On the virtue of traditional wheels when racing Paris-Roubaix

Hobbes@spnb&s.com

On Wed, 16 Apr 2008 17:46:34 -0600, carlfogel@comcast.net wrote:

>On Wed, 16 Apr 2008 12:34:29 -0600, carlfogel@comcast.net wrote:
>
>>Dear Hobbes,
>>
>>Just rolling under the hub on smooth pavement, a rim deflects only a
>>thousandth of an inch or so.
>>
>>That's obviously imperceptible.
>>
>>But some riders occasionally notice spokes rattling when they hit
>>things hard. The rattling means that the rim deflected enough to lose
>>all its tension. That's around 3 to 5 mm, depending on initial
>>tension, spoke length, and spoke gauge.
>>
>>That's getting close to snake-bite territory, where the tire is mashed
>>flat against the rim. (For an impact flat, a tire already mashed flat
>>against the rim must be given a good whack to split the rubber tube
>>pinched between the rim and the road.)
>>
>>So what you're really wondering is how much impact is needed to mash a
>>rim to spoke-rattle depth for deep carbon versus metal box rim.
>>
>>If the deep carbon rim flattened only half as much as the metal box
>>rim, the suspension travel difference would be only half of 3 to 5 mm.
>>
>>Maybe someone can calculate the theoretical difference for a deep
>>carbon versus a metal box rim, but I suspect that difference will
>>remain more theoretical than noticeable to a rider.
>>
>>Cheers,
>>
>>Carl Fogel
>
>Ron Ruff just posted his estimate of only 1 mm of stretch for a thin
>spoke (1.5 mm), 290 mm long, 1250 N tension.
>
>That roused me to check the equations sections at the end of Jobst's
>book.
>
>Sure enough, Jobst's calculations, corrected in the 3rd edition,
>worked out to 0.75 mm stretch for a bit less tension (1000 N) on a bit
>thicker spoke (1.8 mm).
>
>In other words, the 3~5 mm estimate that I carelessly accepted was
>about five times too large.
>
>So a metal box rim will lose spoke tension and twang or rattle the
>spokes if it mashes a millimeter or less under impact. Even an
>infinitely stiff rim would lose only a millimeter of its shock
>absorbing travel on an impressively severe impact, and a carbon rim
>would lose even less than a millimeter.
>
>Less than a millimeter difference in shock travel is unlikely to be
>noticeable to a rider.


Losing spoke tension does not stop a rim from deflecting or consequently
absorbing road shock. In fact it becomes more compliant.

These are not rigid spokes bound to the rim, they rest in sockets in the rim.
Bend the rim enough to remove the tension and there's nothing to stop it from
moving further. In fact the release of tension at the flattened part of the rim
will reduce tension on the rest of the spokes making the assembly more
compliant.

As for this 1mm business, how much spoke thread do you use when tensioning a
wheel from the point that the nipples are seated on the rim and the wheel is up
to tension. A hell of a lot more than 1mm.

I'll agree that my premise that a box section rim is more compliant and therefor
more comfortable under extreme conditions may be wrong. But the arguments
against have been counter to simple observation.

Hobbes@spnb&s.com

On Wed, 16 Apr 2008 14:55:26 -0700 (PDT), Ron Ruff <rruffrruff@yahoo.com> wrote:

>On Apr 16, 9:02*am, Hobbes@spnb&s.com wrote:
>> So how much does a box section rim on a 32 spoke wheel give when a 170 pound guy
>> with a bike hits rocks at 25per? That's a harder question. But I'll bet real
>> cash the answer is not insubstantial compared to the mere 15mm we're allowing
>> from the tire.
>
>I'll take that bet.

Cool, I'm going to have to work out how to test. Need some suitable rims and a
fair loading test. Oh, the assertion is "not insubstantial compared" not
"greater than" or "a whole bunch." Even 5mm is a full third of the travel I'm
allowing for the tire, so that would meet my admittedly low standards. Now I'll
figure out how to test this in a most elegant experiment.

Ron Ruff

On Apr 17, 9:49*am, Hobbes@spnb&s.com wrote:
> As for this 1mm business, how much spoke thread do you use when tensioninga
> wheel from the point that the nipples are seated on the rim and the wheel is up
> to tension. A hell of a lot more than 1mm.

The 1mm is calculated from the cross section and the properties of the
spoke, at the highest tension and smallest cross-section. For 2mm
spokes it is ~0.5mm... worst case! Cut it in half for NDS. This is the
radial movement that will cause the spoke to go slack... ie, if you
reduce the distance from the hub to rim this amount, the spoke will be
slack. When you are building the wheel there are all sorts of other
things going on like bedding in and straightening the spokes and
compressing the rim.

Certainly, you might get a fair amount of rim flex after tension has
been removed... and before the rim buckles. But note that myself and
many other people who build wheels do not use any sort of
threadlock... and the spokes *never* go slack in normal use... else
the nipples would unwind.

unforgiven99@juno.com

On Apr 16, 6:04 pm, Ron Ruff <rruffrr...@yahoo.com> wrote:
> On Apr 16, 9:52 am, unforgive...@juno.com wrote:
>
> > Back of the envelope says that a straight 14ga spoke of 280mm length
> > and 110kgf tension goes slack at 5mm of rim deflection, so that's the
> > practical limit of compliance.
>
> The back of my envelope gives 1mm of length change per 1250N force for
> a 290mm 1.5mm dia spoke. So I'd say the practical limit is ~1mm.

Thanks for the correction. I thought I might have missed a decimal
somewhere. That should have been just under 0.5mm.

unforgiven99@juno.com

On Apr 17, 11:49 am, Hobbes@spnb&s.com wrote:
> On Wed, 16 Apr 2008 17:46:34 -0600, carlfo...@comcast.net wrote:
> >On Wed, 16 Apr 2008 12:34:29 -0600, carlfo...@comcast.net wrote:
>
> >>Dear Hobbes,
>
> >>Just rolling under the hub on smooth pavement, a rim deflects only a
> >>thousandth of an inch or so.
>
> >>That's obviously imperceptible.
>
> >>But some riders occasionally notice spokes rattling when they hit
> >>things hard. The rattling means that the rim deflected enough to lose
> >>all its tension. That's around 3 to 5 mm, depending on initial
> >>tension, spoke length, and spoke gauge.
>
> >>That's getting close to snake-bite territory, where the tire is mashed
> >>flat against the rim. (For an impact flat, a tire already mashed flat
> >>against the rim must be given a good whack to split the rubber tube
> >>pinched between the rim and the road.)
>
> >>So what you're really wondering is how much impact is needed to mash a
> >>rim to spoke-rattle depth for deep carbon versus metal box rim.
>
> >>If the deep carbon rim flattened only half as much as the metal box
> >>rim, the suspension travel difference would be only half of 3 to 5 mm.
>
> >>Maybe someone can calculate the theoretical difference for a deep
> >>carbon versus a metal box rim, but I suspect that difference will
> >>remain more theoretical than noticeable to a rider.
>
> >>Cheers,
>
> >>Carl Fogel
>
> >Ron Ruff just posted his estimate of only 1 mm of stretch for a thin
> >spoke (1.5 mm), 290 mm long, 1250 N tension.
>
> >That roused me to check the equations sections at the end of Jobst's
> >book.
>
> >Sure enough, Jobst's calculations, corrected in the 3rd edition,
> >worked out to 0.75 mm stretch for a bit less tension (1000 N) on a bit
> >thicker spoke (1.8 mm).
>
> >In other words, the 3~5 mm estimate that I carelessly accepted was
> >about five times too large.
>
> >So a metal box rim will lose spoke tension and twang or rattle the
> >spokes if it mashes a millimeter or less under impact. Even an
> >infinitely stiff rim would lose only a millimeter of its shock
> >absorbing travel on an impressively severe impact, and a carbon rim
> >would lose even less than a millimeter.
>
> >Less than a millimeter difference in shock travel is unlikely to be
> >noticeable to a rider.
>
> Losing spoke tension does not stop a rim from deflecting or consequently
> absorbing road shock. In fact it becomes more compliant.
>
> These are not rigid spokes bound to the rim, they rest in sockets in the rim.
> Bend the rim enough to remove the tension and there's nothing to stop it from
> moving further. In fact the release of tension at the flattened part of the rim
> will reduce tension on the rest of the spokes making the assembly more
> compliant.
>
> As for this 1mm business, how much spoke thread do you use when tensioning a
> wheel from the point that the nipples are seated on the rim and the wheel is up
> to tension. A hell of a lot more than 1mm.
>
> I'll agree that my premise that a box section rim is more compliant and therefor
> more comfortable under extreme conditions may be wrong. But the arguments
> against have been counter to simple observation.

There are all kinds of messy things going on when you bring a wheel up
to tension. A better example is how much you need to unscrew the
nipple to get a spoke on a tensioned wheel to go slack. It's not very
much. The wheel may continue to deform past spoke slacking, but it's
essentially failed.

The question by the way is not really whether or not a box section rim
is more compliant. Given similar spoking, it's obvious that it will
be. There are two things going against the comfort argument. First
is the magnitude of the compliance, second is the fact that wheel
compliance is all elastic. Elastic deflection may take the edge off
of very high speed impacts, but for the most part cobblestones are
being hit at the fairly low rate of around 100Hz. Only the parts of
the bike with some viscosity, like tires and bar tape, are going to
contribute much to rider comfort.

Ben C

On 2008-04-17, unforgiven99@juno.com <unforgiven99@juno.com> wrote:
[...]
> There are all kinds of messy things going on when you bring a wheel up
> to tension. A better example is how much you need to unscrew the
> nipple to get a spoke on a tensioned wheel to go slack. It's not very
> much. The wheel may continue to deform past spoke slacking, but it's
> essentially failed.

Note however that the strength of the wheel is just the same when the
spokes are slack as when they are tight, it's just less stiff. If the
spoke tension is excessively high, it actually reduces the strength of
the wheel (in that case the rim would yield before the spokes went
slack).

The reduced stiffness when the spokes go slack means the rim will deform
more for a given load and that extra deformation _may_ cause it get out
of shape and buckle. But spokes can go slack and wheels not fail.

unforgiven99@juno.com

On Apr 17, 2:41 pm, Ben C <spams...@spam.eggs> wrote:
> On 2008-04-17, unforgive...@juno.com <unforgive...@juno.com> wrote:
> [...]
>
> > There are all kinds of messy things going on when you bring a wheel up
> > to tension. A better example is how much you need to unscrew the
> > nipple to get a spoke on a tensioned wheel to go slack. It's not very
> > much. The wheel may continue to deform past spoke slacking, but it's
> > essentially failed.
>
> Note however that the strength of the wheel is just the same when the
> spokes are slack as when they are tight, it's just less stiff. If the
> spoke tension is excessively high, it actually reduces the strength of
> the wheel (in that case the rim would yield before the spokes went
> slack).
>
> The reduced stiffness when the spokes go slack means the rim will deform
> more for a given load and that extra deformation _may_ cause it get out
> of shape and buckle. But spokes can go slack and wheels not fail.

You can't really decouple strength and stiffness that way. It's
exactly because the wheel with the slack spoke is less stiff that an
incremental increase in load gets the rim closer to yield strain than
a wheel without a slack spoke would be. So the strength of the wheel
is not the same. Fatigue failure from overtensioned spokes is a
different issue all together and has been beaten to death elsewhere.

Yes, spokes can go slack without catastrophic wheel failure. You can
also knock quite a few holes in an aircraft fuselage without crashing
it. Once you're outside of design conditions you're bumping up
against the edge of, "how much farther until it collapses?", and the
real world is far too variable to consider that zone to be safe
operating conditions.

Ben C

On 2008-04-17, unforgiven99@juno.com <unforgiven99@juno.com> wrote:
> On Apr 17, 2:41 pm, Ben C <spams...@spam.eggs> wrote:
>> On 2008-04-17, unforgive...@juno.com <unforgive...@juno.com> wrote:
>> [...]
>>
>> > There are all kinds of messy things going on when you bring a wheel up
>> > to tension. A better example is how much you need to unscrew the
>> > nipple to get a spoke on a tensioned wheel to go slack. It's not very
>> > much. The wheel may continue to deform past spoke slacking, but it's
>> > essentially failed.
>>
>> Note however that the strength of the wheel is just the same when the
>> spokes are slack as when they are tight, it's just less stiff. If the
>> spoke tension is excessively high, it actually reduces the strength of
>> the wheel (in that case the rim would yield before the spokes went
>> slack).
>>
>> The reduced stiffness when the spokes go slack means the rim will deform
>> more for a given load and that extra deformation _may_ cause it get out
>> of shape and buckle. But spokes can go slack and wheels not fail.
>
> You can't really decouple strength and stiffness that way.

But strength and stiffness _are_ different things, I'm not decoupling
them. They're already decoupled.

Strength is yield stress, stiffness is strain per unit stress.

> It's exactly because the wheel with the slack spoke is less stiff that
> an incremental increase in load gets the rim closer to yield strain
> than a wheel without a slack spoke would be.

I don't think that's right. Never mind strain, just consider yield
stress.

When the spokes are slack, the structure as a whole is less stiff. But
by definition the rim yields when the total stress on the rim reaches
its yield stress. The more stress already on it from the spokes the less
additional applied stress you need to bring it to yield.

But the other side to the story is you also have to consider the wheel
as a structure, and whether there's any way in which it "collapses"--
i.e. fails as a structure before any of the components in it actually
yield, a bit like a tent folding up in a strong wind. In that case
higher spoke tension may mean it collapses at a higher applied load.

Peter Cole explains the structure well here:

http://groups.google.co.uk/group/re...44e4c7184eef863

There are explanations elsewhere in that thread about how increasing
spoke tension "borrows" compressive strength from the rim as jim beam
puts it.

Which failure mode is significant when you get a buckle or a flat spot:
the materials yielding, or the wheel collapsing? I don't know and I
don't think it's an easy one to call.

Having collapsed in the structural sense bits of the assembly may then
yield because the geometry has changed and you may get more leverage on
parts of the structure that you wouldn't have had before. So post mortem
demonstration of yielded parts doesn't prove the failure actually
started with the components yielding rather than with the structure
collapsing.

Ben C

On 2008-04-17, Ben C <spamspam@spam.eggs> wrote:
[...]
> Strength is yield stress, stiffness is strain per unit stress.

I meant of course stress per unit strain...

unforgiven99@juno.com

On Apr 17, 6:04 pm, Ben C <spams...@spam.eggs> wrote:
> On 2008-04-17, unforgive...@juno.com <unforgive...@juno.com> wrote:
>
>
>
> > On Apr 17, 2:41 pm, Ben C <spams...@spam.eggs> wrote:
> >> On 2008-04-17, unforgive...@juno.com <unforgive...@juno.com> wrote:
> >> [...]
>
> >> > There are all kinds of messy things going on when you bring a wheel up
> >> > to tension. A better example is how much you need to unscrew the
> >> > nipple to get a spoke on a tensioned wheel to go slack. It's not very
> >> > much. The wheel may continue to deform past spoke slacking, but it's
> >> > essentially failed.
>
> >> Note however that the strength of the wheel is just the same when the
> >> spokes are slack as when they are tight, it's just less stiff. If the
> >> spoke tension is excessively high, it actually reduces the strength of
> >> the wheel (in that case the rim would yield before the spokes went
> >> slack).
>
> >> The reduced stiffness when the spokes go slack means the rim will deform
> >> more for a given load and that extra deformation _may_ cause it get out
> >> of shape and buckle. But spokes can go slack and wheels not fail.
>
> > You can't really decouple strength and stiffness that way.
>
> But strength and stiffness _are_ different things, I'm not decoupling
> them. They're already decoupled.
>
> Strength is yield stress, stiffness is strain per unit stress.
>
> > It's exactly because the wheel with the slack spoke is less stiff that
> > an incremental increase in load gets the rim closer to yield strain
> > than a wheel without a slack spoke would be.
>
> I don't think that's right. Never mind strain, just consider yield
> stress.
>
> When the spokes are slack, the structure as a whole is less stiff. But
> by definition the rim yields when the total stress on the rim reaches
> its yield stress. The more stress already on it from the spokes the less
> additional applied stress you need to bring it to yield.
>
> But the other side to the story is you also have to consider the wheel
> as a structure, and whether there's any way in which it "collapses"--
> i.e. fails as a structure before any of the components in it actually
> yield, a bit like a tent folding up in a strong wind. In that case
> higher spoke tension may mean it collapses at a higher applied load.
>
> Peter Cole explains the structure well here:
>
> http://groups.google.co.uk/group/re...44e4c7184eef863
>
> There are explanations elsewhere in that thread about how increasing
> spoke tension "borrows" compressive strength from the rim as jim beam
> puts it.
>
> Which failure mode is significant when you get a buckle or a flat spot:
> the materials yielding, or the wheel collapsing? I don't know and I
> don't think it's an easy one to call.
>
> Having collapsed in the structural sense bits of the assembly may then
> yield because the geometry has changed and you may get more leverage on
> parts of the structure that you wouldn't have had before. So post mortem
> demonstration of yielded parts doesn't prove the failure actually
> started with the components yielding rather than with the structure
> collapsing.

You can think about it in terms of stress if you want to. Yield
strain and yield stress are interchangeable, and are related by
modulus. If a rim is able to deflect more under a given applied load
because of a slack spoke (altered boundary conditions), then the
stress in the rim must be going up simply by virtue of the fact that
it's deflecting more. The incremental load thus brings that rim
closer to failure than a rim that is properly supported by the spokes.

The link you provided does a very good job of explaining how the wheel
works as a structure. It is meant to operate with all of its
components intact. If you take a structural support out of play (de-
tension a spoke) the structure becomes both more compliant and
weaker. Thus, strength and stiffness are in this case coupled because
the function of the spokes lends both properties to the function of
the wheel as a whole.

Peter Cole

Ben C wrote:
> On 2008-04-17, unforgiven99@juno.com <unforgiven99@juno.com> wrote:

>> It's exactly because the wheel with the slack spoke is less stiff that
>> an incremental increase in load gets the rim closer to yield strain
>> than a wheel without a slack spoke would be.
>
> I don't think that's right. Never mind strain, just consider yield
> stress.

He is right.


> When the spokes are slack, the structure as a whole is less stiff. But
> by definition the rim yields when the total stress on the rim reaches
> its yield stress. The more stress already on it from the spokes the less
> additional applied stress you need to bring it to yield.


It is less confusing to think of yield strain and consider the
stress/strain response of the wheel as a structure with and without
loaded spokes.

Spoke stress on the rim is primarily compression across the cross
section (rim). Bending stress (wheel radial load) is compression on the
outer surface, tension on the inner.

Since the rim is pre-loaded with compression (spoke tension), that
compression must be added to the skin compression (outer) caused by a
bending load, if you do the math, you find you still come out ahead
(stronger for radial loads) with higher spoke tension.

> But the other side to the story is you also have to consider the wheel
> as a structure, and whether there's any way in which it "collapses"--
> i.e. fails as a structure before any of the components in it actually
> yield, a bit like a tent folding up in a strong wind. In that case
> higher spoke tension may mean it collapses at a higher applied load.

Taco failure is beam buckling. The higher the rim compression (spoke
tension) the less additional lateral load or compressive load is
required to buckle. Taken to the limit, a wheel will spontaneously
buckle just from spoke tension.

In normal use, lateral and compressive wheel loads are small, so the
increase in radial load capacity given by higher spoke tension is more
relevant than the loss in buckling resistance. The other potential
limiting factor is fatigue at the spoke bed, which is accelerated by
increased spoke tension.

The ideal spoke tension is reached by increasing to the maximum that
still leaves sufficient buckling resistance to normal cycling loads --
you may argue what is "normal". Some rims may not reach that limit
because of relatively weak spoke beds, that's a design parameter, and
the manufacturer's spec must be observed.

As Jobst says, the strongest wheel is made by using the highest spoke
tension the rim can bear. That translates into buckling or spoke bed
fatigue, whichever comes first. Buckling can be experimentally
determined by carefully increasing tension until the wheel starts to
deform into a saddle shape. There is no experimental way to know the
tolerable spoke bed fatigue tension, so the only recourse is to use the
manufacturer's maximum. I can't see any reason for using less than that
maximum, doing so will make a wheel with less radial load capacity.

In practical terms, more spoke tension doesn't make the wheel stiffer,
it just increases the load point where the wheel undergoes a stiffness
transition. Beyond that point, the lower stiffness causes relatively
more strain with load until the rim is permanently bent.

jim beam

unforgiven99@juno.com wrote:
> On Apr 17, 6:04 pm, Ben C <spams...@spam.eggs> wrote:
>> On 2008-04-17, unforgive...@juno.com <unforgive...@juno.com> wrote:
>>
>>
>>
>>> On Apr 17, 2:41 pm, Ben C <spams...@spam.eggs> wrote:
>>>> On 2008-04-17, unforgive...@juno.com <unforgive...@juno.com> wrote:
>>>> [...]
>>>>> There are all kinds of messy things going on when you bring a wheel up
>>>>> to tension. A better example is how much you need to unscrew the
>>>>> nipple to get a spoke on a tensioned wheel to go slack. It's not very
>>>>> much. The wheel may continue to deform past spoke slacking, but it's
>>>>> essentially failed.
>>>> Note however that the strength of the wheel is just the same when the
>>>> spokes are slack as when they are tight, it's just less stiff. If the
>>>> spoke tension is excessively high, it actually reduces the strength of
>>>> the wheel (in that case the rim would yield before the spokes went
>>>> slack).
>>>> The reduced stiffness when the spokes go slack means the rim will deform
>>>> more for a given load and that extra deformation _may_ cause it get out
>>>> of shape and buckle. But spokes can go slack and wheels not fail.
>>> You can't really decouple strength and stiffness that way.
>> But strength and stiffness _are_ different things, I'm not decoupling
>> them. They're already decoupled.
>>
>> Strength is yield stress, stiffness is strain per unit stress.
>>
>>> It's exactly because the wheel with the slack spoke is less stiff that
>>> an incremental increase in load gets the rim closer to yield strain
>>> than a wheel without a slack spoke would be.
>> I don't think that's right. Never mind strain, just consider yield
>> stress.
>>
>> When the spokes are slack, the structure as a whole is less stiff. But
>> by definition the rim yields when the total stress on the rim reaches
>> its yield stress. The more stress already on it from the spokes the less
>> additional applied stress you need to bring it to yield.
>>
>> But the other side to the story is you also have to consider the wheel
>> as a structure, and whether there's any way in which it "collapses"--
>> i.e. fails as a structure before any of the components in it actually
>> yield, a bit like a tent folding up in a strong wind. In that case
>> higher spoke tension may mean it collapses at a higher applied load.
>>
>> Peter Cole explains the structure well here:
>>
>> http://groups.google.co.uk/group/re...44e4c7184eef863
>>
>> There are explanations elsewhere in that thread about how increasing
>> spoke tension "borrows" compressive strength from the rim as jim beam
>> puts it.
>>
>> Which failure mode is significant when you get a buckle or a flat spot:
>> the materials yielding, or the wheel collapsing? I don't know and I
>> don't think it's an easy one to call.
>>
>> Having collapsed in the structural sense bits of the assembly may then
>> yield because the geometry has changed and you may get more leverage on
>> parts of the structure that you wouldn't have had before. So post mortem
>> demonstration of yielded parts doesn't prove the failure actually
>> started with the components yielding rather than with the structure
>> collapsing.
>
> You can think about it in terms of stress if you want to. Yield
> strain and yield stress are interchangeable, and are related by
> modulus.

that's confusing and ugly terminology. "interchangeable" is definitely
not the word to use.


> If a rim is able to deflect more under a given applied load
> because of a slack spoke (altered boundary conditions), then the
> stress in the rim must be going up simply by virtue of the fact that
> it's deflecting more. The incremental load thus brings that rim
> closer to failure than a rim that is properly supported by the spokes.

except that at higher spoke tension the rim is closer to compression
buckling. a beam in 3-point loading can support whatever load causes
material loading below [tensile or compressive] yield. but if the beam
is longitudinally compressed /and/ 3-point loaded, it cannot support as
much because the compression loading available on the upper part of the
beam is decreased by the compressive pre-load.


>
> The link you provided does a very good job of explaining how the wheel
> works as a structure. It is meant to operate with all of its
> components intact. If you take a structural support out of play (de-
> tension a spoke) the structure becomes both more compliant and
> weaker. Thus, strength and stiffness are in this case coupled because
> the function of the spokes lends both properties to the function of
> the wheel as a whole.

but the limit is the strength of the rim material, however is it loaded,
either with spoke tension [and thus circumferential compression] or in
bending [road load]. as the circumferential load is cranked up, the
road load that can be supported decreases. an unsupported [unspoked]
open pro rim can support my full 210lb body weight without buckling, so
this image of a rim being a fragile flower that can't bridge the gap of
one or two slack spokes is somewhat over simplistic.

jim beam

Peter Cole wrote:
> Ben C wrote:
>> On 2008-04-17, unforgiven99@juno.com <unforgiven99@juno.com> wrote:
>
>>> It's exactly because the wheel with the slack spoke is less stiff that
>>> an incremental increase in load gets the rim closer to yield strain
>>> than a wheel without a slack spoke would be.
>>
>> I don't think that's right. Never mind strain, just consider yield
>> stress.
>
> He is right.
>
>
>> When the spokes are slack, the structure as a whole is less stiff. But
>> by definition the rim yields when the total stress on the rim reaches
>> its yield stress. The more stress already on it from the spokes the less
>> additional applied stress you need to bring it to yield.
>
>
> It is less confusing to think of yield strain and consider the
> stress/strain response of the wheel as a structure with and without
> loaded spokes.
>
> Spoke stress on the rim is primarily compression across the cross
> section (rim). Bending stress (wheel radial load) is compression on the
> outer surface, tension on the inner.
>
> Since the rim is pre-loaded with compression (spoke tension), that
> compression must be added to the skin compression (outer) caused by a
> bending load, if you do the math, you find you still come out ahead
> (stronger for radial loads) with higher spoke tension.
>
>> But the other side to the story is you also have to consider the wheel
>> as a structure, and whether there's any way in which it "collapses"--
>> i.e. fails as a structure before any of the components in it actually
>> yield, a bit like a tent folding up in a strong wind. In that case
>> higher spoke tension may mean it collapses at a higher applied load.
>
> Taco failure is beam buckling. The higher the rim compression (spoke
> tension) the less additional lateral load or compressive load is
> required to buckle. Taken to the limit, a wheel will spontaneously
> buckle just from spoke tension.
>
> In normal use, lateral and compressive wheel loads are small, so the
> increase in radial load capacity given by higher spoke tension is more
> relevant than the loss in buckling resistance. The other potential
> limiting factor is fatigue at the spoke bed, which is accelerated by
> increased spoke tension.
>
> The ideal spoke tension is reached by increasing to the maximum that
> still leaves sufficient buckling resistance to normal cycling loads --
> you may argue what is "normal". Some rims may not reach that limit
> because of relatively weak spoke beds, that's a design parameter, and
> the manufacturer's spec must be observed.
>
> As Jobst says, the strongest wheel is made by using the highest spoke
> tension the rim can bear. That translates into buckling or spoke bed
> fatigue, whichever comes first.

except that jobst doesn't address rim cracking in any way as a problem
with spoke tension, simply some underinformed and misdiagnosed rubbish
about it being the fault of anodizing. post-facto re-definition of
"what jobst really meant to say" needs to include, er, "encouragement"
to get the facts correct both in "the book" and the faq's.


> Buckling can be experimentally
> determined by carefully increasing tension until the wheel starts to
> deform into a saddle shape. There is no experimental way to know the
> tolerable spoke bed fatigue tension, so the only recourse is to use the
> manufacturer's maximum.

indeed. and to state anything to the effect that spoke tension can be
determined by the user, as is supposed by jobst, is a signal failure to
understand the principles involved.


> I can't see any reason for using less than that
> maximum, doing so will make a wheel with less radial load capacity.

except that the dish of a rear wheel is not set in stone - it varies
with different hubs. the more extreme the dish, the more spoke tension
can rise on lateral loading, and thus, the higher spoke tension can come
to the cracking limit, even though static load may appear to be ok.


>
> In practical terms, more spoke tension doesn't make the wheel stiffer,
> it just increases the load point where the wheel undergoes a stiffness
> transition. Beyond that point, the lower stiffness causes relatively
> more strain with load until the rim is permanently bent.

a wheel can be ridden with completely slack spokes. to repeat the
jobstian myth that rims are so weak that they collapse without full
spoke tension is simply ignorance.

[having said that however, there are very good reasons to ride with
tensioned spokes - spoke nipple unscrewing and spoke elbow fatigue being
two practical ones. but again, a simple practical experiment that you
can do at home puts jobstian tension myths to rest.]

Tom Sherman

Peter Cole wrote:
> [...]
> As Jobst says, the strongest wheel is made by using the highest spoke
> tension the rim can bear. That translates into buckling or spoke bed
> fatigue, whichever comes first. Buckling can be experimentally
> determined by carefully increasing tension until the wheel starts to
> deform into a saddle shape. There is no experimental way to know the
> tolerable spoke bed fatigue tension,[...]

One could get multiple rims of the same model, spoke them to different
tensions, and cyclically load them until fatigue cracking occurs in the
spoke bed. Of course, this is not a very practical solution.

--
Tom Sherman - Holstein-Friesland Bovinia
The weather is here, wish you were beautiful