Block chain and wooden spokes

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Date: 15 May 2007 15:25:26
From:
Subject: Block chain and wooden spokes

Nice view of block chain and sprocket on an 1893 Elliott hickory
bicycle:

http://www.nostalgic.net/pictures/1649.htm

The compact frame metal bike used not only wooden rims, but wooden
spokes:

http://www.nostalgic.net/pictures/1645.htm

http://www.nostalgic.net/pictures/1650.htm

http://www.nostalgic.net/pictures/1646.htm

Cheers,

Carl Fogel

Date: 17 May 2007 06:53:42
From: Joe Riel
Subject: Re: Block chain and wooden spokes

Ben C <spamspam@spam.eggs > writes:

> I think so. But if the spokes were precompressed with > 220lbf of
> precompression, I am still not sure clear why we wouldn't see a
> reduction in compression of the top spoke and only a faint increase in
> compression of the bottom spoke.

Because the elasticity doesn't change with the load. It is a linear
relationship.

--
Joe Riel

Date: 15 May 2007 22:09:09
From:
Subject: Re: Block chain and wooden spokes

Carl Fogel writes:

> Nice view of block chain and sprocket on an 1893 Elliott hickory
> bicycle:

http://www.nostalgic.net/pictures/1649.htm

> The compact frame metal bike used not only wooden rims, but wooden
> spokes:

http://www.nostalgic.net/pictures/1645.htm
http://www.nostalgic.net/pictures/1650.htm
http://www.nostalgic.net/pictures/1646.htm

You forgot to say that the hubs in these wheels hang from the top
spokes.

Jobst Brandt

Date: 15 May 2007 17:16:16
From: DI
Subject: Re: Block chain and wooden spokes

<jobst.brandt@stanfordalumni.org > wrote in message
news:464a2f85$0$14143$742ec2ed@news.sonic.net...
> Carl Fogel writes:
>
>> Nice view of block chain and sprocket on an 1893 Elliott hickory
>> bicycle:
>
> http://www.nostalgic.net/pictures/1649.htm
>
>> The compact frame metal bike used not only wooden rims, but wooden
>> spokes:
>
> http://www.nostalgic.net/pictures/1645.htm
> http://www.nostalgic.net/pictures/1650.htm
> http://www.nostalgic.net/pictures/1646.htm
>
> You forgot to say that the hubs in these wheels hang from the top
> spokes.
>
> Jobst Brandt

I thought all spoke wheels hung from the top spokes, with the load getting
less as you radiate from the top, with some smaller percentage of the load
being on the bottom spokes.

Date: 15 May 2007 16:33:23
From:
Subject: Re: Block chain and wooden spokes

On Tue, 15 May 2007 17:16:16 -0500, "DI" <di9999@cox.net > wrote:

>
><jobst.brandt@stanfordalumni.org> wrote in message
>news:464a2f85$0$14143$742ec2ed@news.sonic.net...
>> Carl Fogel writes:
>>
>>> Nice view of block chain and sprocket on an 1893 Elliott hickory
>>> bicycle:
>>
>> http://www.nostalgic.net/pictures/1649.htm
>>
>>> The compact frame metal bike used not only wooden rims, but wooden
>>> spokes:
>>
>> http://www.nostalgic.net/pictures/1645.htm
>> http://www.nostalgic.net/pictures/1650.htm
>> http://www.nostalgic.net/pictures/1646.htm
>>
>> You forgot to say that the hubs in these wheels hang from the top
>> spokes.
>>
>> Jobst Brandt
>
>I thought all spoke wheels hung from the top spokes, with the load getting
>less as you radiate from the top, with some smaller percentage of the load
>being on the bottom spokes.

Dear DI,

Sorry, but Jobst is just joking. Both pre-tensioned wire-spoke bicycle
wheels and faintly pre-compressed wooden-spoke wagon wheels behave the
same way--just about all the measurable action occurs in the spokes
under the hub, which show compression (the same thing as loss of
pre-tension).

Both theory and measurement show that 5~6 spokes in a 36-spoke
pre-tensioned wire-spoke wheel _lose_ considerable tension as they
roll under the hub (the rim flattens toward the hub at the contact
patch).

All the other spokes show a slight gain in tension.

Here's a pdf with graphs of actual strain gauge measurements of a
single spoke as the bicycle is ridden:

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

See figures 10 & 11, The huge icicle-spikes are where the
pre-tensioned spoke rolled under the hub and lost tension.

Here's a page with the theory side:

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

In the large table, look at the rightmost two columns, where T
(tension) and C (compression) for the 36 spokes are split by sign. The
tricky part is remembering that a spoke pointing somewhat downward
from the hub (say 8 o'clock) is actually pulling the hub _down_ as its
tension increases.

It's a very annoying concept, since the naive expectation is that the
bicycle spokes pointing up from the hub should show a huge increase in
tension as the hub "hangs" the rider's weight from the rim. But it
doesn't. The rim flattens toward the hub from the contact patch,
shortening the distance between rim and hub and consequently losing
spoke tension in that area. The other spokes stubbornly refuse to
change tension anywhere near as much.

RBT posters love to squabble about this.

Cheers,

Carl Fogel

Date: 16 May 2007 02:10:12
From: Ben C
Subject: Re: Block chain and wooden spokes

On 2007-05-15, carlfogel@comcast.net <carlfogel@comcast.net > wrote:
> On Tue, 15 May 2007 17:16:16 -0500, "DI" <di9999@cox.net> wrote:
[...]
> Sorry, but Jobst is just joking. Both pre-tensioned wire-spoke bicycle
> wheels and faintly pre-compressed wooden-spoke wagon wheels behave the
> same way--just about all the measurable action occurs in the spokes
> under the hub, which show compression (the same thing as loss of
> pre-tension).

If the spokes were pre-compressed with a pre-compression greater than
the load you're putting on the wheel, you would see no change in the
bottom spokes and a reduction in compression in the top spokes.

None of this has anything to do with whether the wheel "hangs from the
top spokes" or "stands on the bottom spokes" in either kind of wheel.
Hanging and standing are both consistent, depending on your use of
language, with the correct physical interpretations of either
pre-tensioned or pre-compressed wheels.

Date: 16 May 2007 06:13:20
From: jim beam
Subject: Re: Block chain and wooden spokes

Ben C wrote:
> On 2007-05-15, carlfogel@comcast.net <carlfogel@comcast.net> wrote:
>> On Tue, 15 May 2007 17:16:16 -0500, "DI" <di9999@cox.net> wrote:
> [...]
>> Sorry, but Jobst is just joking. Both pre-tensioned wire-spoke bicycle
>> wheels and faintly pre-compressed wooden-spoke wagon wheels behave the
>> same way--just about all the measurable action occurs in the spokes
>> under the hub, which show compression (the same thing as loss of
>> pre-tension).
>
> If the spokes were pre-compressed with a pre-compression greater than
> the load you're putting on the wheel, you would see no change in the
> bottom spokes and a reduction in compression in the top spokes.

not true. any change in load, as would happen here, manifests a change
in tension or compression [depending on regime].

if you want to argue principles, argue about where the ability to
experience tension or compression comes from. if the rim were perfectly
rigid, the deformation regime would be somewhat different.

>
> None of this has anything to do with whether the wheel "hangs from the
> top spokes" or "stands on the bottom spokes" in either kind of wheel.
> Hanging and standing are both consistent, depending on your use of
> language, with the correct physical interpretations of either
> pre-tensioned or pre-compressed wheels.

Date: 16 May 2007 07:20:25
From: Peter Cole
Subject: Re: Block chain and wooden spokes

Date: 16 May 2007 01:08:59
From: Michael Press
Subject: Re: Block chain and wooden spokes

In article <slrnf4lbef.g58.spamspam@bowser.marioworld >,
Ben C <spamspam@spam.eggs > wrote:

> On 2007-05-15, carlfogel@comcast.net <carlfogel@comcast.net> wrote:
> > On Tue, 15 May 2007 17:16:16 -0500, "DI" <di9999@cox.net> wrote:
> [...]
> > Sorry, but Jobst is just joking. Both pre-tensioned wire-spoke bicycle
> > wheels and faintly pre-compressed wooden-spoke wagon wheels behave the
> > same way--just about all the measurable action occurs in the spokes
> > under the hub, which show compression (the same thing as loss of
> > pre-tension).
>
> If the spokes were pre-compressed with a pre-compression greater than
> the load you're putting on the wheel, you would see no change in the
> bottom spokes and a reduction in compression in the top spokes.
>
> None of this has anything to do with whether the wheel "hangs from the
> top spokes" or "stands on the bottom spokes" in either kind of wheel.
> Hanging and standing are both consistent, depending on your use of
> language, with the correct physical interpretations of either
> pre-tensioned or pre-compressed wheels.

No, it is not the case that "Hanging and standing are both
consistent, depending on your use of language,". When the wheel is
loaded the spokes between the contact patch shorten a lot, and the
spokes opposite the contact patch spokes change almost not at all.
When a structure is loaded the load path is determined by the
changes in dimensions, not by a debate in the English department
or among the purveyors of critical studies.

--
Michael Press

Date: 16 May 2007 11:49:46
From: p.k.
Subject: Re: Block chain and wooden spokes

Michael Press wrote:
.
> When a structure is loaded the load path is determined by the
> changes in dimensions,

No!

in a static system, the load path is determined by where the forces act and
their direction. the previous history of the system is not relevant to the
current static situation

"The load path is the route by which forces applied by the ground can exert
the forces necessary to balance the loads."
http://www.brantacan.co.uk/loadpath.htm

pk

Date: 16 May 2007 07:39:39
From: Peter Cole
Subject: Re: Block chain and wooden spokes

p.k. wrote:
> Michael Press wrote:
> .
>> When a structure is loaded the load path is determined by the
>> changes in dimensions,
>
> No!
>
> in a static system, the load path is determined by where the forces act and
> their direction. the previous history of the system is not relevant to the
> current static situation
>
> "The load path is the route by which forces applied by the ground can exert
> the forces necessary to balance the loads."

Yes, and in a bicycle wheel, the load path is from the contact patch
through the rim and the few spokes near the contact patch to the axle.

Date: 16 May 2007 12:43:38
From: p.k.
Subject: Re: Block chain and wooden spokes

Peter Cole wrote:
> p.k. wrote:
>> Michael Press wrote:
>> .
>>> When a structure is loaded the load path is determined by the
>>> changes in dimensions,
>>
>> No!
>>
>> in a static system, the load path is determined by where the forces
>> act and their direction. the previous history of the system is not
>> relevant to the current static situation
>>
>> "The load path is the route by which forces applied by the ground
>> can exert the forces necessary to balance the loads."
>
> Yes, and in a bicycle wheel, the load path is from the contact patch
> through the rim and the few spokes near the contact patch to the axle.

What is the direction of the force exerted on the hub by the few spoke near
the contact patch?

Up: supporting

or

Down pulling down?

pk

Date: 16 May 2007 01:39:31
From:
Subject: Re: Block chain and wooden spokes

On Wed, 16 May 2007 02:10:12 -0500, Ben C <spamspam@spam.eggs > wrote:

>On 2007-05-15, carlfogel@comcast.net <carlfogel@comcast.net> wrote:
>> On Tue, 15 May 2007 17:16:16 -0500, "DI" <di9999@cox.net> wrote:
>[...]
>> Sorry, but Jobst is just joking. Both pre-tensioned wire-spoke bicycle
>> wheels and faintly pre-compressed wooden-spoke wagon wheels behave the
>> same way--just about all the measurable action occurs in the spokes
>> under the hub, which show compression (the same thing as loss of
>> pre-tension).
>
>If the spokes were pre-compressed with a pre-compression greater than
>the load you're putting on the wheel, you would see no change in the
>bottom spokes and a reduction in compression in the top spokes.
>
>None of this has anything to do with whether the wheel "hangs from the
>top spokes" or "stands on the bottom spokes" in either kind of wheel.
>Hanging and standing are both consistent, depending on your use of
>language, with the correct physical interpretations of either
>pre-tensioned or pre-compressed wheels.

Dear Ben,

I don't know if your theory about heavily pre-compressed wheels is
correct, but I'd love to see a practical example.

Off-hand, I wonder if you're mistaken. Under load, the round wheel rim
will flatten at the contact patch toward the hub, shortening the
distance between the rim and the hub and compressing the lowermost
spokes even more.

That is, a load acting downward should push even harder on the
pre-compressed spoke under it, compressing it even more. Your theory
seems to require the axle to rise under a load.

But I could be the one who's mistaken.

In any case, a real wooden wagon wheel is only faintly compressed by
the shrinking of an iron band, just enough to keep things together,
not the huge compression that you seem to have in mind.

As the wooden parts dry and compress and shift, the wooden wheel
loosens inside the unchanged iron rim band. There's no wooden
equivalent of a well-built bicycle wheel that lasts until the brakes
wear the rim out.

In fact, really light, elegant wooden carriage wheels should be taken
off. If you leave the weight of the carriage on them, the wood creeps
and deforms and you end up with out-of-round wheels:

"In fact, the rim of the wheel bent, rather like a bow, under the
weight of the chariot, and, just as a bow must not be left strung for
any length of time, so the weight must not be left on the wheels of a
chariot. In the evening, therefore, one either tipped the vehicle
vertically against a wall with the weight off the wheels, as
Telemachus did in Book IV of the Odyssey, or else one took the wheels
off altogether. Even on Mount Olympus the goddess Hebe had the morning
chore of fitting the wheels to the chariot of grey-eyed Athene. With
the much heavier wheels of later times such a procedure is less
necessary and less practicable, although I understand that the wheels
of the present [1978] Lord Mayor's coach are distinctly eccentric,
presumably because the weight has been left on them for long periods.*

*This sort of thing is at the root of most of the stories about
V.I.P.'s becoming seasick when riding in state-coaches."

--"Structures," J.E. Gordon, p. 146

Unlike light wooden wheels, heavy wagon wheels just loosen after
enough use. When a wagon wheel loosens enough to rattle alarmingly,
you take it off, soak it in the creek overnight, and hope that it will
swell up enough to get you into town, where the blacksmith can fit a
new and slightly shorter rim strap.

Cheers,

Carl Fogel

Date: 16 May 2007 09:07:54
From: Ben C
Subject: Re: Block chain and wooden spokes

On 2007-05-16, carlfogel@comcast.net <carlfogel@comcast.net > wrote:
> On Wed, 16 May 2007 02:10:12 -0500, Ben C <spamspam@spam.eggs> wrote:
[...]
>>If the spokes were pre-compressed with a pre-compression greater than
>>the load you're putting on the wheel, you would see no change in the
>>bottom spokes and a reduction in compression in the top spokes.
[...]
> I don't know if your theory about heavily pre-compressed wheels is
> correct, but I'd love to see a practical example.
>
> Off-hand, I wonder if you're mistaken. Under load, the round wheel rim
> will flatten at the contact patch toward the hub, shortening the
> distance between the rim and the hub and compressing the lowermost
> spokes even more.

I think you're right.

If the rim were perfectly rigid, I still think we might see reduction in
compression in the top spokes and no change in the bottom spokes. If not
I would interested to hear the explanation.

But in practice the load is shared between the rim and the spokes. So
the rim will deform a bit, increasing the compression in the bottom
spokes. I would also expect to see a reduction in compression of the top
spokes however.

> That is, a load acting downward should push even harder on the
> pre-compressed spoke under it, compressing it even more. Your theory
> seems to require the axle to rise under a load.

Or to stay exactly where it is if the rim is rigid.

Date: 16 May 2007 13:32:41
From:
Subject: Re: Block chain and wooden spokes

On Wed, 16 May 2007 09:07:54 -0500, Ben C <spamspam@spam.eggs > wrote:

>On 2007-05-16, carlfogel@comcast.net <carlfogel@comcast.net> wrote:
>> On Wed, 16 May 2007 02:10:12 -0500, Ben C <spamspam@spam.eggs> wrote:
>[...]
>>>If the spokes were pre-compressed with a pre-compression greater than
>>>the load you're putting on the wheel, you would see no change in the
>>>bottom spokes and a reduction in compression in the top spokes.
>[...]
>> I don't know if your theory about heavily pre-compressed wheels is
>> correct, but I'd love to see a practical example.
>>
>> Off-hand, I wonder if you're mistaken. Under load, the round wheel rim
>> will flatten at the contact patch toward the hub, shortening the
>> distance between the rim and the hub and compressing the lowermost
>> spokes even more.
>
>I think you're right.
>
>If the rim were perfectly rigid, I still think we might see reduction in
>compression in the top spokes and no change in the bottom spokes. If not
>I would interested to hear the explanation.
>
>But in practice the load is shared between the rim and the spokes. So
>the rim will deform a bit, increasing the compression in the bottom
>spokes. I would also expect to see a reduction in compression of the top
>spokes however.
>
>> That is, a load acting downward should push even harder on the
>> pre-compressed spoke under it, compressing it even more. Your theory
>> seems to require the axle to rise under a load.
>
>Or to stay exactly where it is if the rim is rigid.

Dear Ben,

Alas, no rim is rigid.

Pre-tensioned bicycle wheels, for example, seem to be rigid to the
naked eye, but the actual tiny flattening plays hell with our
preconceptions.

It's well worth reading through Ian's analysis carefully:

"The first thing to do with a FE analysis results set is look at the
deflected shape. Since you normally have tiny deflections, it is
normal to exaggerate them. This is a deflected shape plot with the
deflections multiplied 100 times. The maximum deflection was actually
0.1803 mm, but this plot shows a deflection of 18.03mm."

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

The 220-lb load (roughly double the normal load) on the 36-spoke wheel
flattens it only seven thousandths of an inch. The wheel resists
flattening so amazingly because it's tremendously compressed by all
those spokes.

Reverse the situation and shrink a horribly thick metal rim-band to
pre-compress spokes, and the rim will still deflect under a load. I
suspect that a finite element analysis will show it deflecting at the
contact patch, where the force is applied.

Again, it's worth pointing out how odd things are. The individual
spokes on a pre-tensioned bicycle wheel that gain the most tension are
the ones right next to the handful that lose even more tension, right
under the hub. This means that the greatest individual effect of the
comparatively _slight_ tension increase is to pull the hub downward
toward five and seven o'clock.

(See the rightmost two columns of Ian's table for spokes 14-15-16 and
22-23-24. They increase tension far more than the other spokes, but
only about a tenth as much as the five spokes 17-18-19-20-21 _lose_
tension. And because they're angled downward, their effect is to pull
the hub downward, not for the hub to hang from them. Annoying as
hell.)

The weirdness really does require looking at the numbers. If you look
at a 36-spoke pre-tensioned bicycle wheel with strain gauges attached
to every spoke, the normal and naive expectation is that a 220-lb load
on the hub should "hang" from the upper spokes. That is, they should
show 220 pounds of straight downward force, when tension changes and
angles are calculated.

They don't.

Here's Ian's summary of his finite element analysis, which agrees
pretty much with Jobst's FEA in "The Bicycle Wheel" and with Gavin's
measured spoke tension changes on an actual wheel as it was ridden:

"The tension is taken from the analysis. Multiplying the axial force
by the total angle factor gives the vertical component of the force.
This is the lift that one particular spoke is contributing to the hub.
If we add them up, we should get 1000, and luckily we do."

" . . . I've split the lift forces into two columns, depending upon
whether the spoke force was tensile or compressive. This is to see if
the hub hangs from tensile spokes, or stands on compressive ones."

"There are 31 tensile spokes. On average they contribute 1.436 N (0.14
kg, just under a third of a pound) each to holding up the hub."

"There are 5 compressive spokes. On average they contribute 191.097N
(19 kg, just over 42 lbs) each to holding up the hub."

"Put it another way - the average compressive spoke contributes 133
times as much lift force as the average tensile spoke."

"All sorts of other interesting observations emerge."

"The bottom spoke contributes 345.216 N of lift. The top spoke
contributes only 12.487."

"The compressive spoke that contributes most (spoke 19: 345.216)
contributes more than 15 times as much lift as the tensile spoke which
contributes most (spoke 3: 21.955)."

"The tensile spoke with the greatest impact on the lift figures is
actually one pulling the hub down (spoke 15: -28.712)."

"The least contributing compressive spoke (spoke 21: 60.955)
contributes nearly three times as much as the most contributing
tensile spoke (spoke 3: 21.955)."

"Conclusion"

"From these figures, I conclude that it is perfectly reasonable to say
that the hub stands on the lower spokes, and that it does not hang
from the upper spokes."

"It is also wrong to say that the force distributes all around the rim
and all the spokes contribute to holding up the hub - over a third of
the spokes have an effect that pulls the hub down!"

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

Here's the situation in a nutshell. Imagine a museum in which you look
through a small window at a spoked wheel too far away to identify.
They could be pre-tensioned wire spokes, or they could be slightly
pre-compressed wooden spokes.

The spokes at 6 and 12 o'clock have strain gauges attached to readouts
below the window.

You push a button and a 220-lb is lowered onto the hub.

What does the strain gauge show happening on the uppermost and
lowermost spokes?

(Don't guess--see Ian's table or Gavin's measurements.)

Is there any way to tell from the strain gauges on the spokes whether
it's a pre-tensioned wire-spoke bicycle wheel or a faintly
pre-compressed wooden-spoke wagon wheel?

(The wagon wheel spokes will show massive compression on the lower
spoke and faint tension--loss of compression--on the upper spoke.)

Cheers,

Carl Fogel

Date: 17 May 2007 03:19:07
From: Ben C
Subject: Re: Block chain and wooden spokes

On 2007-05-16, carlfogel@comcast.net <carlfogel@comcast.net > wrote:
> On Wed, 16 May 2007 09:07:54 -0500, Ben C <spamspam@spam.eggs> wrote:
[...]
> Dear Ben,
>
> Alas, no rim is rigid.
>
> Pre-tensioned bicycle wheels, for example, seem to be rigid to the
> naked eye, but the actual tiny flattening plays hell with our
> preconceptions.
>
> It's well worth reading through Ian's analysis carefully:
>
> "The first thing to do with a FE analysis results set is look at the
> deflected shape. Since you normally have tiny deflections, it is
> normal to exaggerate them. This is a deflected shape plot with the
> deflections multiplied 100 times. The maximum deflection was actually
> 0.1803 mm, but this plot shows a deflection of 18.03mm."
>
> http://www.astounding.org.uk/ian/wheel/index.html

Thanks for that, and the explanation. I have read that before from a
link from RBT.

[...]
> "The bottom spoke contributes 345.216 N of lift. The top spoke
> contributes only 12.487."
>
> "The compressive spoke that contributes most (spoke 19: 345.216)
> contributes more than 15 times as much lift as the tensile spoke which
> contributes most (spoke 3: 21.955)."
>
> "The tensile spoke with the greatest impact on the lift figures is
> actually one pulling the hub down (spoke 15: -28.712)."
>
> "The least contributing compressive spoke (spoke 21: 60.955)
> contributes nearly three times as much as the most contributing
> tensile spoke (spoke 3: 21.955)."
>
> "Conclusion"
>
> "From these figures, I conclude that it is perfectly reasonable to say
> that the hub stands on the lower spokes, and that it does not hang
> from the upper spokes."
[...]

I conclude from the same figures that it's also reasonable to say it
hangs from the upper spokes. But never mind that. I'm interested in the
physics again because I'm now not so sure I understand it as well as I
thought I had the last time this discussion came up :)

> Here's the situation in a nutshell. Imagine a museum in which you look
> through a small window at a spoked wheel too far away to identify.
> They could be pre-tensioned wire spokes, or they could be slightly
> pre-compressed wooden spokes.
>
> The spokes at 6 and 12 o'clock have strain gauges attached to readouts
> below the window.
>
> You push a button and a 220-lb is lowered onto the hub.
>
> What does the strain gauge show happening on the uppermost and
> lowermost spokes?
>
> (Don't guess--see Ian's table or Gavin's measurements.)
>
> Is there any way to tell from the strain gauges on the spokes whether
> it's a pre-tensioned wire-spoke bicycle wheel or a faintly
> pre-compressed wooden-spoke wagon wheel?
>
> (The wagon wheel spokes will show massive compression on the lower
> spoke and faint tension--loss of compression--on the upper spoke.)

I think so. But if the spokes were precompressed with > 220lbf of
precompression, I am still not sure clear why we wouldn't see a
reduction in compression of the top spoke and only a faint increase in
compression of the bottom spoke.

Date: 17 May 2007 12:39:20
From:
Subject: Re: Block chain and wooden spokes

On Thu, 17 May 2007 03:19:07 -0500, Ben C <spamspam@spam.eggs > wrote:

>On 2007-05-16, carlfogel@comcast.net <carlfogel@comcast.net> wrote:
>> On Wed, 16 May 2007 09:07:54 -0500, Ben C <spamspam@spam.eggs> wrote:
>[...]
>> Dear Ben,
>>
>> Alas, no rim is rigid.
>>
>> Pre-tensioned bicycle wheels, for example, seem to be rigid to the
>> naked eye, but the actual tiny flattening plays hell with our
>> preconceptions.
>>
>> It's well worth reading through Ian's analysis carefully:
>>
>> "The first thing to do with a FE analysis results set is look at the
>> deflected shape. Since you normally have tiny deflections, it is
>> normal to exaggerate them. This is a deflected shape plot with the
>> deflections multiplied 100 times. The maximum deflection was actually
>> 0.1803 mm, but this plot shows a deflection of 18.03mm."
>>
>> http://www.astounding.org.uk/ian/wheel/index.html
>
>Thanks for that, and the explanation. I have read that before from a
>link from RBT.
>
>[...]
>> "The bottom spoke contributes 345.216 N of lift. The top spoke
>> contributes only 12.487."
>>
>> "The compressive spoke that contributes most (spoke 19: 345.216)
>> contributes more than 15 times as much lift as the tensile spoke which
>> contributes most (spoke 3: 21.955)."
>>
>> "The tensile spoke with the greatest impact on the lift figures is
>> actually one pulling the hub down (spoke 15: -28.712)."
>>
>> "The least contributing compressive spoke (spoke 21: 60.955)
>> contributes nearly three times as much as the most contributing
>> tensile spoke (spoke 3: 21.955)."
>>
>> "Conclusion"
>>
>> "From these figures, I conclude that it is perfectly reasonable to say
>> that the hub stands on the lower spokes, and that it does not hang
>> from the upper spokes."
>[...]
>
>I conclude from the same figures that it's also reasonable to say it
>hangs from the upper spokes. But never mind that. I'm interested in the
>physics again because I'm now not so sure I understand it as well as I
>thought I had the last time this discussion came up :)

Dear Ben,

It's not unusual to become doubtful when RBT gets into wild theories
that ignore measured results and rely on false premises.

People are easily tempted to construct elaborate schemes that depend
on impossible situations like perfectly rigid rims.

The reason that in logic no valid conclusions can be drawn from false
premises is that if you allow just one false premise, then there is no
logical reason to stop. If the rim is perfectly rigid in defiance of
all we know about physics, why aren't the spokes perfectly rigid, too?

If the load "hangs" from the upper spokes, why don't the upper spokes
show any significant changes?

When we hang a 220-pound load from a chain, theory predicts and strain
gauges confirm a 220-pound increase in tension in the chain.

It's not a case of choosing between 220 pounds plus or minus, upper or
lower spokes, rabbit or duck.

With pre-tensioned wheels, no measurements and no FEA show the upper
spokes doing anything significantly different when the load is
applied.

All the significant change is in the spokes under the hub.

Arguments to the contrary never hang from any test measurements or FEA
calculations. They dangle in thin air, unsupported by anything except
false premises and imaginary results.

Yes, it only works with a rim and pre-tensioned spokes. But the spokes
stubbornly insist on behaving as if they were in a wooden wagon wheel.

Anyone who wants to construct an alternate theory needs to show their
work with specific calculations and actual measurements. All the
efforts that I've seen involve hand-waving, semantic squabbling, and a
complete lack of concrete detail.

Cheers,

Carl Fogel

Date: 17 May 2007 23:20:48
From: p.k.
Subject: Re: Block chain and wooden spokes

carlfogel@comcast.net wrote:

> If the load "hangs" from the upper spokes,

omit the first bit:

>why don't the upper spokes
> show any significant changes?
>

Because, the compressive load on the hub is transferred to the hub by the
spokes in tension, the hub distorts at the contact point shortening the
lower spokes thereby reducing their tension. The upper spokes are
consequently carrying more of the load than the lower spoke, thus if people
persist in asking the wrong question (hang or stand?) then the only
"correct" answer to that wrong question is "it hangs".

BUT, it is the wrong question!

A better, and more scientific, formulation of the question is: How does a
bicycle wheel work?

Answer: It works by the spokes in tension transferring the compressive load
from the hub to the rim.

pk

Date: 17 May 2007 15:13:56
From: DI
Subject: Re: Block chain and wooden spokes

<carlfogel@comcast.net > wrote in message
news:1s6p439guist0fvunp05p7tprpk301nt5v@4ax.com...
> On Thu, 17 May 2007 03:19:07 -0500, Ben C <spamspam@spam.eggs> wrote:
>
>>On 2007-05-16, carlfogel@comcast.net <carlfogel@comcast.net> wrote:
>>> On Wed, 16 May 2007 09:07:54 -0500, Ben C <spamspam@spam.eggs> wrote:
>>[...]
>>> Dear Ben,
>>>
>>> Alas, no rim is rigid.
>>>
>>> Pre-tensioned bicycle wheels, for example, seem to be rigid to the
>>> naked eye, but the actual tiny flattening plays hell with our
>>> preconceptions.
>>>
>>> It's well worth reading through Ian's analysis carefully:
>>>
>>> "The first thing to do with a FE analysis results set is look at the
>>> deflected shape. Since you normally have tiny deflections, it is
>>> normal to exaggerate them. This is a deflected shape plot with the
>>> deflections multiplied 100 times. The maximum deflection was actually
>>> 0.1803 mm, but this plot shows a deflection of 18.03mm."
>>>
>>> http://www.astounding.org.uk/ian/wheel/index.html
>>
>>Thanks for that, and the explanation. I have read that before from a
>>link from RBT.
>>
>>[...]
>>> "The bottom spoke contributes 345.216 N of lift. The top spoke
>>> contributes only 12.487."
>>>
>>> "The compressive spoke that contributes most (spoke 19: 345.216)
>>> contributes more than 15 times as much lift as the tensile spoke which
>>> contributes most (spoke 3: 21.955)."
>>>
>>> "The tensile spoke with the greatest impact on the lift figures is
>>> actually one pulling the hub down (spoke 15: -28.712)."
>>>
>>> "The least contributing compressive spoke (spoke 21: 60.955)
>>> contributes nearly three times as much as the most contributing
>>> tensile spoke (spoke 3: 21.955)."
>>>
>>> "Conclusion"
>>>
>>> "From these figures, I conclude that it is perfectly reasonable to say
>>> that the hub stands on the lower spokes, and that it does not hang
>>> from the upper spokes."
>>[...]
>>
>>I conclude from the same figures that it's also reasonable to say it
>>hangs from the upper spokes. But never mind that. I'm interested in the
>>physics again because I'm now not so sure I understand it as well as I
>>thought I had the last time this discussion came up :)
>
> Dear Ben,
>
> It's not unusual to become doubtful when RBT gets into wild theories
> that ignore measured results and rely on false premises.
>
> People are easily tempted to construct elaborate schemes that depend
> on impossible situations like perfectly rigid rims.
>
> The reason that in logic no valid conclusions can be drawn from false
> premises is that if you allow just one false premise, then there is no
> logical reason to stop. If the rim is perfectly rigid in defiance of
> all we know about physics, why aren't the spokes perfectly rigid, too?
>
> If the load "hangs" from the upper spokes, why don't the upper spokes
> show any significant changes?
>
> When we hang a 220-pound load from a chain, theory predicts and strain
> gauges confirm a 220-pound increase in tension in the chain.
>
> It's not a case of choosing between 220 pounds plus or minus, upper or
> lower spokes, rabbit or duck.
>
> With pre-tensioned wheels, no measurements and no FEA show the upper
> spokes doing anything significantly different when the load is
> applied.
>
> All the significant change is in the spokes under the hub.
>
> Arguments to the contrary never hang from any test measurements or FEA
> calculations. They dangle in thin air, unsupported by anything except
> false premises and imaginary results.
>
> Yes, it only works with a rim and pre-tensioned spokes. But the spokes
> stubbornly insist on behaving as if they were in a wooden wagon wheel.
>
> Anyone who wants to construct an alternate theory needs to show their
> work with specific calculations and actual measurements. All the
> efforts that I've seen involve hand-waving, semantic squabbling, and a
> complete lack of concrete detail.
>
> Cheers,
>
> Carl Fogel

I'm throwing another situation at the group, if the load does not hang from
the top spokes, but indeed does sit on the lower spokes, how in hell do the
flexible kevlar spokes work?

Date: 17 May 2007 20:52:59
From: A Muzi
Subject: Re: Block chain and wooden spokes

-snip how wheels don't work-
>>> carlfogel@comcast.net <carlfogel@comcast.net> wrote:
-quoting-
>>>> "From these figures, I conclude that it is perfectly reasonable to say
>>>> that the hub stands on the lower spokes, and that it does not hang
>>>> from the upper spokes."
>>> [...]

>> Ben C <spamspam@spam.eggs> wrote:
>>> I conclude from the same figures that it's also reasonable to say it
>>> hangs from the upper spokes. But never mind that. I'm interested in the
>>> physics again because I'm now not so sure I understand it as well as I
>>> thought I had the last time this discussion came up :)

> <carlfogel@comcast.net> wrote in message
>> It's not unusual to become doubtful when RBT gets into wild theories
>> that ignore measured results and rely on false premises.
-snip-
>> With pre-tensioned wheels, no measurements and no FEA show the upper
>> spokes doing anything significantly different when the load is
>> applied.
>> All the significant change is in the spokes under the hub.
-snip-
>> Anyone who wants to construct an alternate theory needs to show their
>> work with specific calculations and actual measurements. All the
>> efforts that I've seen involve hand-waving, semantic squabbling, and a
>> complete lack of concrete detail.

DI wrote:
> I'm throwing another situation at the group, if the load does not hang from
> the top spokes, but indeed does sit on the lower spokes, how in hell do the
> flexible kevlar spokes work?

Just like a tensioned steel or stainless steel spoke. Much better than
those awful once-trendy titanium spokes!

--
Andrew Muzi
www.yellowjersey.org
Open every day since 1 April, 1971

Date: 18 May 2007 01:46:57
From: Michael Press
Subject: Re: Block chain and wooden spokes

In article <7I23i.309543$JN6.190395@newsfe17.phx >,
"DI" <di9999@cox.net > wrote:

> I'm throwing another situation at the group, if the load does not hang from
> the top spokes, but indeed does sit on the lower spokes, how in hell do the
> flexible kevlar spokes work?

Here is a kevlar spoke hanging for the ceiling joist
with two sacks of portland cement attached to the lower end.

/ / / / / / / / / / / / / / / / / / / / /
/ / / / / / / / / / / / / / / / / / / / /
~~~~~~~~~~~~~~~~~~~~~~

Date: 17 May 2007 21:07:25
From: DI
Subject: Re: Block chain and wooden spokes

"Michael Press" <rubrum@pacbell.net > wrote in message
news:rubrum-2DB145.18465817052007@newsclstr02.news.prodigy.com...
> In article <7I23i.309543$JN6.190395@newsfe17.phx>,
> "DI" <di9999@cox.net> wrote:
>
>> I'm throwing another situation at the group, if the load does not hang
>> from
>> the top spokes, but indeed does sit on the lower spokes, how in hell do
>> the
>> flexible kevlar spokes work?
>
> Here is a kevlar spoke hanging for the ceiling joist
> with two sacks of portland cement attached to the lower end.
>
> / / / / / / / / / / / / / / / / / / / / /
> / / / / / / / / / / / / / / / / / / / / /
> ~~~~~~~~~~~~~~~~~~~~~~

Date: 19 May 2007 00:35:51
From: Michael Press
Subject: Re: Block chain and wooden spokes

In article <vT73i.317130$g24.241378@newsfe12.phx >,
"DI" <di9999@cox.net > wrote:

> "Michael Press" <rubrum@pacbell.net> wrote in message
> news:rubrum-2DB145.18465817052007@newsclstr02.news.prodigy.com...
> > In article <7I23i.309543$JN6.190395@newsfe17.phx>,
> > "DI" <di9999@cox.net> wrote:
> >
> >> I'm throwing another situation at the group, if the load does not hang
> >> from
> >> the top spokes, but indeed does sit on the lower spokes, how in hell do
> >> the
> >> flexible kevlar spokes work?
> >
> > Here is a kevlar spoke hanging for the ceiling joist
> > with two sacks of portland cement attached to the lower end.
> >
> > / / / / / / / / / / / / / / / / / / / / /
> > / / / / / / / / / / / / / / / / / / / / /
> >~~~~~~~~~~~~~~~~~~~~~~

Date: 17 May 2007 20:47:11
From:
Subject: Re: Block chain and wooden spokes

On Thu, 17 May 2007 21:07:25 -0500, "DI" <di9999@cox.net > wrote:

>
>"Michael Press" <rubrum@pacbell.net> wrote in message
>news:rubrum-2DB145.18465817052007@newsclstr02.news.prodigy.com...
>> In article <7I23i.309543$JN6.190395@newsfe17.phx>,
>> "DI" <di9999@cox.net> wrote:
>>
>>> I'm throwing another situation at the group, if the load does not hang
>>> from
>>> the top spokes, but indeed does sit on the lower spokes, how in hell do
>>> the
>>> flexible kevlar spokes work?
>>
>> Here is a kevlar spoke hanging for the ceiling joist
>> with two sacks of portland cement attached to the lower end.
>>
>> / / / / / / / / / / / / / / / / / / / / /
>> / / / / / / / / / / / / / / / / / / / / /
>> ~~~~~~~~~~~~~~~~~~~~~~

Date: 17 May 2007 20:25:38
From: jim beam
Subject: Re: Block chain and wooden spokes

carlfogel@comcast.net wrote:
> On Thu, 17 May 2007 21:07:25 -0500, "DI" <di9999@cox.net> wrote:
>
>> "Michael Press" <rubrum@pacbell.net> wrote in message
>> news:rubrum-2DB145.18465817052007@newsclstr02.news.prodigy.com...
>>> In article <7I23i.309543$JN6.190395@newsfe17.phx>,
>>> "DI" <di9999@cox.net> wrote:
>>>
>>>> I'm throwing another situation at the group, if the load does not hang
>>>> from
>>>> the top spokes, but indeed does sit on the lower spokes, how in hell do
>>>> the
>>>> flexible kevlar spokes work?
>>> Here is a kevlar spoke hanging for the ceiling joist
>>> with two sacks of portland cement attached to the lower end.
>>>
>>> / / / / / / / / / / / / / / / / / / / / /
>>> / / / / / / / / / / / / / / / / / / / / /
>>> ~~~~~~~~~~~~~~~~~~~~~~

Date: 17 May 2007 22:54:24
From:
Subject: Re: Block chain and wooden spokes

On Thu, 17 May 2007 20:25:38 -0700, jim beam
<spamvortex@bad.example.net > wrote:

>carlfogel@comcast.net wrote:
>> On Thu, 17 May 2007 21:07:25 -0500, "DI" <di9999@cox.net> wrote:
>>
>>> "Michael Press" <rubrum@pacbell.net> wrote in message
>>> news:rubrum-2DB145.18465817052007@newsclstr02.news.prodigy.com...
>>>> In article <7I23i.309543$JN6.190395@newsfe17.phx>,
>>>> "DI" <di9999@cox.net> wrote:
>>>>
>>>>> I'm throwing another situation at the group, if the load does not hang
>>>>> from
>>>>> the top spokes, but indeed does sit on the lower spokes, how in hell do
>>>>> the
>>>>> flexible kevlar spokes work?
>>>> Here is a kevlar spoke hanging for the ceiling joist
>>>> with two sacks of portland cement attached to the lower end.
>>>>
>>>> / / / / / / / / / / / / / / / / / / / / /
>>>> / / / / / / / / / / / / / / / / / / / / /
>>>> ~~~~~~~~~~~~~~~~~~~~~~

Date: 18 May 2007 06:08:57
From: jim beam
Subject: Re: Block chain and wooden spokes

carlfogel@comcast.net wrote:
> On Thu, 17 May 2007 20:25:38 -0700, jim beam
> <spamvortex@bad.example.net> wrote:
>
>> carlfogel@comcast.net wrote:
>>> On Thu, 17 May 2007 21:07:25 -0500, "DI" <di9999@cox.net> wrote:
>>>
>>>> "Michael Press" <rubrum@pacbell.net> wrote in message
>>>> news:rubrum-2DB145.18465817052007@newsclstr02.news.prodigy.com...
>>>>> In article <7I23i.309543$JN6.190395@newsfe17.phx>,
>>>>> "DI" <di9999@cox.net> wrote:
>>>>>
>>>>>> I'm throwing another situation at the group, if the load does not hang
>>>>>> from
>>>>>> the top spokes, but indeed does sit on the lower spokes, how in hell do
>>>>>> the
>>>>>> flexible kevlar spokes work?
>>>>> Here is a kevlar spoke hanging for the ceiling joist
>>>>> with two sacks of portland cement attached to the lower end.
>>>>>
>>>>> / / / / / / / / / / / / / / / / / / / / /
>>>>> / / / / / / / / / / / / / / / / / / / / /
>>>>> ~~~~~~~~~~~~~~~~~~~~~~

Date: 18 May 2007 10:27:03
From: Peter Cole
Subject: Re: Block chain and wooden spokes

jim beam wrote:

> 2. the spoke-only model is a jobstian sound-bite, not the big picture.

I have no idea what you mean by "spoke-only", I think you're just making
things up (again).

Jobst wrote a book, not a "sound-bite", you should read it.

> jobst is anxious to convey [and get credit for] the "dark art" of
> compressive strength from tensile components, but in doing so, loses
> sight of the rest of the concept of how the structure supports load.

There is nothing "dark" in Jobst's descriptions/analyses, quite the
contrary, it's all explained and backed up with a detailed FEA model.

> mess about with the concept of the wheel being simply a "circular
> bridge" braced by span wires and see how far you get. works for
> compression and tension structures.

From Gavin:

"A useful analogy for a bicycle wheel supporting vertical loads is that
of a circular beam on a prestressed elastic foundation, fixed at the
center and loaded radially at the circumference. To apply this analogy,
the system of interlacing spokes can be modeled as a disk of uniform
stiffness per length of circumference."

The quibble I have with this is the superfluous use of "prestressed". It
doesn't matter that the foundation is prestressed, or what the sign of
the prestress is, it only matters what the elasticities of the
foundation and the beam are.

Date: 18 May 2007 14:21:04
From: p.k.
Subject: Re: Block chain and wooden spokes

jim beam wrote:
.
>
> mess about with the concept of the wheel being simply a "circular
> bridge" braced by span wires and see how far you get. works for
> compression and tension structures.

Have a look at some of the Bioengineering stuff on the web such as
http://www.intensiondesigns.com/itd-biotensegrity/biotensegrity/resources_levinpapers/paper4.html

Models of shoulders, pelvic girdles and other bodily structures are based on
a proper understanding that the Wagon wheel (compression on a single spoke
in turn) works in a fundamentally different way from the bicycle wheel
(transfer of compressive load by tensile members to the rim in compression)

There is loads of stuff out there.

pk

Date: 17 May 2007 16:03:05
From:
Subject: Re: Block chain and wooden spokes

On Thu, 17 May 2007 15:13:56 -0500, "DI" <di9999@cox.net > wrote:

>I'm throwing another situation at the group, if the load does not hang from
>the top spokes, but indeed does sit on the lower spokes, how in hell do the
>flexible kevlar spokes work?

Dear DI,

Kevlar spokes are often mentioned in these threads.

They work because the bicycle wheel (unlike a wagon wheel) is
pre-tensioned, meaning that it is stretched out.

As the contact patch area flattens, the rim closer to the hub.

The stretched spoke loses tension, whether it's wire or Kevlar.

If the rim flattens enough from its pre-tensioned state, the spoke
loses all tension and rattles loose, whether it's wire of Kevlar.

As the spoke rolls out from under the hub, its flattened section of
the rim is unloaded and pops back out into a circular shape, moving
away from the hub and the spoke tension returns to a little more than
its unloaded state.

So if you put a strain gauge on a spoke to record its tension as it
rolls under a load, you get a graph with huge tension losses spiking
downward like massive icicles.

That is, the spoke tensioned to 200 lbs will rise to a little over 200
lbs when you sit on the bike for most of its circular trip. But as it
rolls under the hub, you'll see its tension drop dramatically.

Here again is Gavin's experimental graph of a single spoke that keeps
losing tension as it rolls under a real hub supporting a real rider:

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

Page down to figures 10 & 11.

And here again is Ian's Finite Element Analysis of an idealized
36-spoke wheel:

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

The table shows a snapshot of the _effects_ of the tension changes for
all 36 spoke under a 1000 newton (220 lb) load.

Spokes 17-21 are under the hub and support 65-244-345-239-60 newtons
of vertical load--955 of the 1,000 newtons needed.

The other 31 spokes support only 5% of the vertical load, 45 newtons.

They're much trickier to calculate because they are gaining tension at
angles almost all the way around the wheel. They all increase in
tension, but the ones at 3 and 9 o'clock provide no lift (they're
pulling dead sideways) and the ones below that level are actually
pulling the hub _down_, not up.

It's emphatically not a case of the lower spokes losing 1,000 newtons
and the upper spokes gaining 1,000 newtons.

Amusingly, the greatest increase in raw tension in individual spokes
occurs not in the upper spokes, but in the lower spokes to either side
of the flattened contact patch--pulling the hub downward.

Until you understand that a loss of pre-tension is the same as a gain
in compression, the pre-tensioned wheel whose rim is in compression is
incomprehensible.

Cheers,

Carl Fogel

Date: 17 May 2007 16:00:00
From: Ben C
Subject: Re: Block chain and wooden spokes

On 2007-05-17, DI <di9999@cox.net > wrote:
[...]
> I'm throwing another situation at the group, if the load does not hang from
> the top spokes, but indeed does sit on the lower spokes, how in hell do the
> flexible kevlar spokes work?

Just the same as wire ones-- the bottom spokes lose tension as the load
is applied, but you hope they're tight enough to start with that they
will never go completely slack. The top spokes remain pretty much at the
pre-tension amount.

If you want to call that either "hanging from the top spokes" or
"sitting on the lower spokes" I won't complain.

Ideally with wire spokes the spokes will never go completely slack
either. But sometimes they do, especially on the non-drive side of
highly dished rear wheels.

But don't take my word for it. Here is a previous discussion about it,
which contains quite a bit of interesting stuff:

http://groups.google.co.uk/group/rec.bicycles.tech/browse_thread/thread/9436aa0458b273ce/0eecbf0181efd826?hl=en#0eecbf0181efd826

Date: 17 May 2007 13:52:28
From: Ben C
Subject: Re: Block chain and wooden spokes

On 2007-05-17, carlfogel@comcast.net <carlfogel@comcast.net > wrote:
[...]
> It's not a case of choosing between 220 pounds plus or minus, upper or
> lower spokes, rabbit or duck.

You misunderstand what was meant by "rabbit or duck". I don't dispute
the FEA, I don't dispute that the top spokes show only a very small
change in tension and that all the significant change is in the spokes
under the hub. But _in spite of all that_, I think it is reasonable
reasonable to say that the spoke hangs from the top spokes.

> With pre-tensioned wheels, no measurements and no FEA show the upper
> spokes doing anything significantly different when the load is
> applied.
>
> All the significant change is in the spokes under the hub.
[...]
> Anyone who wants to construct an alternate theory needs to show their
> work with specific calculations and actual measurements. All the
> efforts that I've seen involve hand-waving, semantic squabbling, and a
> complete lack of concrete detail.

I think an alternate theory would be hard to justify in the face of
experimental evidence to the contrary, which is abundant.

Date: 17 May 2007 15:37:49
From:
Subject: Re: Block chain and wooden spokes

On Thu, 17 May 2007 13:52:28 -0500, Ben C <spamspam@spam.eggs > wrote:

>On 2007-05-17, carlfogel@comcast.net <carlfogel@comcast.net> wrote:
>[...]
>> It's not a case of choosing between 220 pounds plus or minus, upper or
>> lower spokes, rabbit or duck.
>
>You misunderstand what was meant by "rabbit or duck". I don't dispute
>the FEA, I don't dispute that the top spokes show only a very small
>change in tension and that all the significant change is in the spokes
>under the hub. But _in spite of all that_, I think it is reasonable
>reasonable to say that the spoke hangs from the top spokes.
>
>> With pre-tensioned wheels, no measurements and no FEA show the upper
>> spokes doing anything significantly different when the load is
>> applied.
>>
>> All the significant change is in the spokes under the hub.
>[...]
>> Anyone who wants to construct an alternate theory needs to show their
>> work with specific calculations and actual measurements. All the
>> efforts that I've seen involve hand-waving, semantic squabbling, and a
>> complete lack of concrete detail.
>
>I think an alternate theory would be hard to justify in the face of
>experimental evidence to the contrary, which is abundant.

Dear Ben,

If you hang a load from something, a strain gauge will show an
increase in strain sufficient to support the load.

What is reasonable about saying that a 220-pound load added to a hub
hangs from the upper spokes if the upper spokes show no significant
change in tension?

It's about the same as arguing that the lower run of the chain pushes
the rear sprocket, in spite of the massive tension increase that
occurs on the top run when we push down on the pedals.

Again, no theoretical analysis and no practical measurements show
anything significantly different between a pre-tensioned wire-spoke
wheel and a faintly pre-compressed wooden wagon wheel.

If someone comes up with a detailed theoretical model with numbers
like the FEA's performed by Ian and Jobst, then we'll have an
interesting debate.

Similarly, if someone comes up with a repeatable test that shows the
top spokes doing something significantly different than they've done
so far for testers like Gavin, we'll have an interesting experiment.

Cheers,

Carl Fogel

Date: 18 May 2007 02:04:29
From: Ben C
Subject: Re: Block chain and wooden spokes

On 2007-05-17, carlfogel@comcast.net <carlfogel@comcast.net > wrote:
[...]
> What is reasonable about saying that a 220-pound load added to a hub
> hangs from the upper spokes if the upper spokes show no significant
> change in tension?

p.k. has answered that well, as have others in earlier threads. I have
nothing to add to that. I am sticking to my duck-rabbit.

> It's about the same as arguing that the lower run of the chain pushes
> the rear sprocket, in spite of the massive tension increase that
> occurs on the top run when we push down on the pedals.

Not really, since no-one has any trouble with the idea that a chain can
support a tensile load rather than a compressive one. There's no paradox
there, everyone can agree on that one.

> Again, no theoretical analysis and no practical measurements show
> anything significantly different between a pre-tensioned wire-spoke
> wheel and a faintly pre-compressed wooden wagon wheel.

Indeed, although I am still curious about the heavily pre-compressed
wheel. You made a good point about contact patch deformation, but it
still doesn't seem right to me for that to happen; I still think,
strange as it may sound, the top spoke may decompress, the bottom stay
the same, and the rim rise very slightly at the top.

The more you push down on the hub the less the top spring does. This
keeps the force on the bottom spring constant until the top spring runs
out of precompression. The rim will therefore have to move upwards at
the top to keep the hub-rim distance constant at the bottom and
increasing at the top reflecting the compression changes.

That the rim should deform less at the bottom than in the pre-tensioned
wheel shouldn't be all that surprising since in this wheel it's being
pushed outwards by all the spokes rather than being pulled inwards.

Date: 18 May 2007 12:58:47
From:
Subject: Re: Block chain and wooden spokes

On Fri, 18 May 2007 02:04:29 -0500, Ben C <spamspam@spam.eggs > wrote:

>On 2007-05-17, carlfogel@comcast.net <carlfogel@comcast.net> wrote:
>[...]
>> What is reasonable about saying that a 220-pound load added to a hub
>> hangs from the upper spokes if the upper spokes show no significant
>> change in tension?
>
>p.k. has answered that well, as have others in earlier threads. I have
>nothing to add to that. I am sticking to my duck-rabbit.
>
>> It's about the same as arguing that the lower run of the chain pushes
>> the rear sprocket, in spite of the massive tension increase that
>> occurs on the top run when we push down on the pedals.
>
>Not really, since no-one has any trouble with the idea that a chain can
>support a tensile load rather than a compressive one. There's no paradox
>there, everyone can agree on that one.
>
>> Again, no theoretical analysis and no practical measurements show
>> anything significantly different between a pre-tensioned wire-spoke
>> wheel and a faintly pre-compressed wooden wagon wheel.
>
>Indeed, although I am still curious about the heavily pre-compressed
>wheel. You made a good point about contact patch deformation, but it
>still doesn't seem right to me for that to happen; I still think,
>strange as it may sound, the top spoke may decompress, the bottom stay
>the same, and the rim rise very slightly at the top.
>
>The more you push down on the hub the less the top spring does. This
>keeps the force on the bottom spring constant until the top spring runs
>out of precompression. The rim will therefore have to move upwards at
>the top to keep the hub-rim distance constant at the bottom and
>increasing at the top reflecting the compression changes.
>
>That the rim should deform less at the bottom than in the pre-tensioned
>wheel shouldn't be all that surprising since in this wheel it's being
>pushed outwards by all the spokes rather than being pulled inwards.

Dear Ben,

No, the sort of posters you have in mind do not explain things well.

They have no detailed model or detailed set of measurements that show
upper spokes changing in a way that provably supports a known load
that is different from what Ian, Gavin, and Jobst give us.

They have nothing that you could teach in a physics class that is
different from what Ian, Gavin, and Jobst give us.

Spokes and axles are the only things that touch the hub. The hub
provides the load. The spokes support it.

What spokes do when a load is added to the hub may be paradoxical or
counter-intuitive, but theoretical FEA's and physical strain gauge
measurements show what happens.

No explanations that disagree with Ian, Gavin, and Jobst use FEA's or
strain gauge measurements. They either brush theory and measurement
aside with half-thought-out objections or else insist that things as
brutally simple as vertical force must be "interpreted" in ways never
explained.

You can figure out the approach used by Ian, Gavin, and Jobst. It's
the approach used to teach physics and engineering classes. The
material appears in books and articles with detailed calculations,
models, and testing. It can be learned and taught to others.

Try to put together a course that teaches the other approach. You'll
find no books, no articles, no detailed models, no testing. A
collection of semantic quibbles and half-thought-out examples is not
an explanation.

Here is a wheel with 36 spokes, each of which has a strain gauge. Add
a 220 pound load to the hub.

Ian, Gavin, and Jobst can tell us how the spoke forces support the
hub. It isn't obvious, but the forces can and have been measured, and
physics doesn't depend on whether we find things intuitive. Anyone can
check which spokes change when a heavy load is applied.

The other explanations require forces that cannot be measured or
described, which is why such explanations do best on internet
newsgroups. The load must somehow "hang" from upper spokes that show
no significant change when tested.

When you start insisting on clear evidence and complete explanations
that you can present to someone else, you'll find that both sides
insist that they're clear and correct, but only one side has tests and
models.

If I'm wrong, let me know where to find the tests and models.

I do sympathize. Like you, I had a hard time figuring out what was
going on in the debate and what was going on in the wheel.

Embarrassingly, it turned out to be something that should have been
familiar to me:

http://shakespeareauthorship.com

Cheers,

Carl Fogel

Date: 17 May 2007 23:24:55
From: p.k.
Subject: Re: Block chain and wooden spokes

carlfogel@comcast.net wrote:
>
> If someone comes up with a detailed theoretical model with numbers
> like the FEA's performed by Ian and Jobst, then we'll have an
> interesting debate.

The FEA calculations are correct, that is not in dispute.

The dispute is their interpretation.

Simple question, amenable to a yes or no answer:

In a static, loaded bicycle wheel, do the bottom spokes push up on the hub
to support it?

Yes or no?

pk

Date: 16 May 2007 20:42:37
From: p.k.
Subject: Re: Block chain and wooden spokes

carlfogel@comcast.net wrote:

> "The bottom spoke contributes 345.216 N of lift. The top spoke
> contributes only 12.487."

That line contains the conceptual error that Ian compounds in his. He has
subtracted the initial pretension, as is valid for computational purposes,
but it must be added back in before physical interpretations are made. Once
it is added back it is clear that the lower spokes do not contribute lift at
all, they pull down less as the rim deforms and they shorten.

Ian's FEA and maths are excellent engineering calculations, but his
interpretation of the physics is wrong.

pk

Date: 16 May 2007 23:09:09
From: Michael Press
Subject: Re: Block chain and wooden spokes

In article <UMqdncIk8OJZw9bbRVnyhgA@bt.com >,
"p.k." <pgkaddy-groups@yahoo.com > wrote:

> carlfogel@comcast.net wrote:
>
> > "The bottom spoke contributes 345.216 N of lift. The top spoke
> > contributes only 12.487."
>
>
> That line contains the conceptual error that Ian compounds in his. He has
> subtracted the initial pretension, as is valid for computational purposes,
> but it must be added back in before physical interpretations are made. Once
> it is added back it is clear that the lower spokes do not contribute lift at
> all, they pull down less as the rim deforms and they shorten.
>
> Ian's FEA and maths are excellent engineering calculations, but his
> interpretation of the physics is wrong.

You are right and everyone else is wrong.
Time to go home guys, the jig is up.

--
Michael Press

Date: 16 May 2007 23:08:54
From:
Subject: Re: Block chain and wooden spokes

Paul Kaddy writes:

>>>> Spokes do their work in compression as they pass the ground
>>>> contact point of the wheel.

>>> So you mean that, as it passes through the ground contact point,
>>> the spoke pushes up on the hub?

As I said, non-algebraic thinking is the greatest hurdle to
understanding what occurs in prestressed structures. You must be able
to add and subtract positive and negative numbers. I take it you
don't do that or you would see that adding a -200 lbs to each spoke
doesn't change the problem but allows adding 200 lbs downward load on
the hub without any spokes becoming slack.

>> "The bottom spoke contributes 345.216 N of lift. The top spoke
>> contributes only 12.487."

> That line contains the conceptual error that Ian compounds in
> his. He has subtracted the initial pretension, as is valid for
> computational purposes, but it must be added back in before physical
> interpretations are made. Once it is added back it is clear that the
> lower spokes do not contribute lift at all, they pull down less as
> the rim deforms and they shorten.

You may believe there is an error but your concept is the one that is
amiss. If you were to cyclically load such a wheel without rotation,
you would find that the bottom few spokes are the ones that would fail
in fatigue, not the upper ones, since they see no significant tension
change from any downward load placed on the hub.

> Ian's FEA and maths are excellent engineering calculations, but his
> interpretation of the physics is wrong.

I think you'll need to do more than say so to show that he, Professor
Wiedemer (whose work is cited in "the Bicycle Wheel"), and others who
have analyzed spoked wheel stresses are wrong.

Have you dropped in on your bicycle shop and perused "the Bicycle
Wheel" so you can see what has been researched?

Jobst Brandt

Date: 17 May 2007 08:55:40
From: p.k.
Subject: Re: Block chain and wooden spokes

jobst.brandt@stanfordalumni.org wrote:

> If you were to cyclically load such a wheel without rotation,
> you would find that the bottom few spokes are the ones that would fail
> in fatigue, not the upper ones, since they see no significant tension
> change from any downward load placed on the hub.

That is correct. The bottom spokes show the greatest change in tension when
the wheel is loaded.

But the physics is clear: the hub does not experience any upward push from
the lower spokes.

Can you clarify so that I can really understand what you are saying: Are you
saying that the hub experiences an upward push from the lower spokes?

>> Ian's FEA and maths are excellent engineering calculations, but his
>> interpretation of the physics is wrong.
>
> I think you'll need to do more than say so to show that he, Professor
> Wiedemer (whose work is cited in "the Bicycle Wheel"), and others who
> have analyzed spoked wheel stresses are wrong.

The analysis is correct the interpretation is wrong.

>
> Have you dropped in on your bicycle shop and perused "the Bicycle
> Wheel" so you can see what has been researched?

I have copies of the relevant bits in front of me now!

You also said:
>As I said, non-algebraic thinking is the greatest hurdle to
>understanding what occurs in prestressed structures

No, a failure to understand that a compressive load can be transferred by
tensile members to another element in compression is the greatest hurdle

pk

Date: 16 May 2007 21:50:59
From: jim beam
Subject: Re: Block chain and wooden spokes

jobst.brandt@stanfordalumni.org wrote:
> Paul Kaddy writes:
>
>>>>> Spokes do their work in compression as they pass the ground
>>>>> contact point of the wheel.
>
>>>> So you mean that, as it passes through the ground contact point,
>>>> the spoke pushes up on the hub?
>
> As I said, non-algebraic thinking is the greatest hurdle to
> understanding what occurs in prestressed structures. You must be able
> to add and subtract positive and negative numbers. I take it you
> don't do that or you would see that adding a -200 lbs to each spoke
> doesn't change the problem but allows adding 200 lbs downward load on
> the hub without any spokes becoming slack.
>
>>> "The bottom spoke contributes 345.216 N of lift. The top spoke
>>> contributes only 12.487."
>
>> That line contains the conceptual error that Ian compounds in
>> his. He has subtracted the initial pretension, as is valid for
>> computational purposes, but it must be added back in before physical
>> interpretations are made. Once it is added back it is clear that the
>> lower spokes do not contribute lift at all, they pull down less as
>> the rim deforms and they shorten.
>
> You may believe there is an error but your concept is the one that is
> amiss. If you were to cyclically load such a wheel without rotation,
> you would find that the bottom few spokes are the ones that would fail
> in fatigue, not the upper ones, since they see no significant tension
> change from any downward load placed on the hub.
>
>> Ian's FEA and maths are excellent engineering calculations, but his
>> interpretation of the physics is wrong.
>
> I think you'll need to do more than say so to show that he, Professor
> Wiedemer (whose work is cited in "the Bicycle Wheel"), and others who
> have analyzed spoked wheel stresses are wrong.
>
> Have you dropped in on your bicycle shop and perused "the Bicycle
> Wheel" so you can see what has been researched?

is this the book that alleges that it's possible to eliminate fatigue
from spokes with no endurance limit? is this the book that gets, er,
"confused" about strain aging materials and their deformation without
work hardening? is this the book that recommends spoke tension "as high
as the rim can bear" without demonstrating any understanding of the
effect this has on buckling or fatigue? is this the book that
criticizes anodized rims based on a fundamental misinterpretation of an
inappropriate test and non-comprehension of basic fracture mechanics?
is this the book that fails to account for spoke gauge in its
tensiometer math? is this the book that... hang it. does this list
have to be repeated endlessly before the book's author gets a clue and
publishes corrections?

Date: 16 May 2007 20:56:33
From: Clive George
Subject: Re: Block chain and wooden spokes

"p.k." <pgkaddy-groups@yahoo.com > wrote in message
news:UMqdncIk8OJZw9bbRVnyhgA@bt.com...
> carlfogel@comcast.net wrote:
>
>> "The bottom spoke contributes 345.216 N of lift. The top spoke
>> contributes only 12.487."
>
>
> That line contains the conceptual error that Ian compounds in his. He has
> subtracted the initial pretension, as is valid for computational purposes,
> but it must be added back in before physical interpretations are made.
> Once it is added back it is clear that the lower spokes do not contribute
> lift at all, they pull down less as the rim deforms and they shorten.
>
> Ian's FEA and maths are excellent engineering calculations, but his
> interpretation of the physics is wrong.

You bored or something? While you're at it why not start a helmet thread?

clive

Date: 16 May 2007 21:09:06
From: p.k.
Subject: Re: Block chain and wooden spokes

Clive George wrote:
> You bored or something? While you're at it why not start a helmet
> thread?
> clive

I am, actually! Bee waiting in all day for a repair man and its too wet to
garden.

But the thread started so I thought I'd join in!

Helmet threads are no fun as both sides have valid arguments and the
sensible thing is to agree to differ.

The hub support argument is much more fun!

pk

Date: 16 May 2007 17:59:10
From:
Subject: Re: Block chain and wooden spokes

Ben C? writes:

>>> If the spokes were pre-compressed with a pre-compression greater
>>> than the load you're putting on the wheel, you would see no change
>>> in the bottom spokes and a reduction in compression in the top
>>> spokes.

>> I don't know if your theory about heavily pre-compressed wheels is
>> correct, but I'd love to see a practical example.

>> Off-hand, I wonder if you're mistaken. Under load, the round wheel
>> rim will flatten at the contact patch toward the hub, shortening
>> the distance between the rim and the hub and compressing the
>> lowermost spokes even more.

> I think you're right.

> If the rim were perfectly rigid, I still think we might see
> reduction in compression in the top spokes and no change in the
> bottom spokes. If not I would interested to hear the explanation.

In a perfectly rigid rim the hub would displace downward under load,
the lengthening and shortening of the "membrane" of spokes being given
by trigonometric functions of their angular positions in the wheel.

This is not a bicycle wheel! The rim of a bicycle wheel has little
bending strength and can be deflected, by the push of a thumb on a
bare rim, many times more than when heavily loaded in a built-up
wheel. The elasticity of the wheel is given primarily by spoke
elasticity, which itself is imperceptibly small. Therefore most
visualizations fall far from actual deformation of a bicycle wheel.

I suggest you peruse the derivations and graphic explanations of how
spoked wheels support loads before deciding what net forces act in a
wheel. This requires adding and subtracting positive and negative
numbers and there is where the problem of visualization begins to
falter.

> But in practice the load is shared between the rim and the
> spokes. So the rim will deform a bit, increasing the compression in
> the bottom spokes. I would also expect to see a reduction in
> compression of the top spokes however.

Well it isn't so. For this reason technical aspects precede practical
aspects of building bicycle wheels in "the Bicycle Wheel".
Understanding the problem helps in building wheels correctly so they
don't fall apart from insufficient tension. The bottom (4-6) spokes
must be able to compress without slackening to be a durable wheel.

Spokes do their work in compression as they pass the ground contact
point of the wheel. That is why it is appropriate to say the wheel
stands on its bottom spokes, be that a wooden wagon wheel, die cast
moped wheel, or wire spoked bicycle/motorcycle wheel.

>> That is, a load acting downward should push even harder on the
>> pre-compressed spoke under it, compressing it even more. Your
>> theory seems to require the axle to rise under a load.

> Or to stay exactly where it is if the rim is rigid.

There are no "rigid" rims in real life.

Jobst Brandt

Date: 17 May 2007 00:41:21
From: Ben C
Subject: Re: Block chain and wooden spokes

On 2007-05-16, jobst.brandt@stanfordalumni.org <jobst.brandt@stanfordalumni.org > wrote:
> Ben C? writes:
[...]
>> But in practice the load is shared between the rim and the
>> spokes. So the rim will deform a bit, increasing the compression in
>> the bottom spokes. I would also expect to see a reduction in
>> compression of the top spokes however.
>
> Well it isn't so. For this reason technical aspects precede practical
> aspects of building bicycle wheels in "the Bicycle Wheel".
> Understanding the problem helps in building wheels correctly so they
> don't fall apart from insufficient tension. The bottom (4-6) spokes
> must be able to compress without slackening to be a durable wheel.

It's possible you have misunderstood. I'm not talking here about a
bicycle wheel, but about a wheel with precompressed spokes, where the
precompression exceeds the load.

I have a concrete slab sitting on a table, the slab is pushing down on
the table with a force of -1000N and the table is pushing back up with a
force of 1000N. If I try to lift up the slab, adding 100N, you might
think there is now 1000N + 100N - 1000N = 100N on the slab and that it
will therefore start to accelerate upwards.

Of course it doesn't. What happens is that as soon as I apply 100N, the
table goes from applying 1000N to only applying 900N and the system
remains static until I apply > 1000N myself, at which point the table
is contributing nothing, and the slab rises.

But if I apply -100N (i.e. downwards), the slab's weight doesn't
suddenly drop to -900N, leaving the table pushing up with 1000N. Instead
the table responds with an extra 100N and we have 1100N up and -1100N
down.

How do we explain this asymmetry? Well, the slab's role is very
different from that of the table. The slab always applies -1000N, and
the table always resists whatever is applied to it (until it breaks).
Why? The slab's -1000N because of gravity, the table's resistance just
because it is a "rigid body". Probably, at one step less abstraction,
both the slab and table are like very stiff compression springs, and as
I take 100N of the weight of the slab, it will rise an imperceptible
amount as the springs become slightly longer. But as the stiffness of
those springs approaches infinity, the situation approaches that of the
rigidy body model.

So what about a hub in a perfectly rigid two-spoked wheel, where the
spoke above and the spoke below are both in compression? The lower spoke
is applying say 1000N and the upper one -1000N. If I apply -100N at the
hub, what happens? Does (A) the top spoke keep up its -1000N so now the
lower spoke has to react with 1100N? Or does (B) the top spoke drop to
only -900N while the lower spoke continues to push up against the hub
with 1000N (to match my -100N and the top spoke's -900N)?

In scenario (A), the top spoke is unaffected and the bottom spoke
experiences an increase in compression. In scenario (B), the top spoke
experiences a reduction in compression, and the bottom spoke is
unaffected.

I'm pretty sure (A) is wrong and (B) is right. Both of the spoke forces
in this wheel are "rigid body forces" of the kind that the table was
resisting the slab with in the first example. The more I push down on the
the hub, the less the top spoke does, until eventually its contribution
goes to zero. At that point there is no compression in the top spoke and
only then I am able to increase the force on the bottom spoke.

So what happens if we take a step closer to the "real" world and think
of everything as a stiff, but not infinitely stiff, spring? In that
case, Hooke's law applies, and if we see a reduction in compression we
must see an increase in length, and vice versa. I am therefore led to
the conclusion that this wheel, rather than flattening at the bottom,
must bulge slightly at the top when it is loaded, while the distance
from the hub to the contact patch remains constant.

Note that if we consider a pre-tensioned wheel in the same way, we see a
precisely symmetric situation, with a reduction in tension of the bottom
spoke, no change in the top spoke, and a flattening of the rim towards
the hub at the bottom. This is consistent with observations.

> Spokes do their work in compression as they pass the ground contact
> point of the wheel. That is why it is appropriate to say the wheel
> stands on its bottom spokes, be that a wooden wagon wheel, die cast
> moped wheel, or wire spoked bicycle/motorcycle wheel.
>
>>> That is, a load acting downward should push even harder on the
>>> pre-compressed spoke under it, compressing it even more. Your
>>> theory seems to require the axle to rise under a load.
>
>> Or to stay exactly where it is if the rim is rigid.
>
> There are no "rigid" rims in real life.

Of course not, but the physics is still interesting, and helps in
understanding how it works when you then consider deformability.

Date: 18 May 2007 17:47:20
From:
Subject: Re: Block chain and wooden spokes

Ben C? writes:

>>> But in practice the load is shared between the rim and the
>>> spokes. So the rim will deform a bit, increasing the compression
>>> in the bottom spokes. I would also expect to see a reduction in
>>> compression of the top spokes however.

>> Well it isn't so. For this reason technical aspects precede
>> practical aspects of building bicycle wheels in "the Bicycle
>> Wheel". Understanding the problem helps in building wheels
>> correctly so they don't fall apart from insufficient tension. The
>> bottom (4-6) spokes must be able to compress without slackening to
>> be a durable wheel.

> It's possible you have misunderstood. I'm not talking here about a
> bicycle wheel, but about a wheel with precompressed spokes, where
> the precompression exceeds the load.

> ...

Just to add a bit of prestressed bicycle technology to spoked wheels,
consider the inflated tire on which the wheel stands. What keeps the
rim of the wheel off the ground? By your definition, it cannot he be
the tire casing, made of flexible cords, because they cannot support
compression.

======================================================================
What holds the rim off the ground?

What forces keep the rim of a wheel with pneumatic tires off the
ground. It can't be the inflation pressure because it is uniform
around the rim so it must be the tire casing of flexible cords.

The casing walls are pretensioned by inflation pressure and pull on
the rim (or its equivalent) and thereby support the load. The casing
leaves the rim at about a 45 degree angle, and being essentially a
circular cross section, it is in contact with the rim over
approximately a quarter of its inner cross section. The visualization
may be simpler if a tubular tire is considered. It makes no
difference whether the tire is held on by glue or is attached as a
clincher tire.

When loaded, the tire bulges laterally in the ground contact zone
causing two effects that reduce downward pull (increase the net upward
force) of the casing. First, the most obvious one is that the casing
pulls more to the sides than downward (than it did in its unloaded
condition); the second is that the side wall tension is reduced. The
reduction arises from the relationship that unit casing tension is
equivalent to inflation pressure times the radius of curvature divided
by pi. As the curvature reduces when the tire bulges out, the casing
tension decreases correspondingly. The inflated tire supports the rim
primarily by these two effects that reduce downward force on the rim.

Tire pressure changes imperceptibly when the tire is loaded because
the volume does not change appreciably. Also, the volume change is
insignificantly small in comparison to the volume change the air has
undergone when being compressed into the tire. In that respect, it
takes several strokes of a frame pump to increase the pressure of a
tire from 100 psi to 101. The air has a low spring constant that acts
like a long soft spring that has been preloaded over a long stroke.
Small deflections do not change its force materially. For example,
car and truck tires are regularly inflated to their proper pressure
before being mounted on the vehicle.

======================================================================
Hoyt McKagen writes:

> That's a nice offer, but with no disrespect I think you should
> yourself review the terms as defined by convention, in reference to
> actual molecular behavior. I will continue to soldier along on my
> previous eight years of employment in a materials testing
> environment, with nearly daily exposure to and practice with the
> actual devices and concepts, and of course with frequent inteactions
> the people who were adaquately based in theory.

Let's take another example of superposition. Assume two tubular
concentric columns, one of steel the other aluminum, both exactly the
same length and attached firmly to common end plates. Their cross
sectional areas are chosen to be proportional to the elasticities of
steel and aluminum, so each supports half of any axial load. The
length change from loads is predictable from the column dimensions.

Because aluminum and steel have different coefficients of thermal
expansion, heating or cooling the unloaded column will cause tension
and compression in the two parts. However, when a load is applied,
the axial length change will be identical regardless of the
temperature, and therefore, the stresses in the two components.

Regardless of temperature, both parts support half the load, and both
parts change length identically whether the load is tensile or
compressive. A compressive load, for instance, stands half and half
on the aluminum and steel columns whether they are above or below the
equilibrium temperature, regardless of whether the separate components
are under tension or compression.

This example demonstrates that preload in a structure affects the
stress in the elements, but not whether they support load. In a
tensioned wire spoked wheel the spokes between the hub and road are
compressed to give a net upward force, an algebraic addition of forces
that leaves the affected spokes in tension but compressed to a lower
tension than when unloaded. They are tensioned only to prevent
buckling, behaving as compression members otherwise.
======================================================================

Jobst Brandt

Date: 17 May 2007 07:46:42
From:
Subject: Re: Block chain and wooden spokes

Ben C? writes:

>>> But in practice the load is shared between the rim and the
>>> spokes. So the rim will deform a bit, increasing the compression
>>> in the bottom spokes. I would also expect to see a reduction in
>>> compression of the top spokes however.

>> Well it isn't so. For this reason technical aspects precede
>> practical aspects of building bicycle wheels in "the Bicycle
>> Wheel". Understanding the problem helps in building wheels
>> correctly so they don't fall apart from insufficient tension. The
>> bottom (4-6) spokes must be able to compress without slackening to
>> be a durable wheel.

> It's possible you have misunderstood. I'm not talking here about a
> bicycle wheel, but about a wheel with pre-compressed spokes, where
> the pre-compression exceeds the load.

The preload has no effect on the load path from hum to road other than
to assure that the spoke does not buckle if it is slender. Equations
involving elastic modulus and length to diameter ratios govern that
limit. See buckling of beams in strength of materials texts.

> I have a concrete slab sitting on a table, the slab is pushing down
> on the table with a force of -1000N and the table is pushing back up
> with a force of 1000N. If I try to lift up the slab, adding 100N,
> you might think there is now 1000N + 100N - 1000N = 100N on the slab
> and that it will therefore start to accelerate upward.

I don't see where you get that notion. I think you need to visualize
some free body diagrams and resolve the forces involved. I think you
are building a straw man with incorrect assumptions that support your
perception of the problem.

> Of course it doesn't. What happens is that as soon as I apply 100N,
> the table goes from applying 1000N to only applying 900N and the
> system remains static until I apply > 1000N myself, at which point
> the table is contributing nothing, and the slab rises.

> But if I apply -100N (i.e. downward), the slab's weight doesn't
> suddenly drop to -900N, leaving the table pushing up with 1000N.
> Instead the table responds with an extra 100N and we have 1100N up
> and -1100N down.

I don't see where this is leading. It make no sense to me.

> How do we explain this asymmetry? Well, the slab's role is very
> different from that of the table. The slab always applies -1000N,
> and the table always resists whatever is applied to it (until it
> breaks). Why? The slab's -1000N because of gravity, the table's
> resistance just because it is a "rigid body". Probably, at one step
> less abstraction, both the slab and table are like very stiff
> compression springs, and as I take 100N of the weight of the slab,
> it will rise an imperceptible amount as the springs become slightly
> longer. But as the stiffness of those springs approaches infinity,
> the situation approaches that of the rigid body model.

This is becoming weirderer and weirderer, in a manner of speaking.
This is not the way structural engineering is analyzed.

> So what about a hub in a perfectly rigid two-spoked wheel, where the
> spoke above and the spoke below are both in compression? The lower
> spoke is applying say 1000N and the upper one -1000N. If I apply
> -100N at the hub, what happens? Does (A) the top spoke keep up its
> -1000N so now the lower spoke has to react with 1100N? Or does (B)
> the top spoke drop to only -900N while the lower spoke continues to
> push up against the hub with 1000N (to match my -100N and the top
> spoke's -900N)?

There is no perfectly rigid material, especially as a hoop with one
spoke up and one down from the center. You are building an artificial
model that doesn't reflect reality.

> In scenario (A), the top spoke is unaffected and the bottom spoke
> experiences an increase in compression. In scenario (B), the top
> spoke experiences a reduction in compression, and the bottom spoke
> is unaffected.

You didn't specify relative elasticities of the hoop and spokes so you
cannot say anything about load distribution from an applied force at
the center.

> I'm pretty sure (A) is wrong and (B) is right. Both of the spoke
> forces in this wheel are "rigid body forces" of the kind that the
> table was resisting the slab with in the first example. The more I
> push down on the the hub, the less the top spoke does, until
> eventually its contribution goes to zero. At that point there is no
> compression in the top spoke and only then I am able to increase the
> force on the bottom spoke.

I cannot comment on this because your model defies structural reality.
You can do that if you want, but it has no bearing on how actual
wheels respond to loads.

> So what happens if we take a step closer to the "real" world and
> think of everything as a stiff, but not infinitely stiff, spring?
> In that case, Hooke's law applies, and if we see a reduction in
> compression we must see an increase in length, and vice versa. I am
> therefore led to the conclusion that this wheel, rather than
> flattening at the bottom, must bulge slightly at the top when it is
> loaded, while the distance from the hub to the contact patch remains
> constant.

I don't think you understand elasticities and relative stiffnesses of
materials, or you wouldn't be constructing such an unreal model to
describe what occurs when a wheel is loaded at the hub.

> Note that if we consider a pre-tensioned wheel in the same way, we
> see a precisely symmetric situation, with a reduction in tension of
> the bottom spoke, no change in the top spoke, and a flattening of
> the rim toward the hub at the bottom. This is consistent with
> observations.

>> Spokes do their work in compression as they pass the ground contact
>> point of the wheel. That is why it is appropriate to say the wheel
>> stands on its bottom spokes, be that a wooden wagon wheel, die cast
>> moped wheel, or wire spoked bicycle/motorcycle wheel.

>>>> That is, a load acting downward should push even harder on the
>>>> pre-compressed spoke under it, compressing it even more. Your
>>>> theory seems to require the axle to rise under a load.

>>> Or to stay exactly where it is if the rim is rigid.

>> There are no "rigid" rims in real life.

> Of course not, but the physics is still interesting, and helps in
> understanding how it works when you then consider deformability.

You may feel comfortable with what you have constructed, but it is
unreal and does not help understand what occurs in a real wheel. Have
you looked at "the Bicycle Wheel" in which these assumptions were
anticipated and explained with examples for how to verify load paths
from hub to road?

Please do that. You probably do not know that all this has come up at
least once per year for the last twenty or more years with the same
non-engineering arguments. Some readers express little patience with
your approach, because it has been argued equally ineffectively often.

Jobst Brandt

Date: 17 May 2007 04:33:30
From: Ben C
Subject: Re: Block chain and wooden spokes

On 2007-05-17, jobst.brandt@stanfordalumni.org <jobst.brandt@stanfordalumni.org > wrote:
> Ben C? writes:
[...]
>> I have a concrete slab sitting on a table, the slab is pushing down
>> on the table with a force of -1000N and the table is pushing back up
>> with a force of 1000N. If I try to lift up the slab, adding 100N,
>> you might think there is now 1000N + 100N - 1000N = 100N on the slab
>> and that it will therefore start to accelerate upward.
>
> I don't see where you get that notion.

I think you missed my next sentence. "Of course it doesn't".

> I think you need to visualize
> some free body diagrams and resolve the forces involved. I think you
> are building a straw man with incorrect assumptions that support your
> perception of the problem.

That may very well be true.

>> Of course it doesn't. What happens is that as soon as I apply 100N,
>> the table goes from applying 1000N to only applying 900N and the
>> system remains static until I apply > 1000N myself, at which point
>> the table is contributing nothing, and the slab rises.
>
>> But if I apply -100N (i.e. downward), the slab's weight doesn't
>> suddenly drop to -900N, leaving the table pushing up with 1000N.
>> Instead the table responds with an extra 100N and we have 1100N up
>> and -1100N down.
>
> I don't see where this is leading. It make no sense to me.

A slab on a table pushing down with 1000N. I also push down with 1000N.
The table resists with 1100N. Where's the problem?

>> How do we explain this asymmetry? Well, the slab's role is very
>> different from that of the table. The slab always applies -1000N,
>> and the table always resists whatever is applied to it (until it
>> breaks). Why? The slab's -1000N because of gravity, the table's
>> resistance just because it is a "rigid body". Probably, at one step
>> less abstraction, both the slab and table are like very stiff
>> compression springs, and as I take 100N of the weight of the slab,
>> it will rise an imperceptible amount as the springs become slightly
>> longer. But as the stiffness of those springs approaches infinity,
>> the situation approaches that of the rigid body model.
>
> This is becoming weirderer and weirderer, in a manner of speaking.
> This is not the way structural engineering is analyzed.

Surely you've done those basic physics problems, with books on tables,
ladders leaning against walls, things hanging off ropes? In all these
models the bodies are assumed to be rigid. No-one says "Impossible,
nothing is rigid!" and refuses to answer the question. It is possible to
analyze things in these terms.

If the bodies are thought of as stiff springs, the behaviour approaches
the behaviour of the rigid body analysis as the springs' stiffnesses
approach infinity. If the springs are significantly less stiff, the
configuration alters as forces are applied and the rigid body model is
no longer applicable.

I don't see what's so weird about this.

>> So what about a hub in a perfectly rigid two-spoked wheel, where the
>> spoke above and the spoke below are both in compression? The lower
>> spoke is applying say 1000N and the upper one -1000N. If I apply
>> -100N at the hub, what happens? Does (A) the top spoke keep up its
>> -1000N so now the lower spoke has to react with 1100N? Or does (B)
>> the top spoke drop to only -900N while the lower spoke continues to
>> push up against the hub with 1000N (to match my -100N and the top
>> spoke's -900N)?
>
> There is no perfectly rigid material, especially as a hoop with one
> spoke up and one down from the center. You are building an artificial
> model that doesn't reflect reality.

I believe not. I've done enough physics questions involving books
sitting on tables etc. to know that one can do better than "Rubbish! the
question makes no sense since nothing is rigid".

[...]
>> I'm pretty sure (A) is wrong and (B) is right. Both of the spoke
>> forces in this wheel are "rigid body forces" of the kind that the
>> table was resisting the slab with in the first example. The more I
>> push down on the the hub, the less the top spoke does, until
>> eventually its contribution goes to zero. At that point there is no
>> compression in the top spoke and only then I am able to increase the
>> force on the bottom spoke.
>
> I cannot comment on this because your model defies structural reality.
> You can do that if you want, but it has no bearing on how actual
> wheels respond to loads.

Well I would be interested to hear your analysis of the forces in a
completely rigid precompressed wheel.

>> So what happens if we take a step closer to the "real" world and
>> think of everything as a stiff, but not infinitely stiff, spring?
>> In that case, Hooke's law applies, and if we see a reduction in
>> compression we must see an increase in length, and vice versa. I am
>> therefore led to the conclusion that this wheel, rather than
>> flattening at the bottom, must bulge slightly at the top when it is
>> loaded, while the distance from the hub to the contact patch remains
>> constant.
>
> I don't think you understand elasticities and relative stiffnesses of
> materials, or you wouldn't be constructing such an unreal model to
> describe what occurs when a wheel is loaded at the hub.
[...]
>> Of course not, but the physics is still interesting, and helps in
>> understanding how it works when you then consider deformability.
>
> You may feel comfortable with what you have constructed, but it is
> unreal and does not help understand what occurs in a real wheel. Have
> you looked at "the Bicycle Wheel" in which these assumptions were
> anticipated and explained with examples for how to verify load paths
> from hub to road?

Does it explain forces in rigid, highly precompressed wheels?

> Please do that. You probably do not know that all this has come up at
> least once per year for the last twenty or more years with the same
> non-engineering arguments.
> Some readers express little patience with your approach, because it
> has been argued equally ineffectively often.

I've seen very little on RBT (and just searched the archives) about
forces in precompressed wheels in which precompression exceeds load.

I have not found anyone give an explanation of the kind I just did. You
said yourself it was "weirderer".

My understanding of pre-tensioned wheels is consistent with yours,
although it may be that my perception of their behaviour is right but
for the wrong reasons. That is why I am interested in the pre-compressed
case. I am _not_ talking about faintly precompressed wagon wheels, but
about wheels in which the precompression exceeds the load.

No-one's forcing you to follow up if you aren't interested.

Date: 17 May 2007 16:33:28
From:
Subject: Re: Block chain and wooden spokes

Ben C? writes:

>>> I have a concrete slab sitting on a table, the slab is pushing
>>> down on the table with a force of -1000N and the table is pushing
>>> back up with a force of 1000N. If I try to lift up the slab,
>>> adding 100N, you might think there is now 1000N + 100N - 1000N =
>>> 100N on the slab and that it will therefore start to accelerate
>>> upward.

>> I don't see where you get that notion.

> I think you missed my next sentence. "Of course it doesn't".

>> I think you need to visualize some free body diagrams and resolve
>> the forces involved. I think you are building a straw man with
>> incorrect assumptions that support your perception of the problem.

> That may very well be true.

>>> Of course it doesn't. What happens is that as soon as I apply
>>> 100N, the table goes from applying 1000N to only applying 900N and
>>> the system remains static until I apply > 1000N myself, at which
>>> point the table is contributing nothing, and the slab rises.

>>> But if I apply -100N (i.e. downward), the slab's weight doesn't
>>> suddenly drop to -900N, leaving the table pushing up with 1000N.
>>> Instead the table responds with an extra 100N and we have 1100N up
>>> and -1100N down.

>> I don't see where this is leading. It makes no sense to me.

> A slab on a table pushing down with 1000N. I also push down with
> 1000N. The table resists with 1100N. Where's the problem?

You are ignoring elasticity in the components and therefore, it
doesn't have any parallel to do with a prestressed spoked wheel.

>>> How do we explain this asymmetry? Well, the slab's role is very
>>> different from that of the table. The slab always applies -1000N,
>>> and the table always resists whatever is applied to it (until it
>>> breaks). Why? The slab's -1000N because of gravity, the table's
>>> resistance just because it is a "rigid body". Probably, at one
>>> step less abstraction, both the slab and table are like very stiff
>>> compression springs, and as I take 100N of the weight of the slab,
>>> it will rise an imperceptible amount as the springs become
>>> slightly longer. But as the stiffness of those springs approaches
>>> infinity, the situation approaches that of the rigid body model.

>> This is becoming weirderer and weirderer, in a manner of speaking.
>> This is not the way structural engineering is analyzed.

> Surely you've done those basic physics problems, with books on
> tables, ladders leaning against walls, things hanging off ropes? In
> all these models the bodies are assumed to be rigid. No-one says
> "Impossible, nothing is rigid!" and refuses to answer the
> question. It is possible to analyze things in these terms.

> If the bodies are thought of as stiff springs, the behaviour
> approaches the behaviour of the rigid body analysis as the springs'
> stiffnesses approach infinity. If the springs are significantly less
> stiff, the configuration alters as forces are applied and the rigid
> body model is no longer applicable.

> I don't see what's so weird about this.

You are mixing disparate models. The book-on-a-table model is not a
prestressed structure but rather layered objects with uni-directional
loading. The bicycle wheel is a prestressed structure that enables
wires to support tensile loads.

As an example, concrete is incapable of supporting significant tension
just as wire spokes are unable to support significant compression, yet
they are both strong structural materials and, prestressed they can
perform the functions that are not normally in their capabilities.

Concrete highway bridges have long horizontal beams that, from all
external appearances, are loaded in bending and therefore have their
bottom surface in tension and the top in compression. However, these
are prestressed beams in which steel rods in the lower portion of the
concrete beam are highly tensioned acting as preload springs. Steel
having a far greater elasticity than concrete, these rods remain at
essentially constant tension putting the concrete in high compression.

When prestressed concrete beams are loaded in bending, they gives up
some compression, appearing externally as if the underside were
stretching in tension. If these beams were to exceed their preload
and go into tension, they would crack, expose the steel to rusting and
collapse in time.

These are not inelastic rigid structures, just as a prestressed
bicycle wheel is not rigid. Elasticities play a role in the load
paths and the response of the structure.

>>> So what about a hub in a perfectly rigid two-spoked wheel, where
>>> the spoke above and the spoke below are both in compression? The
>>> lower spoke is applying say 1000N and the upper one -1000N. If I
>>> apply -100N at the hub, what happens? Does (A) the top spoke keep
>>> up its -1000N so now the lower spoke has to react with 1100N? Or
>>> does (B) the top spoke drop to only -900N while the lower spoke
>>> continues to push up against the hub with 1000N (to match my -100N
>>> and the top spoke's -900N)?

>> There is no perfectly rigid material, especially as a hoop with one
>> spoke up and one down from the center. You are building an
>> artificial model that doesn't reflect reality.

> I believe not. I've done enough physics questions involving books
> sitting on tables etc. to know that one can do better than "Rubbish!
> the question makes no sense since nothing is rigid".

Your "physics" is walking a narrow path, ignoring elasticities,
preloads and free body diagrams.

>> I'm pretty sure (A) is wrong and (B) is right. Both of the spoke
>> forces in this wheel are "rigid body forces" of the kind that the
>> table was resisting the slab with in the first example. The more I
>> push down on the the hub, the less the top spoke does, until
>> eventually its contribution goes to zero. At that point there is
>> no compression in the top spoke and only then I am able to increase
>> the force on the bottom spoke.

>> I cannot comment on this because your model defies structural
>> reality. You can do that if you want, but it has no bearing on how
>> actual wheels respond to loads.

> Well I would be interested to hear your analysis of the forces in a
> completely rigid pre-compressed wheel.

I cannot visualize that. How does your model get compressed if it is
not elastic? There is no compression in your proposal.

>>> So what happens if we take a step closer to the "real" world and
>>> think of everything as a stiff, but not infinitely stiff, spring?
>>> In that case, Hooke's law applies, and if we see a reduction in
>>> compression we must see an increase in length, and vice versa. I
>>> am therefore led to the conclusion that this wheel, rather than
>>> flattening at the bottom, must bulge slightly at the top when it
>>> is loaded, while the distance from the hub to the contact patch
>>> remains constant.

>> I don't think you understand elasticities and relative stiffnesses
>> of materials, or you wouldn't be constructing such an unreal model
>> to describe what occurs when a wheel is loaded at the hub. > [...]
>> >>> Of course not, but the physics is still interesting, and helps
>> in >>> understanding how it works when you then consider
>> deformability.

Leave "physics" out of this. That just makes it sound important but
adds nothing to the faulty models you propose. I don't believe you
have studied engineering from what you say and trying to describe how
it works is out of place.

>> You may feel comfortable with what you have constructed, but it is
>> unreal and does not help understand what occurs in a real wheel.
>> Have you looked at "the Bicycle Wheel" in which these assumptions
>> were anticipated and explained with examples for how to verify load
>> paths from hub to road?

> Does it explain forces in rigid, highly pre-compressed wheels?

That is a contradiction in terms.

>> Please do that. You probably do not know that all this has come up
>> at least once per year for the last twenty or more years with the
>> same non-engineering arguments. Some readers express little
>> patience with your approach, because it has been argued equally
>> ineffectively often.

> I've seen very little on RBT (and just searched the archives) about
> forces in pre-compressed wheels in which pre-compression exceeds
> load.

I don't think you searched correctly. I have encountered your
approach often over the years with little variation in perception of
prestressed structures.

> I have not found anyone give an explanation of the kind I just did.
> You said yourself it was "weirderer".

> My understanding of pre-tensioned wheels is consistent with yours,
> although it may be that my perception of their behaviour is right
> but for the wrong reasons. That is why I am interested in the
> pre-compressed case. I am _not_ talking about faintly pre-compressed
> wagon wheels, but about wheels in which the pre-compression exceeds
> the load.

I disagree with that statement. We do not see the problem in a
similar manner. Just consider that the bicycle wheel went more than
100 years without published understanding and analysis before "the
Bicycle Wheel", inspired by having heard enough of the
misrepresentations and mysteries of bicycle wheels.

> No-one's forcing you to follow up if you aren't interested.

What do you mean by that?

Jobst Brandt

Date: 17 May 2007 12:11:02
From: Ben C
Subject: Re: Block chain and wooden spokes

On 2007-05-17, jobst.brandt@stanfordalumni.org <jobst.brandt@stanfordalumni.org > wrote:
> Ben C? writes:
[...]
>>> Some readers express little patience with your approach, because it
>>> has been argued equally ineffectively often.
[...]
>> No-one's forcing you to follow up if you aren't interested.
>
> What do you mean by that?

I mean if you have little patience with my approach then don't worry
about it.

I know what you mean about the rigid body model being difficult to apply
in this situation, because how can those spokes be "compressed" if they
are rigid? It seems we need to think of them as stiff springs.

But how are they different from the table top supporting a book? Isn't
that also just an infinitely stiff spring for the purposes of the model?

Stiff springs are often used to model forces between rigid bodies (in
computer simulations for example), why can't the transformation go the
other way, provided deformations are small and don't alter the geometry
of the system?

I do not dismiss the rigid body model as easily as you do. But perhaps
this is not the right place for that discussion.

Date: 17 May 2007 04:36:45
From: Ben C
Subject: Re: Block chain and wooden spokes

On 2007-05-17, Ben C <spamspam@spam.eggs > wrote:
> On 2007-05-17, jobst.brandt@stanfordalumni.org <jobst.brandt@stanfordalumni.org> wrote:
[...]
>> I don't see where this is leading. It make no sense to me.
>
> A slab on a table pushing down with 1000N. I also push down with 1000N.
> The table resists with 1100N. Where's the problem?

Sorry I meant I push down with 100N!

Date: 16 May 2007 21:18:32
From: jim beam
Subject: Re: Block chain and wooden spokes

jobst.brandt@stanfordalumni.org wrote:
> Ben C? writes:
>
>>>> If the spokes were pre-compressed with a pre-compression greater
>>>> than the load you're putting on the wheel, you would see no change
>>>> in the bottom spokes and a reduction in compression in the top
>>>> spokes.
>
>>> I don't know if your theory about heavily pre-compressed wheels is
>>> correct, but I'd love to see a practical example.
>
>>> Off-hand, I wonder if you're mistaken. Under load, the round wheel
>>> rim will flatten at the contact patch toward the hub, shortening
>>> the distance between the rim and the hub and compressing the
>>> lowermost spokes even more.
>
>> I think you're right.
>
>> If the rim were perfectly rigid, I still think we might see
>> reduction in compression in the top spokes and no change in the
>> bottom spokes. If not I would interested to hear the explanation.
>
> In a perfectly rigid rim the hub would displace downward under load,
> the lengthening and shortening of the "membrane" of spokes being given
> by trigonometric functions of their angular positions in the wheel.

yes, but what's the load distribution???

>
> This is not a bicycle wheel! The rim of a bicycle wheel has little
> bending strength and can be deflected, by the push of a thumb on a
> bare rim, many times more than when heavily loaded in a built-up
> wheel. The elasticity of the wheel is given primarily by spoke
> elasticity, which itself is imperceptibly small.

bull.

> Therefore most
> visualizations fall far from actual deformation of a bicycle wheel.

evidently!

>
> I suggest you peruse the derivations and graphic explanations of how
> spoked wheels support loads before deciding what net forces act in a
> wheel. This requires adding and subtracting positive and negative
> numbers and there is where the problem of visualization begins to
> falter.

why not do it for a rigid rim and explain the principles of equilibrium?

>
>> But in practice the load is shared between the rim and the
>> spokes. So the rim will deform a bit, increasing the compression in
>> the bottom spokes. I would also expect to see a reduction in
>> compression of the top spokes however.
>
> Well it isn't so. For this reason technical aspects precede practical
> aspects of building bicycle wheels in "the Bicycle Wheel".
> Understanding the problem helps in building wheels correctly so they
> don't fall apart from insufficient tension.

but wheels don't fall apart from insufficient tension.
http://www.flickr.com/photos/38636024@N00/417157612/

> The bottom (4-6) spokes
> must be able to compress without slackening to be a durable wheel.

apparently not!

>
> Spokes do their work in compression as they pass the ground contact
> point of the wheel. That is why it is appropriate to say the wheel
> stands on its bottom spokes, be that a wooden wagon wheel, die cast
> moped wheel, or wire spoked bicycle/motorcycle wheel.

if by some convoluted quirk of nature, rim deformation occurred on the
opposite side of the wheel to that touching the ground, the spokes
furthest from the ground would lose the most tension. so would the
wheel then be standing on its lower spokes?

bottom line, the wheel is an equilibrium structure - if part distorts,
load on spokes is distributed accordingly. if the rim was perfectly
rigid, spoke load distribution would be different and your explanation
would be shown as incomplete. a wheel without any bottom spokes shows
your explanation incomplete come to that.

>
>>> That is, a load acting downward should push even harder on the
>>> pre-compressed spoke under it, compressing it even more. Your
>>> theory seems to require the axle to rise under a load.
>
>> Or to stay exactly where it is if the rim is rigid.
>
> There are no "rigid" rims in real life.

he said. searching for an excuse.

Date: 17 May 2007 14:45:01
From: waxbytes
Subject: Re: Block chain and wooden spokes

What supports the the hub on a disk wheel like they use in timetrials

--
waxbytes

Date: 17 May 2007 05:09:04
From: Steve Gravrock
Subject: Re: Block chain and wooden spokes

On 2007-05-17, waxbytes <waxbytes.2qpo1n@no-mx.forums.cyclingforums.com > wrote:
>
> What supports the the hub on a disk wheel like they use in timetrials?

Clearly, it hangs from the upper half of the disk.

Date: 16 May 2007 20:00:14
From: p.k.
Subject: Re: Block chain and wooden spokes

jobst.brandt@stanfordalumni.org wrote:
>
> Spokes do their work in compression as they pass the ground contact
> point of the wheel.

So you mean that, as it passes through the ground contact point, the spoke
pushes up on the hub?

pk

Date: 16 May 2007 08:36:22
From: p.k.
Subject: Re: Block chain and wooden spokes

Ben C wrote:
> On 2007-05-15, carlfogel@comcast.net <carlfogel@comcast.net> wrote:
>> On Tue, 15 May 2007 17:16:16 -0500, "DI" <di9999@cox.net> wrote:
>> [...] Sorry, but Jobst is just joking. Both pre-tensioned wire-spoke
>> bicycle wheels and faintly pre-compressed wooden-spoke wagon wheels
>> behave the same way--just about all the measurable action occurs in
>> the spokes under the hub, which show compression (the same thing as
>> loss of pre-tension).
>
> If the spokes were pre-compressed with a pre-compression greater than
> the load you're putting on the wheel, you would see no change in the
> bottom spokes and a reduction in compression in the top spokes.
>
> None of this has anything to do with whether the wheel "hangs from the
> top spokes" or "stands on the bottom spokes" in either kind of wheel.
> Hanging and standing are both consistent, depending on your use of
> language, with the correct physical interpretations of either
> pre-tensioned or pre-compressed wheels.

It's all very simple really, in any sensible and self consistent use of
English

A
: Something is standing if the forces which support it push up from below
: Something is hanging if the forces which support it pull up from above

B
:The spokes below a cycle wheel hub, pull down
:The spokes above a cycle wheel hub pull up.

C
:The forces supporting the hub pull up from above

http://home.comcast.net/~jlulm/Free_Body_Diagram_of_hub.pdf

pk

Date: 16 May 2007 07:26:20
From: Peter Cole
Subject: Re: Block chain and wooden spokes

p.k. wrote:
> Ben C wrote:
>> On 2007-05-15, carlfogel@comcast.net <carlfogel@comcast.net> wrote:
>>> On Tue, 15 May 2007 17:16:16 -0500, "DI" <di9999@cox.net> wrote:
>>> [...] Sorry, but Jobst is just joking. Both pre-tensioned wire-spoke
>>> bicycle wheels and faintly pre-compressed wooden-spoke wagon wheels
>>> behave the same way--just about all the measurable action occurs in
>>> the spokes under the hub, which show compression (the same thing as
>>> loss of pre-tension).
>> If the spokes were pre-compressed with a pre-compression greater than
>> the load you're putting on the wheel, you would see no change in the
>> bottom spokes and a reduction in compression in the top spokes.
>>
>> None of this has anything to do with whether the wheel "hangs from the
>> top spokes" or "stands on the bottom spokes" in either kind of wheel.
>> Hanging and standing are both consistent, depending on your use of
>> language, with the correct physical interpretations of either
>> pre-tensioned or pre-compressed wheels.
>
> It's all very simple really, in any sensible and self consistent use of
> English
>
> A
> : Something is standing if the forces which support it push up from below
> : Something is hanging if the forces which support it pull up from above
>
> B
> :The spokes below a cycle wheel hub, pull down
> :The spokes above a cycle wheel hub pull up.
>
> C
> :The forces supporting the hub pull up from above
>
> http://home.comcast.net/~jlulm/Free_Body_Diagram_of_hub.pdf
>
> pk
>
>
>
>

This is wrong.

The bottom spokes actually contribute to the net downward force on the
hub; i.e., they pull down on the hub, not push up, regardless of their
value, ***change in value***, or force history.

The "change in value" part is where it goes wrong.

Date: 16 May 2007 03:31:03
From: Ben C
Subject: Re: Block chain and wooden spokes

On 2007-05-16, p.k. <pgkaddy-groups@yahoo.com > wrote:
> Ben C wrote:
>> On 2007-05-15, carlfogel@comcast.net <carlfogel@comcast.net> wrote:
>>> On Tue, 15 May 2007 17:16:16 -0500, "DI" <di9999@cox.net> wrote:
>>> [...] Sorry, but Jobst is just joking. Both pre-tensioned wire-spoke
>>> bicycle wheels and faintly pre-compressed wooden-spoke wagon wheels
>>> behave the same way--just about all the measurable action occurs in
>>> the spokes under the hub, which show compression (the same thing as
>>> loss of pre-tension).
>>
>> If the spokes were pre-compressed with a pre-compression greater than
>> the load you're putting on the wheel, you would see no change in the
>> bottom spokes and a reduction in compression in the top spokes.
>>
>> None of this has anything to do with whether the wheel "hangs from the
>> top spokes" or "stands on the bottom spokes" in either kind of wheel.
>> Hanging and standing are both consistent, depending on your use of
>> language, with the correct physical interpretations of either
>> pre-tensioned or pre-compressed wheels.
>
> It's all very simple really, in any sensible and self consistent use of
> English
>
> A
>: Something is standing if the forces which support it push up from below
>: Something is hanging if the forces which support it pull up from above
>
> B
>:The spokes below a cycle wheel hub, pull down
>:The spokes above a cycle wheel hub pull up.
>
> C
>:The forces supporting the hub pull up from above

I think this is perfectly clear and makes good sense. But on the other
hand, Michael Press also makes a good point. This is why I think it's a
duck-rabbit. It may be that in more technical circles the idea that load
path is represented by strain change (i.e. weight stands on bottom
spokes) ahem carries more weight.

Date: 16 May 2007 09:44:11
From: p.k.
Subject: Re: Block chain and wooden spokes

Ben C wrote:
>
> I think this is perfectly clear and makes good sense. But on the other
> hand, Michael Press also makes a good point. This is why I think it's
> a duck-rabbit. It may be that in more technical circles the idea that
> load path is represented by strain change (i.e. weight stands on
> bottom spokes) ahem carries more weight.

Good artcle on load path here:

http://www.brantacan.co.uk/loadpath.htm

have a look at the diagram 5 on page 1.

A vertical mast supported by tensioned stays.

Consider a steady wind from the left to right.

The stays on the right increase in tension, the stays on the left decrease
in tension.

Which stays are stopping the mast falling?

pk

Date: 16 May 2007 12:25:10
From: Ben C
Subject: Re: Block chain and wooden spokes

On 2007-05-16, p.k. <pgkaddy-groups@yahoo.com > wrote:
> Ben C wrote:
>>
>> I think this is perfectly clear and makes good sense. But on the other
>> hand, Michael Press also makes a good point. This is why I think it's
>> a duck-rabbit. It may be that in more technical circles the idea that
>> load path is represented by strain change (i.e. weight stands on
>> bottom spokes) ahem carries more weight.
>
> Good artcle on load path here:
>
> http://www.brantacan.co.uk/loadpath.htm
>
> have a look at the diagram 5 on page 1.
>
> A vertical mast supported by tensioned stays.
>
> Consider a steady wind from the left to right.
>
> The stays on the right increase in tension, the stays on the left decrease
> in tension.

Don't you mean they increase in tension on the left, and decrease on the
right? If the stays are pretensioned enough, you will get the left one
remaining at the same tension and the right one slackening off a bit.

> Which stays are stopping the mast falling?

Both of them :)

Date: 16 May 2007 07:27:55
From: Peter Cole
Subject: Re: Block chain and wooden spokes

p.k. wrote:
> Ben C wrote:
>> I think this is perfectly clear and makes good sense. But on the other
>> hand, Michael Press also makes a good point. This is why I think it's
>> a duck-rabbit. It may be that in more technical circles the idea that
>> load path is represented by strain change (i.e. weight stands on
>> bottom spokes) ahem carries more weight.
>
> Good artcle on load path here:
>
> http://www.brantacan.co.uk/loadpath.htm

A rather bad article, actually.

>
> have a look at the diagram 5 on page 1.
>
> A vertical mast supported by tensioned stays.
>
> Consider a steady wind from the left to right.
>
> The stays on the right increase in tension, the stays on the left decrease
> in tension.

Not on my mast.

Date: 16 May 2007 12:32:28
From: p.k.
Subject: Re: Block chain and wooden spokes

Peter Cole wrote:
> p.k. wrote:
>> Ben C wrote:
>>> I think this is perfectly clear and makes good sense. But on the
>>> other hand, Michael Press also makes a good point. This is why I
>>> think it's a duck-rabbit. It may be that in more technical circles
>>> the idea that load path is represented by strain change (i.e.
>>> weight stands on bottom spokes) ahem carries more weight.
>>
>> Good artcle on load path here:
>>
>> http://www.brantacan.co.uk/loadpath.htm
>
> A rather bad article, actually.
>
>
>>
>> have a look at the diagram 5 on page 1.
>>
>> A vertical mast supported by tensioned stays.
>>
>> Consider a steady wind from the left to right.
>>
>> The stays on the right increase in tension, the stays on the left
>> decrease in tension.
>
> Not on my mast.

oops , i stasted the opposite wind direction!

pk

Date: 16 May 2007 01:25:51
From:
Subject: Re: Block chain and wooden spokes

Carl Fogel writes:

> Here's a pdf with graphs of actual strain gauge measurements of a
> single spoke as the bicycle is ridden:

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

> See figures 10 & 11, The huge icicle-spikes are where the
> pre-tensioned spoke rolled under the hub and lost tension.

I find interesting that Gavin still avoids even slight mention of what
moved him to perform this work. He cites Pippard, who really did have
it all wrong. As I experienced it, Gavin was originally spurred on by
publication of "the Bicycle Wheel" with which he strongly disagreed at
the time. The paper in the above pdf takes a more parallel view but
has enough Greek letters and log, log/log, and linear graphs to
impress the man on the street. In contrast, the web site below shows
roughly the same figures as shown in "the Bicycle Wheel".

I wonder if these authors also get the "you have it all wrong! The
wheel cannot stand on its spokes." that appears here from the UK about
once per year.

> Here's a page with the theory side:

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

> In the large table, look at the rightmost two columns, where T
> (tension) and C (compression) for the 36 spokes are split by
> sign. The tricky part is remembering that a spoke pointing somewhat
> downward from the hub (say 8 o'clock) is actually pulling the hub
> _down_ as its tension increases.

> It's a very annoying concept, since the naive expectation is that
> the bicycle spokes pointing up from the hub should show a huge
> increase in tension as the hub "hangs" the rider's weight from the
> rim. But it doesn't. The rim flattens toward the hub from the
> contact patch, shortening the distance between rim and hub and
> consequently losing spoke tension in that area. The other spokes
> stubbornly refuse to change tension anywhere near as much.

> RBT posters love to squabble about this.

Especially from the UK

Jobst Brandt

Date: 16 May 2007 06:10:17
From: jim beam
Subject: Re: Block chain and wooden spokes

jobst.brandt@stanfordalumni.org wrote:
> Carl Fogel writes:
>
>> Here's a pdf with graphs of actual strain gauge measurements of a
>> single spoke as the bicycle is ridden:
>
> http://www.duke.edu/~hpgavin/papers/HPGavin-Wheel-Paper.pdf
>
>> See figures 10 & 11, The huge icicle-spikes are where the
>> pre-tensioned spoke rolled under the hub and lost tension.
>
> I find interesting that Gavin still avoids even slight mention of what
> moved him to perform this work. He cites Pippard, who really did have
> it all wrong. As I experienced it, Gavin was originally spurred on by
> publication of "the Bicycle Wheel" with which he strongly disagreed at
> the time. The paper in the above pdf takes a more parallel view but
> has enough Greek letters and log, log/log, and linear graphs to
> impress the man on the street. In contrast, the web site below shows
> roughly the same figures as shown in "the Bicycle Wheel".
>
> I wonder if these authors also get the "you have it all wrong! The
> wheel cannot stand on its spokes." that appears here from the UK about
> once per year.
>
>> Here's a page with the theory side:
>
>> http://www.astounding.org.uk/ian/wheel/index.html
>
>> In the large table, look at the rightmost two columns, where T
>> (tension) and C (compression) for the 36 spokes are split by
>> sign. The tricky part is remembering that a spoke pointing somewhat
>> downward from the hub (say 8 o'clock) is actually pulling the hub
>> _down_ as its tension increases.
>
>> It's a very annoying concept, since the naive expectation is that
>> the bicycle spokes pointing up from the hub should show a huge
>> increase in tension as the hub "hangs" the rider's weight from the
>> rim. But it doesn't. The rim flattens toward the hub from the
>> contact patch, shortening the distance between rim and hub and
>> consequently losing spoke tension in that area. The other spokes
>> stubbornly refuse to change tension anywhere near as much.
>
>> RBT posters love to squabble about this.
>
> Especially from the UK
>
here's another example of geographically based ignorance: palo alto
"engineers" seem to know nothing about fatigue, fracture mechanics,
principles of deformation, anisotropy, ndt, bearings, etc. or even that
wheels "standing" on their spokes is simply a function of localized rim
deformation....

Date: 16 May 2007 08:40:51
From: DI
Subject: Re: Block chain and wooden spokes

"jim beam" <spamvortex@bad.example.net > wrote in message
news:zu6dnUvpvKkkn9bbnZ2dnUVZ_gGdnZ2d@speakeasy.net...

>>
> here's another example of geographically based ignorance: palo alto
> "engineers" seem to know nothing about fatigue, fracture mechanics,
> principles of deformation, anisotropy, ndt, bearings, etc. or even that
> wheels "standing" on their spokes is simply a function of localized rim
> deformation....

wheels "standing" on their spokes is simply a function of localized rim
deformation....

well said.

Date: 16 May 2007 09:52:46
From: Peter Cole
Subject: Re: Block chain and wooden spokes

DI wrote:
> "jim beam" <spamvortex@bad.example.net> wrote in message
> news:zu6dnUvpvKkkn9bbnZ2dnUVZ_gGdnZ2d@speakeasy.net...
>
>> here's another example of geographically based ignorance: palo alto
>> "engineers" seem to know nothing about fatigue, fracture mechanics,
>> principles of deformation, anisotropy, ndt, bearings, etc. or even that
>> wheels "standing" on their spokes is simply a function of localized rim
>> deformation....
>
> wheels "standing" on their spokes is simply a function of localized rim
> deformation....
>
> well said.
>
>

Actually it reveals a complete lack of understanding of the engineering
principles involved in bicycle wheels. There are books, for those who read.

Date: 16 May 2007 21:04:54
From: jim beam
Subject: Re: Block chain and wooden spokes

Peter Cole wrote:
> DI wrote:
>> "jim beam" <spamvortex@bad.example.net> wrote in message
>> news:zu6dnUvpvKkkn9bbnZ2dnUVZ_gGdnZ2d@speakeasy.net...
>>
>>> here's another example of geographically based ignorance: palo alto
>>> "engineers" seem to know nothing about fatigue, fracture mechanics,
>>> principles of deformation, anisotropy, ndt, bearings, etc. or even
>>> that wheels "standing" on their spokes is simply a function of
>>> localized rim deformation....
>>
>> wheels "standing" on their spokes is simply a function of localized
>> rim deformation....
>>
>> well said.
>>
>
> Actually it reveals a complete lack of understanding of the engineering
> principles involved in bicycle wheels. There are books, for those who read.

actually, failure to address rim behavior when analyzing spoke tension
deltas reveals a complete lack of understanding of engineering
principles involved in bicycle wheels. there are books, for those who
bother to enter engineering libraries.

Date: 16 May 2007 02:11:43
From: Ben C
Subject: Re: Block chain and wooden spokes

On 2007-05-16, jobst.brandt@stanfordalumni.org <jobst.brandt@stanfordalumni.org > wrote:
> Carl Fogel writes:
[...]
>> It's a very annoying concept, since the naive expectation is that
>> the bicycle spokes pointing up from the hub should show a huge
>> increase in tension as the hub "hangs" the rider's weight from the
>> rim. But it doesn't. The rim flattens toward the hub from the
>> contact patch, shortening the distance between rim and hub and
>> consequently losing spoke tension in that area. The other spokes
>> stubbornly refuse to change tension anywhere near as much.
>
>> RBT posters love to squabble about this.
>
> Especially from the UK

http://mathworld.wolfram.com/Rabbit-DuckIllusion.html

Is this a duck or a rabbit?