How much does tension rise on squeezed spokes?

[[email protected]]

Peter Cole wrote:
> [email protected] wrote:

> The force on the rim section has 2 components, tangential (small) and
> radial (large). It's the small force that's transferred to the
> "orthogonal" spokes.

I'm not sure that I agree that's how the force is transferred. I think
that it may be something more like a complex lever- the inward motion
of the rim under the axle levers the rim outward progressively up to
90o.

> > However, Gavin's data also shows a significant amount of tension rise
> > in the orthogonal spokes. That tension rise shows that the effect that
> > you admit to in Carl's experiment is far from absent when the wheel is
> > used as a wheel instead of as a stress relieving test instrument.
>
> Gavin's data shows a relatively small increase in tension spread over a
> large part of the rim circumference, which was no surprise to anyone.

Actually, that's not what it shows. It shows an increasing rate of
tension increase moving away from the vertical spokes until 90o. Taken
as an aggregate, I would say that the amount of force required to raise
the tension in all those spokes is considerable.

> It's much larger in Carl's configuration, which is why I called it
> degenerate.

It's not clear to me that the increase in tension at 90o is much
larger; what is clear is that the decrease in tension in the spokes
under the axle in the Gavin wheel is much larger.

 

[jim beam]

Peter Cole wrote:
> [email protected] wrote:
>
>> Peter Cole wrote:
>>
>>> You can visualize a small section of wheel as an arched beam supported
>>> by a spring (spoke).
>>
>>
>> But it's not an arched beam, it's a hoop, and the forces that act on
>> any given arc of the wheel are not independent of the rest of the
>> wheel.
>
>
> No, but the small section under load is an arch, and the way that
> section transfers loads to the rest of the rim is determined by
> geometry. Since the arch is shallow, the tangential component is small.
>
>
>>> In a typical rim, under normal loading, the normal force is much larger
>>> than the tangential force (very shallow arch), and the spoke and rim
>>> (bending) stiffness provide the bulk of the force, acting in parallel,
>>> with spoke stiffness dominating.
>>>
>>> When the spokes are squeezed, the spoke and rim stiffnesses are in
>>> series, and the lateral spoke displacement shows the combined effects.
>>> The extra tension applied to the squeezed spokes goes directly into
>>> bending the rim.
>>
>>
>> If it were that simple then the tension would not rise in the
>> orthogonal spokes.
>
>
> The force on the rim section has 2 components, tangential (small) and
> radial (large). It's the small force that's transferred to the
> "orthogonal" spokes.
>
>
>>> In Carl's "experiments", squeezing 2 pairs of spokes, on the same side
>>> of the wheel, 180 deg apart, loads about 1/4 of the wheel circumference,
>>> causing rim deformations much larger than those seen in normal
>>> operation. That, in turn, caused relatively large forces tangential to
>>> the rim, and relatively large increases in tension in the spokes facing
>>> in that direction.
>>
>>
>> Yep, although I still think the evidence points toward the rim itself
>> as the agent that transfers the load to the 90o spokes. Note that the
>> effect was present when he squeezed only a single pair of spokes as
>> well.
>
>
> Yes, of course, but in normal loading the transfer is small.
>
>
>>> A more tensioned wheel, with more spokes, stiffer rim, squeezed on
>>> opposite sides (left/right, not up/down) would have localized the rim
>>> deflection (flattening) more, causing much less of a tangential
>>> component and rise of spoke tension in that direction.
>>
>>
>> I believe that's the case with any adjacent pair of squeezed spokes and
>> have already suggested such. You can easily demonstrate the rise in
>> tension at the 90o spokes yourself with 2 adjacent spokes, same side,
>> or w adjacent spokes opposite side. But like you say, I think the load
>> will be more localized as the wheel is tensioned up and a stiffer rim
>> is used.
>
>
> The more force applied to the rim, the more will be transferred in both
> directions, but the tangential force is normally small. In spoke
> squeezing the rim deflections are large because the spoke stiffness is
> out of the picture.
>
>
>>> In short,
>>> relative to normal wheel operation and loading, Carl's efforts can be
>>> thought of as a "degenerate" case of little practical significance or
>>> surprise.
>>
>>
>> However, Gavin's data also shows a significant amount of tension rise
>> in the orthogonal spokes. That tension rise shows that the effect that
>> you admit to in Carl's experiment is far from absent when the wheel is
>> used as a wheel instead of as a stress relieving test instrument.
>
>
> Gavin's data shows a relatively small increase in tension spread over a
> large part of the rim circumference, which was no surprise to anyone.
>
> It's much larger in Carl's configuration, which is why I called it
> degenerate.
>
>> I am not sure that this effect is of no practical significance. It may
>> be that this effect, small as it may be relative to the loss of tension
>> below the axle, provides an important function in spreading the force
>> of impacts and protecting the wheel from denting over relatively minor
>> bumps in the road.
>
>
> At the point of impact, the rim is supported by spoke stiffness
> (primary), rim stiffness (secondary). The amount of load in the
> tangential direction is small and distributed better. That's why rims
> dent where they strike.
>
>
>> It may also help to define the answer to "how tight
>> should the spokes be?" I think it raises doubts that wheel strength
>> increases as static spoke tension is increased.
>
>
> I don't think so. As I described earlier, once the spoke goes slack, the
> wheel stiffness changes greatly, both radially and laterally and the rim
> strains to failure.

peter, that's not my experience. there's an experiment you can easily
try at home. press a rear wheel hub against a bench with your hands at
opposite points of the rim, with the cassette towards you. you can
easily make the non-drive side spokes go slack. there is no noticeable
decrease in lateral stiffness of the wheel at slackness point. i
therefore conclude that bracing ratio, as determined by the spokes'
angle with the rim, is /far/ more significant than spoke tension. i
further conclude that rim stiffness [and strength] is the biggest factor
in the wheel equation, not spoke tension. perhaps that also explains
why almost all modern rims are deeper section than the rims of yore.
and that must in turn be related to my being able to exert 205lbs onto
an unspoked mavic cosmos hoop [like the open pro] without it collapsing.

>
>
>> It could negatively
>> affect rolling resistance and spoke fatigue.
>
>
> Metal forms almost perfect springs, so I don't see where the loss would
> be. I don't see what you're recommending to improve spoke fatigue
> resistance.

he's not. he's stating that increasing tension increases liability to
fatigue, which it does. [doubt the rolling resistance thing though.]

 

[Peter Cole]

[email protected] wrote:
> Peter Cole wrote:
>> [email protected] wrote:
>
>> The force on the rim section has 2 components, tangential (small) and
>> radial (large). It's the small force that's transferred to the
>> "orthogonal" spokes.
>
> I'm not sure that I agree that's how the force is transferred. I think
> that it may be something more like a complex lever- the inward motion
> of the rim under the axle levers the rim outward progressively up to
> 90o.

As Jobst says, when a section of the rim is flattened, the forces try to
increase the circumference of the wheel. There's a tangential force
created at either side of load zone, which raises tension around the
wheel (modestly).

Given the model of the rim as a circular beam on an elastic foundation,
the tangential displacement (at the load zone) creates a shear between
the rim and the foundation that goes to 0 at 180 deg from the load zone.
That shear will raise spoke tension slightly an additional amount, the
effect being largest in a radially spoked wheel, decreasing with 2x, 3x,
4x, etc. Although he didn't measure a 0x wheel, I think Gavin's data
show that effect.


>>> However, Gavin's data also shows a significant amount of tension rise
>>> in the orthogonal spokes. That tension rise shows that the effect that
>>> you admit to in Carl's experiment is far from absent when the wheel is
>>> used as a wheel instead of as a stress relieving test instrument.
>> Gavin's data shows a relatively small increase in tension spread over a
>> large part of the rim circumference, which was no surprise to anyone.
>
> Actually, that's not what it shows. It shows an increasing rate of
> tension increase moving away from the vertical spokes until 90o. Taken
> as an aggregate, I would say that the amount of force required to raise
> the tension in all those spokes is considerable.
>
>> It's much larger in Carl's configuration, which is why I called it
>> degenerate.
>
> It's not clear to me that the increase in tension at 90o is much
> larger; what is clear is that the decrease in tension in the spokes
> under the axle in the Gavin wheel is much larger.

I'm not sure what you're saying. I don't see the point in comparing
spoke tension changes at the load zone in such different modes
(squeezing and normal loading).

 

[Peter Cole]

[email protected] wrote:
> Peter Cole wrote:
>> [email protected] wrote:
>
>> The force on the rim section has 2 components, tangential (small) and
>> radial (large). It's the small force that's transferred to the
>> "orthogonal" spokes.
>
> I'm not sure that I agree that's how the force is transferred. I think
> that it may be something more like a complex lever- the inward motion
> of the rim under the axle levers the rim outward progressively up to
> 90o.

As Jobst says, when a section of the rim is flattened, the forces try to
increase the circumference of the wheel. There's a tangential force
created at either side of load zone, which raises tension around the
wheel (modestly).

Given the model of the rim as a circular beam on an elastic foundation,
the tangential displacement (at the load zone) creates a shear between
the rim and the foundation that goes to 0 at 180 deg from the load zone.
That shear will raise spoke tension slightly an additional amount, the
effect being largest in a radially spoked wheel, decreasing with 2x, 3x,
4x, etc. Although he didn't measure a 0x wheel, I think Gavin's data
show that effect.


>>> However, Gavin's data also shows a significant amount of tension rise
>>> in the orthogonal spokes. That tension rise shows that the effect that
>>> you admit to in Carl's experiment is far from absent when the wheel is
>>> used as a wheel instead of as a stress relieving test instrument.
>> Gavin's data shows a relatively small increase in tension spread over a
>> large part of the rim circumference, which was no surprise to anyone.
>
> Actually, that's not what it shows. It shows an increasing rate of
> tension increase moving away from the vertical spokes until 90o. Taken
> as an aggregate, I would say that the amount of force required to raise
> the tension in all those spokes is considerable.
>
>> It's much larger in Carl's configuration, which is why I called it
>> degenerate.
>
> It's not clear to me that the increase in tension at 90o is much
> larger; what is clear is that the decrease in tension in the spokes
> under the axle in the Gavin wheel is much larger.

I'm not sure what you're saying. I don't see the point in comparing
spoke tension changes at the load zone in such different modes
(squeezing and normal loading).

 

[Peter Cole]

jim beam wrote:
> Peter Cole wrote:
>
>> I don't think so. As I described earlier, once the spoke goes slack,
>> the wheel stiffness changes greatly, both radially and laterally and
>> the rim strains to failure.
>
> peter, that's not my experience. there's an experiment you can easily
> try at home. press a rear wheel hub against a bench with your hands at
> opposite points of the rim, with the cassette towards you. you can
> easily make the non-drive side spokes go slack. there is no noticeable
> decrease in lateral stiffness of the wheel at slackness point.

The more interesting case is where spokes on both sides of the rim go slack.


> i
> therefore conclude that bracing ratio, as determined by the spokes'
> angle with the rim, is /far/ more significant than spoke tension.

Significant to what?

> i
> further conclude that rim stiffness [and strength] is the biggest factor
> in the wheel equation, not spoke tension.

What equation?


> perhaps that also explains
> why almost all modern rims are deeper section than the rims of yore. and
> that must in turn be related to my being able to exert 205lbs onto an
> unspoked mavic cosmos hoop [like the open pro] without it collapsing.

If you look at Gavin's measurements, you'll see that the wheel stiffness
in the radial direction is only modestly affected by the rim stiffness,
it's much more affected by the spoke stiffness.

Taller rims are necessary to span larger sections in low spoke count
wheels. Cross section design is a trade off, like anything else, tall
rims will have better radial stiffness, all things being equal (which
they usually aren't).


>>> It could negatively
>>> affect rolling resistance and spoke fatigue.
>>
>>
>> Metal forms almost perfect springs, so I don't see where the loss
>> would be. I don't see what you're recommending to improve spoke
>> fatigue resistance.
>
> he's not. he's stating that increasing tension increases liability to
> fatigue, which it does. [doubt the rolling resistance thing though.]

Well, he's making 2 claims -- my "perfect spring" comment was re:
rolling resistance claim.

Re: fatigue--
Increasing tension, or increasing tension cycle (delta)? Check out the
concluding sections of Gavin's paper where he discusses fatigue.

 

[[email protected]]

Peter Cole wrote:

> > It's not clear to me that the increase in tension at 90o is much
> > larger; what is clear is that the decrease in tension in the spokes
> > under the axle in the Gavin wheel is much larger.
>
> I'm not sure what you're saying.

I'm saying that I'm not able to convert the measurements in the Gavin
data to the units used by Carl, and because of that I'm not sure that I
agree that the effect on the 90o spokes is much less in the Gavin data.


> I don't see the point in comparing
> spoke tension changes at the load zone in such different modes
> (squeezing and normal loading).

What do you consider the load zones? I'm not really comparing what I
think are the load zones at 0 and 180 degrees. I'm comparing the zones
at 90o (+-~80o) where they look very similar, with an implication of an
oval shape of the wheel.

 

[[email protected]]

jim beam wrote:
> Peter Cole wrote:
> > [email protected] wrote:

> >> It could negatively
> >> affect rolling resistance and spoke fatigue.
> >
> >
> > Metal forms almost perfect springs, so I don't see where the loss would
> > be. I don't see what you're recommending to improve spoke fatigue
> > resistance.
>
> he's not. he's stating that increasing tension increases liability to
> fatigue, which it does. [doubt the rolling resistance thing though.]

I was suggesting that increasing tension might make a spoke less
susceptible to fatigue by making it less subject to movement. I'm _not_
claiming it would or recommending anything; I was simply saying that if
a significant portion of the load on a wheel is dispersed throughout
the structure of the wheel by an oval deformation of the hoop, there
could be some undesirable consequences of reducing that tendency as
well as desirable ones. I don't know, though. If I had to make a guess,
it would be, "not too tight, not too loose."

 

[Peter Cole]

[email protected] wrote:
> jim beam wrote:
>> Peter Cole wrote:
>>> [email protected] wrote:
>
>>>> It could negatively
>>>> affect rolling resistance and spoke fatigue.
>>>
>>> Metal forms almost perfect springs, so I don't see where the loss would
>>> be. I don't see what you're recommending to improve spoke fatigue
>>> resistance.
>> he's not. he's stating that increasing tension increases liability to
>> fatigue, which it does. [doubt the rolling resistance thing though.]
>
> I was suggesting that increasing tension might make a spoke less
> susceptible to fatigue by making it less subject to movement. I'm _not_
> claiming it would or recommending anything; I was simply saying that if
> a significant portion of the load on a wheel is dispersed throughout
> the structure of the wheel by an oval deformation of the hoop, there
> could be some undesirable consequences of reducing that tendency as
> well as desirable ones. I don't know, though. If I had to make a guess,
> it would be, "not too tight, not too loose."
>

You are confusing stress (force) and strain (movement, in the sense of
"stretch"). The relationship (ratio/slope) of stress/strain is the
stiffness. In spokes, that's a straight line, in other words, the amount
of "movement" doesn't change for a given load (force) no matter what the
pre-load is. The stiffness of a wheel doesn't change with spoke tension
(pre-load).

 

[[email protected]]

Peter Cole wrote:
> You are confusing stress (force) and strain (movement, in the sense of
> "stretch").

No, I'm not.

> The relationship (ratio/slope) of stress/strain is the
> stiffness. In spokes, that's a straight line, in other words, the amount
> of "movement" doesn't change for a given load (force) no matter what the
> pre-load is. The stiffness of a wheel doesn't change with spoke tension
> (pre-load).

I think it does, and I think that as a wheel rotates and the load
rotates, there will be small changes in the angles of the spokes.
Whether it's significant or not, I don't know.

 

[Peter Cole]

[email protected] wrote:

> This is getting pretty circular. The models don't predict the outcome
> of the experiments. Build a model that does and then we can discuss
> further what seems to be happening. It's pretty pointless to continue a
> discussion where deviations from the model are deemed insignificant
> basically because they deviate from the model,

They're insignificant because they're very small.


> and then to further
> argue about what's happening in the wheel based on the model that
> dismisses the experimental data.

I'm not dismissing data, I'm explaining it.


> If someone wants to explain the tension rise from +-~10o from 0 and
> 180o to a peak at +-90o, I'd be interested in hearing their theory; in
> the absence of anything new, this is getting pretty boring.

I have, but I'll do it again.

When you flatten a section of the rim, you increase its circumference.
If you increased the circumference uniformly around the rim, you
wouldn't get any angular displacement, you'd only get a slightly larger
circle, with correspondingly greater spoke tensions. Since you are
increasing the circumference in only one region, you'll also get angular
displacements from there. These displacements will be largest near the
load. Jobst shows these in the tables in the appendix of his book as
part of the FEA. How those displacements translate into changes in spoke
tension depend on spoking pattern (as Gavin says & shows).

The larger the flattened area is, the proportionally greater the effect.
Squeezing spokes generates relatively large rim deflections.

 

[jim beam]

Peter Cole wrote:
> [email protected] wrote:
>
>> This is getting pretty circular. The models don't predict the outcome
>> of the experiments. Build a model that does and then we can discuss
>> further what seems to be happening. It's pretty pointless to continue a
>> discussion where deviations from the model are deemed insignificant
>> basically because they deviate from the model,
>
>
> They're insignificant because they're very small.
>
>
>> and then to further
>> argue about what's happening in the wheel based on the model that
>> dismisses the experimental data.
>
>
> I'm not dismissing data, I'm explaining it.
>
>
>> If someone wants to explain the tension rise from +-~10o from 0 and
>> 180o to a peak at +-90o, I'd be interested in hearing their theory; in
>> the absence of anything new, this is getting pretty boring.
>
>
> I have, but I'll do it again.
>
> When you flatten a section of the rim, you increase its circumference.

peter, that's categorically incorrect. the only way the circumference
changes is if the circumferential load changes. and that's a trivial
amount. the /radius/ at various points about the rim changes, so maybe
that's what you're thinking of, but the circumference is definitely
constant for constant average spoke tension.

> If you increased the circumference uniformly around the rim, you
> wouldn't get any angular displacement, you'd only get a slightly larger
> circle, with correspondingly greater spoke tensions. Since you are
> increasing the circumference in only one region, you'll also get angular
> displacements from there. These displacements will be largest near the
> load. Jobst shows these in the tables in the appendix of his book as
> part of the FEA. How those displacements translate into changes in spoke
> tension depend on spoking pattern (as Gavin says & shows).
>
> The larger the flattened area is, the proportionally greater the effect.
> Squeezing spokes generates relatively large rim deflections.

 

[Peter Cole]

jim beam wrote:
> Peter Cole wrote:

>>
>> When you flatten a section of the rim, you increase its circumference.
>
> peter, that's categorically incorrect. the only way the circumference
> changes is if the circumferential load changes. and that's a trivial
> amount. the /radius/ at various points about the rim changes, so maybe
> that's what you're thinking of, but the circumference is definitely
> constant for constant average spoke tension.

When you flatten a rim section, you are converting that section from an
arc to a chord. Since the arc and the chord are the same length (same
piece of metal) and have the same endpoints on the circle, the new
circle must be larger. There is also a tangential displacement.

 

[jim beam]

Peter Cole wrote:
> jim beam wrote:
>
>> Peter Cole wrote:
>
>
>>>
>>> When you flatten a section of the rim, you increase its circumference.
>>
>>
>> peter, that's categorically incorrect. the only way the circumference
>> changes is if the circumferential load changes. and that's a trivial
>> amount. the /radius/ at various points about the rim changes, so
>> maybe that's what you're thinking of, but the circumference is
>> definitely constant for constant average spoke tension.
>
>
> When you flatten a rim section, you are converting that section from an
> arc to a chord. Since the arc and the chord are the same length (same
> piece of metal) and have the same endpoints on the circle, the new
> circle must be larger.

you're talking radius/diameter, NOT circumference. the rim hoop remains
the same length.

> There is also a tangential displacement.

 

[Joe Riel]

jim beam <[email protected]> writes:

> Peter Cole wrote:
>> When you flatten a rim section, you are converting that section from
>> an arc to a chord. Since the arc and the chord are the same length
>> (same piece of metal) and have the same endpoints on the circle, the
>> new circle must be larger.
>
> you're talking radius/diameter, NOT circumference. the rim hoop
> remains the same length.

Practically, yes. Aluminum being elastic there is some compression.
For a rim brought from 0 to full tension, the change in perimeter
is on the order of 0.15%, or about 1/8 inch. The change due to local
loading is going to be much smaller than that.


--
Joe Riel

 

[Joe Riel]

Joe Riel <[email protected]> writes:

> Practically, yes. Aluminum being elastic there is some compression.
> For a rim brought from 0 to full tension, the change in perimeter
> is on the order of 0.15%, or about 1/8 inch. The change due to local
> loading is going to be much smaller than that.

Wrong by an order of magnitude (missed a decimal). The relative
change is 0.015%, the change in length is 1/80 inch.

--
Joe Riel

 

[Peter Cole]

jim beam wrote:
> Peter Cole wrote:
>> jim beam wrote:
>>
>>> Peter Cole wrote:
>>
>>
>>>>
>>>> When you flatten a section of the rim, you increase its circumference.
>>>
>>>
>>> peter, that's categorically incorrect. the only way the
>>> circumference changes is if the circumferential load changes. and
>>> that's a trivial amount. the /radius/ at various points about the
>>> rim changes, so maybe that's what you're thinking of, but the
>>> circumference is definitely constant for constant average spoke tension.
>>
>>
>> When you flatten a rim section, you are converting that section from
>> an arc to a chord. Since the arc and the chord are the same length
>> (same piece of metal) and have the same endpoints on the circle, the
>> new circle must be larger.
>
> you're talking radius/diameter, NOT circumference. the rim hoop remains
> the same length.

I was referring to the circumference of the circle formed by the rim,
not the actual rim itself. Sorry, I thought that was obvious.