude?

Quoted message said:

Quoted message said:

Perhaps I'm being stupid but I don't see why you would get a larger
amplitude for a tighter spoke.

Quoted message said:

Because you would not. If tensioned to, say 200 lbs, and 200 lbs is
suspended from roughly8 of the 28 spokes, you might end up with
something like 250 lbs tension on any one spoke. That tension would
only change something like 60 lbs in use, and at all times the spoke
would be under a minimum of something like 140 lbs. With a 15 or 14
guage spoke,that tension would keep the spoke from fatigue.

I think you misunderstand how loads are supported by spoked wheels.
Such wheels support loads through the spoke(s) between hub and road.
In a wooden wagon wheel, that seems obvious to most observers, but
that a tensioned wire wheel does the same is less apparent. I think
you should read about this in "the Bicycle Wheel" where the statics
and effects of supporting loads, transmitting torque and rim brake
forces, are explained in extensive detail.

Basically, spokes in a bicycle wheel do not experience an increase in
tension when a rider loads the wheel with his weight, but in contrast,
lose tension when spokes pass through the tire-to-road contact patch.

Quoted message said:

Think of the spoke as a bolt, and read the following from
Writetool.com:

The following has nothing to do with load distribution in spoked
wheels and is wholly inappropriate with respect to bicycle wheels.

---------------------------------------------------------------------

Quoted message said:

Tension Joints

Quoted message said:

The shear joint does not rely on tension in the bolt to hold parts
together. The tension joint, however, relies on the tension of the
bolt to hold two joined parts together. The greater the tension on
the bolt, the more force holding them together. Steel and most
metals have a property known as fatigue, which means that they lose
strength upon repeated loads. For example, a bolt with an ultimate
strength of 1,000 lbs. will carry a load of 1,000 lbs. once. It
will carry a load of 500 lbs. millions of times. It will carry a
load between 500 lbs. and 1,000 lbs. for a limited number of times
between 1 and 1 million, depending on whether the load is closer to
the 1,000-lbs.-value or the 500-lbs.-value. It doesn't matter how
long the heavy load is carried; it can carry 1,000 lbs. forever, as
long as it is only one cycle. Most joints are subject to variations
in load that either adds or decreases the tension in the bolt.

Quoted message said:

How can we get all of the strength we pay for, or do we assume the
bolt strength is only 500 lbs. and use twice as many bolts in the
joint? If the joint has been properly designed, the clamping
surfaces around the bolt will take almost all of the variation if
the bolt is properly tightened. In this scenario, a load of close
to 1,000 lbs. can be used because the load will not fluctuate very
much. But if the joint is not properly tightened, the joined parts
will separate and the full increase on the load will be on the
fastener, which will overload it. Or, the load could go to zero,
which means it is in a fatigue condition and the bolt will fail
because of the repeated application of a load that it could have
easily carried except for the fatigue factor. Therefore, a bolt in
a tension joint will fail from fatigue if it is not tightened
enough, and it will fail from fatigue and overload, if it is
tightened beyond its ultimate strength.

Quoted message said:

In our example the bolt's ultimate strength is 1,000 lbs.; in actual
practice there is a safety factor that extends the range beyond the
1,000 lbs., before the bolt actually breaks from simple overload.
Therefore, it is extremely important that we achieve the proper
tension on the bolt-not too much and not too little.

Jobst Brandt

Quoted message said:

My experience agrees with Jobst's experience, with Professor Gavin's
strain gauge measurements, and with Ian's theoretical calculations.

The spokes lose huge amounts of pre-tension as they roll under the
wheel. The individual the spokes all the way around the wheel show an
increase of only up to 10% in tension, compared to the spoke directly
under the axle's loss of tension.

So, this means those Kevlar "emergency" spokes I've carried with me on tours
are basicallly useless?

You can't "pull" them because the cord is strong, but you can "push" them
like cooked spaghetti.

Here's the product I'm referring to:
http://www.yellowjersey.org/fiberfix.html

On Tue, 04 Sep 2007 18:12:52 -0600, [email hidden] wrote:

Snipped.

Quoted message said:

As Jobst points out in "The Bicycle Wheel," it doesn't matter whether
a wheel has solid wooden spokes with no pre-tension or thin wire
spokes with lots of pre-tension--measurements will show that action
takes place in the spokes under the axle.

The solid wooden spokes under the axle will show a straightforward
gain in compression, which makes sense.

The thin wire pre-tensioned spokes under the axle will show a loss of
tension, which is the same thing, but confusing at first.

In both cases, the spokes under the axle shorten. A gain in
compression is the same as a loss of tension.

Cheers,

Carl Fogel

OK, Carl - I understand - it DOES make sense.
However, the fact that the LOWER spokes loose tension has the same
effect as the upper spokes gaining tension - if the spoke is too loose
to star with, when it looses tension then regains it's tension it
flexes at the elbow. An adequately tensioned spoke will reduce
tension, but will not loose tension - and the flex at the elbow will
be reduced - perhaps to the point where fatique does not occur in an
appreciable amount (like a spring operated within it's design limits)

Loose spokes still break faster than properly tensioned spokes (and
perhaps even faster than "overtensioned" spokes, as the yeild strength
of the spoke is virtually never exceded)

--
Posted via a free Usenet account from http://www.teranews.com

Quoted message said:

Clare who? said:

Quoted message said:

> With a tighter spoke the stress variation can have a larger excursion
> than that of a looser spoke.

Quoted message said:

Quoted message said:

Why?

Quoted message said:

Quoted message said:

Just to clarify: suppose I plot a graph of stress against time for
a spoke on a wheel on a bicycle that's being ridden down the
road. I expect the graph would be some kind of wave, going up and
down as the spoke passes over the contact patch.

Quoted message said:

Quoted message said:

By "larger excursion" do you mean that this wave would have a
greater amplitude?

Quoted message said:

Quoted message said:

Perhaps I'm being stupid but I don't see why you would get a larger
amplitude for a tighter spoke.

Quoted message said:

Because you would not. If tensioned to, say 200 lbs, and 200 lbs is
suspended from roughly8 of the 28 spokes, you might end up with
something like 250 lbs tension on any one spoke. That tension would
only change something like 60 lbs in use, and at all times the spoke
would be under a minimum of something like 140 lbs. With a 15 or 14
guage spoke,that tension would keep the spoke from fatigue.

I think you misunderstand how loads are supported by spoked wheels.

[here we go...]

Quoted message said:

Such wheels support loads through the spoke(s) between hub and road.
In a wooden wagon wheel, that seems obvious to most observers, but
that a tensioned wire wheel does the same is less apparent. I think
you should read about this in "the Bicycle Wheel" where the statics
and effects of supporting loads, transmitting torque and rim brake
forces, are explained in extensive detail.

and "the bicycle wheel" fails to address the fundamental issue of metal
fatigue and how it originates. spokes elbows, by definition and due to
the fact that they are not loaded axial to the rest of the spoke,
experience a bending moment on loading. hence they fatigue. end of
story. how an "engineer" can make such an enormous oversight is pretty
surprising. how one can /keep on/ making it after all this time and
exposure is truly spectacular.

Quoted message said:

Basically, spokes in a bicycle wheel do not experience an increase in
tension when a rider loads the wheel with his weight, but in contrast,
lose tension when spokes pass through the tire-to-road contact patch.

Quoted message said:

Think of the spoke as a bolt, and read the following from
Writetool.com:

The following has nothing to do with load distribution in spoked
wheels and is wholly inappropriate with respect to bicycle wheels.

---------------------------------------------------------------------

Quoted message said:

Tension Joints

Quoted message said:

The shear joint does not rely on tension in the bolt to hold parts
together. The tension joint, however, relies on the tension of the
bolt to hold two joined parts together. The greater the tension on
the bolt, the more force holding them together. Steel and most
metals have a property known as fatigue, which means that they lose
strength upon repeated loads. For example, a bolt with an ultimate
strength of 1,000 lbs. will carry a load of 1,000 lbs. once. It
will carry a load of 500 lbs. millions of times. It will carry a
load between 500 lbs. and 1,000 lbs. for a limited number of times
between 1 and 1 million, depending on whether the load is closer to
the 1,000-lbs.-value or the 500-lbs.-value. It doesn't matter how
long the heavy load is carried; it can carry 1,000 lbs. forever, as
long as it is only one cycle. Most joints are subject to variations
in load that either adds or decreases the tension in the bolt.

Quoted message said:

How can we get all of the strength we pay for, or do we assume the
bolt strength is only 500 lbs. and use twice as many bolts in the
joint? If the joint has been properly designed, the clamping
surfaces around the bolt will take almost all of the variation if
the bolt is properly tightened. In this scenario, a load of close
to 1,000 lbs. can be used because the load will not fluctuate very
much. But if the joint is not properly tightened, the joined parts
will separate and the full increase on the load will be on the
fastener, which will overload it. Or, the load could go to zero,
which means it is in a fatigue condition and the bolt will fail
because of the repeated application of a load that it could have
easily carried except for the fatigue factor. Therefore, a bolt in
a tension joint will fail from fatigue if it is not tightened
enough, and it will fail from fatigue and overload, if it is
tightened beyond its ultimate strength.

Quoted message said:

In our example the bolt's ultimate strength is 1,000 lbs.; in actual
practice there is a safety factor that extends the range beyond the
1,000 lbs., before the bolt actually breaks from simple overload.
Therefore, it is extremely important that we achieve the proper
tension on the bolt-not too much and not too little.

Jobst Brandt

clare at snyder.on.ca said:

Ben C said:

clare at snyder.on.ca said:

On Tue, 04 Sep 2007 15:35:56 -0500, Ben C <[email hidden]> wrote:

> On 2007-09-04, [email hidden] <[email hidden]> wrote:
> [...]
>> With a tighter spoke the stress variation can have a larger excursion
>> than that of a looser spoke.
> Why?
>
> Just to clarify: suppose I plot a graph of stress against time for a
> spoke on a wheel on a bicycle that's being ridden down the road. I
> expect the graph would be some kind of wave, going up and down as the
> spoke passes over the contact patch.
>
> By "larger excursion" do you mean that this wave would have a greater
> amplitude?
>
> Perhaps I'm being stupid but I don't see why you would get a larger
> amplitude for a tighter spoke.

Because you would not. If tensioned to, say 200 lbs, and 200 lbs is
suspended from roughly8 of the 28 spokes, you might end up with
something like 250 lbs tension on any one spoke.

Are we still talking about riding on the wheel here? You say "suspended"
and I'm not sure.

If you had 200lbf spoke tension (which is a bit high, usually it's more
like 100lbf I think), about 28 spokes, and you put a weight of 250lbs on
the bike, so acting at the hub, you'd expect to see some of the spokes
in the bottom part of the wheel lose a bit of tension, and little or no
tension change in the spokes in the top half. No spoke would go up to
250lbf tension.

Quoted message said:

That tension would only change something like 60 lbs in use, and at
all times the spoke would be under a minimum of something like 140
lbs. With a 15 or 14 guage spoke,that tension would keep the spoke
from fatigue.

Think of the spoke as a bolt, and read the following from
Writetool.com:

[...]

Quoted message said:

How can we get all of the strength we pay for, or do we assume the
bolt strength is only 500 lbs. and use twice as many bolts in the
joint? If the joint has been properly designed, the clamping surfaces
around the bolt will take almost all of the variation if the bolt is
properly tightened.

This is an interesting theory, but I'm not sure it's correct to think of
the spoke as a bolt this way. The equivalent of "the clamping surfaces
around the bolt" is the rest of the wheel, i.e. the rim basically. The
rim is quite stiff, and so I don't think we can build the wheel tight
enough so that the rim flexes but the spokes don't.

But in the bolt example the idea is that the bolt doesn't get a stress
cycle at all (or not much of a one).

The spokes are always going to have a stress cycle. We don't care about
the axial stress cycle (stretching the spoke along its length and
letting it relax again), because the size of the stress in that cycle is
very small compared to the yield strength of the spoke in that
direction, which means fatigue life in that direction is very long and
not a problem.

The key thing is the elbow. If the spoke goes loose, does the elbow bend
and unbend? Bending and unbending means leverage, and therefore much
higher stresses on parts of the spoke. Not enough stress to break it in
one go, but enough to reduce the number of cycles to failure to only a
few hundred miles of riding.

So does it bend and unbend? Jobst says no, jim beam says yes, although
it's not unusual for those guys to disagree with each other.

I think it's very hard to say because how much leverage there is depends
on the details of how the spoke is supported at the elbow and just how
things move around (and don't forget about the interleaving) when the
rim deforms at the contact patch.

It doesn't take much force to bend a spoke (i.e. bring it right up to
yield) when one end of it is anchored in a hub and you're pulling on the
long end. We do it all the time when building wheels often without
thinking about it or doing it deliberately. So I can easily believe that
a slack spoke does receive a cycle that involves stresses close to yield
at the elbow that therefore lead it to premature fatigue failure.

But one cannot rule out the opinion of Jobst easily, and he has a much
better quantitative idea of things like how much the rim does move by
and how much clearance is present in the hub hole than I do.

Like a said, my numbers were picked from thin air - but the tension
and related bending at the elbow are real. I've never had a properly
tensioned spoke break, and I've had some pretty crappy wheels over the
years. I've had lots of loose spokes break.

Today when I work on a bike with a broken spoke, invariably I find a
generally sloppy wheel.(loose spokes)

and that is the crux of the matter. jobst claims to "solve" the fatigue
problem with a bunch of underinformed [censored] and suppositional
fantasy, but reality is, the /process/ he describes [claims to have
"invented"] is that of the european masters - and which works for
exactly the reason you say - spokes stay tight, hence they do not bend
as much, hence they do not fatigue as fast.

and that's all there is to it.

Clare who? said:

Snipped.

Quoted message said:

Quoted message said:

As Jobst points out in "The Bicycle Wheel," it doesn't matter
whether a wheel has solid wooden spokes with no pre-tension or thin
wire spokes with lots of pre-tension--measurements will show that
action takes place in the spokes under the axle.

Quoted message said:

Quoted message said:

The solid wooden spokes under the axle will show a straightforward
gain in compression, which makes sense.

Quoted message said:

Quoted message said:

The thin wire pre-tensioned spokes under the axle will show a loss
of tension, which is the same thing, but confusing at first.

Quoted message said:

Quoted message said:

In both cases, the spokes under the axle shorten. A gain in
compression is the same as a loss of tension.

Quoted message said:

OK, Carl - I understand - it DOES make sense.

Quoted message said:

However, the fact that the LOWER spokes loose tension has the same
effect as the upper spokes gaining tension - if the spoke is too
loose to star with, when it looses tension then regains it's tension
it flexes at the elbow. An adequately tensioned spoke will reduce
tension, but will not loose tension - and the flex at the elbow will
be reduced - perhaps to the point where fatigue does not occur in an
appreciable amount (like a spring operated within it's design
limits)

What is bending the elbow in your perception? If it is carrying less
force and losing less tension, then the stress must be lower. Stress
is what causes spoke failure and the higher and the greater the
variation, the more fatigue damage it causes. The lower tensioned
spoke cannot cause greater bending, there being less force and force
change.

Quoted message said:

Loose spokes still break faster than properly tensioned spokes (and
perhaps even faster than "overtensioned" spokes, as the yeild
strength of the spoke is virtually never exceded)

I don't know where you derive that statement but it is incorrect.
You'll need to explain the mechanism by which you believe this occurs
before it becomes credible because it goes against conventional
engineering principles.

Jobst Brandt

Mike Kruger said:

Quoted message said:

My experience agrees with Jobst's experience, with Professor Gavin's
strain gauge measurements, and with Ian's theoretical calculations.

The spokes lose huge amounts of pre-tension as they roll under the
wheel. The individual the spokes all the way around the wheel show an
increase of only up to 10% in tension, compared to the spoke directly
under the axle's loss of tension.

So, this means those Kevlar "emergency" spokes I've carried with me on tours
are basicallly useless?

You can't "pull" them because the cord is strong, but you can "push" them
like cooked spaghetti.

Here's the product I'm referring to:
http://www.yellowjersey.org/fiberfix.html

Dear Mark,

Sorry, but you're still misunderstanding how pre-tension works. (Don't
feel bad--it's a common mistake.)

The Kevlar spokes work just like wire spokes.

You pre-tension the Kevlar spoke to 200 pounds.

As it rolls under the wheel, it loses considerable tension.

You can see how this works with a brick, a hefty weight, and a
bathroom scale.

Put the weight on the scale and note what the scale says, say 10
pounds.

Now tie the rubber band to the weight and pull up, putting tension on
the rubber "spoke" as if it were a wire or kevlar spoke. Rubber
stretches much more visibly than steel or kevlar, so you can see that
tension means elongation.

Note that the scale now reads less, say 5 pounds.

To push down with the pre-tensioned rubber "spoke", just relax your
hand a little. The rubber "spoke" visibly shortens (compression) and
the scale gains what the pre-tensioned rubber band loses.

Once you lose _all_ the pre-tension, the spoke becomes literally loose
and rattles or flops uselessly, whether it's steel wire, kevlar cord,
or rubber band.

Until you work your way through how pre-tension actually works, it
will seem absolutely ridiculous.

And yes, I carry a spare Kevlar spoke, whose pre-tensioned physics
have been repeatedly discussed on RBT. Again, don't feel bad about the
misunderstanding--I've been in your position, and so have most people
who glance at a wheel and mistakenly assume that the load must hang
from the upper spokes because it seems so damned obvious and logical.

The trouble is, engineering theory predicts and strain gauge
measurements confirm that the stupid wheel works almost exactly the
opposite of what we expect. Work your way through those links,
remember that Kevlar stretches and pre-tensions much like steel (an
amount invisible to the naked eye), and you'll see why the tension
drops dramatically for the spokes _under_ the axle, but scarcely rises
at all for _all_ the other spokes, including the ones pulling sideways
and downward.

Cheers,

Carl Fogel

Quoted message said:

Clare who? said:

Snipped.

Quoted message said:

Quoted message said:

As Jobst points out in "The Bicycle Wheel," it doesn't matter
whether a wheel has solid wooden spokes with no pre-tension or thin
wire spokes with lots of pre-tension--measurements will show that
action takes place in the spokes under the axle.

Quoted message said:

Quoted message said:

The solid wooden spokes under the axle will show a straightforward
gain in compression, which makes sense.

Quoted message said:

Quoted message said:

The thin wire pre-tensioned spokes under the axle will show a loss
of tension, which is the same thing, but confusing at first.

Quoted message said:

Quoted message said:

In both cases, the spokes under the axle shorten. A gain in
compression is the same as a loss of tension.

Quoted message said:

OK, Carl - I understand - it DOES make sense.

Quoted message said:

However, the fact that the LOWER spokes loose tension has the same
effect as the upper spokes gaining tension - if the spoke is too
loose to star with, when it looses tension then regains it's tension
it flexes at the elbow. An adequately tensioned spoke will reduce
tension, but will not loose tension - and the flex at the elbow will
be reduced - perhaps to the point where fatigue does not occur in an
appreciable amount (like a spring operated within it's design
limits)

What is bending the elbow in your perception? If it is carrying less
force and losing less tension, then the stress must be lower. Stress
is what causes spoke failure and the higher and the greater the
variation, the more fatigue damage it causes. The lower tensioned
spoke cannot cause greater bending, there being less force and force
change.

Quoted message said:

Loose spokes still break faster than properly tensioned spokes (and
perhaps even faster than "overtensioned" spokes, as the yeild
strength of the spoke is virtually never exceded)

I don't know where you derive that statement but it is incorrect.
You'll need to explain the mechanism by which you believe this occurs
before it becomes credible because it goes against conventional
engineering principles.

Jobst Brandt

I've explained it. You do not understand it or dissagree. Your
peroggotive, either way.
The simple fact of the matter remains. Loose spokes break (at the
elbow). Tight spokes (properly tensioned) do NOT. When metal is pre
stretched or pre tensioned, a change in tension does NOT cause
appreciable fatigue. It is when the metal is taken through the initial
ternsioning and when that tension is lost that the fatigue happens.
The fatigue does NOT happen when the tension changes within a
perscribed range. A properly tensioned spoke never gets out of that
safe tension range, where a loose spoke goes through that transition
at least once (I think even twice or more)) every turn of the wheel.

Over tensioned spokes generally snap the nipples when they fail, but
can also snap at the elbow.(or pull out of the rim)

Loose spokes also wear the holes in the hubs - and wear the spokes
where they go through the hub. I've replaced numerous spokes that were
worn half way through before breaking (and some that had not yet
broken)

--
Posted via a free Usenet account from http://www.teranews.com

Quoted message said:

Clare who? said:

Snipped.

Quoted message said:

Quoted message said:

As Jobst points out in "The Bicycle Wheel," it doesn't matter
whether a wheel has solid wooden spokes with no pre-tension or thin
wire spokes with lots of pre-tension--measurements will show that
action takes place in the spokes under the axle.

Quoted message said:

Quoted message said:

The solid wooden spokes under the axle will show a straightforward
gain in compression, which makes sense.

Quoted message said:

Quoted message said:

The thin wire pre-tensioned spokes under the axle will show a loss
of tension, which is the same thing, but confusing at first.

Quoted message said:

Quoted message said:

In both cases, the spokes under the axle shorten. A gain in
compression is the same as a loss of tension.

Quoted message said:

OK, Carl - I understand - it DOES make sense.

Quoted message said:

However, the fact that the LOWER spokes loose tension has the same
effect as the upper spokes gaining tension - if the spoke is too
loose to star with, when it looses tension then regains it's tension
it flexes at the elbow. An adequately tensioned spoke will reduce
tension, but will not loose tension - and the flex at the elbow will
be reduced - perhaps to the point where fatigue does not occur in an
appreciable amount (like a spring operated within it's design
limits)

What is bending the elbow in your perception?

simple loading!!! the spoke elbow is offset from the spoke axis, thus
is it subject to bending - by definition!!!

Quoted message said:

If it is carrying less
force and losing less tension, then the stress must be lower. Stress
is what causes spoke failure and the higher and the greater the
variation, the more fatigue damage it causes. The lower tensioned
spoke cannot cause greater bending, there being less force and force
change.

except that it /is/ being bent back and forth more, simply because it's
interleaved.

Quoted message said:

Quoted message said:

Loose spokes still break faster than properly tensioned spokes (and
perhaps even faster than "overtensioned" spokes, as the yeild
strength of the spoke is virtually never exceded)

I don't know where you derive that statement but it is incorrect.

er, even /you/ say that loose spokes break...

Quoted message said:

You'll need to explain the mechanism by which you believe this occurs
before it becomes credible because it goes against conventional
engineering principles.

it's already been discussed. the only one here having problems
recognizing it appears to be you.