wheel puzzle

Re: wheel puzzle

On Sun, 19 May 2002 19:04:25 +0100,
Naomi Sajeri <Naomi_Sajeri@hotmail.com> wrote:

> And don’t wave your qualifications at me, and expect me to shrink
> back like a scared little girl:

I didn’t. If you recall you launched into your “I teach this stuff so
I must be right” before I made any comment about qualifications. What I
said is that you don’t need to provide incomplete explanations of linear
elasticity to me. Also, I observe that I merely suggested you assume that
I have an engineering degree in formulating your response. I made no
claim to qualifications.

> I assure you I outrank you considerably in
> both engineering qualifications and experience.

Interesting. How did you determine that? What are your qualifications?

Also, I would genuinely like to know what you have found out about my
qualifications, and what assumptions you are making about them. Please
feel free to drop the snide insinuations and be explicit.

> As regards your own engineering degree, your inability to understand
> resolution of forces into their vertical and horizontal components

Nope, sorry. What I said is that it’s not relevant, not that I didn’t
understand it. It’s not relevant because there’s no need to artificially
eliminate the horizontal components of the spoke forces because they all
cancel out anyway. Just vector sum the spoke tensions.

> totally incompatible with your having such a degree, save perhaps one of
> those offered for sale regularly in junk E-mails.

Hmm. Very amusing. Please explain what you know about my engineering
qualifications. I’m not really a great fan of insinuation - please be
specific.

> I saw no reason to go into fine scientific detail, for I had deduced
> from your post that it would have passed you by even more widely than
> did the simplified explanations.

I see. It appears that you are so confident in your argument that you’ve
decided it is better simply to descend to personal abuse. Oh well, I’d
still like to hear your response to my engineering.

> What we have here is simple school level physics/mechanics, it is not
> degree level…most bright 15 year olds could work most of the qualitative
> aspects of this out for themselves.

I agree, simple school mechanics can give you an answer. The problem is
determining whether the answer is right. I still believe you are assuming
an infinitely stiff rim, or at the very least a rim that is orders of
magnitude stiffer than the spokes.

> Using your engineering degree, rotate our 4 spoked wheel by 45 degrees.

As I noted earlier, the 4 spoke wheel is not a useful concept, since the
relative stiffness of rim and spokes is critical to teh distribution of
forces. The four spoke wheel, if rotated 45 degress, would collapse,
because the rim is insufficiently strong. Unless you’re assuming it’s
infinitely stiff and equivalently strong, of course…

> THROUGH THE SPOKES, and only through the spokes. If no force were being
> transmitted via the spokes, to the rim, the hub, you are gonna fall.

No-one has denied this. You’re arguing with a made-up person again. It
looks most like you can’t explain why you disagree with what I’ve said, so
instead you’ll disagree vehemently with something I didn’t say, and hope
that confuses me. It doesn’t.

I’ve never disagreed that load is transmitted through teh spokes. What
I’ve disagreed with is WHICH spokes conduct force. I maintain that the
force is conducted only through spokes local to the lowest part of the
rim. You disagreed with me, and have yet to provide any justification for
the disagreement that works for any wheel that actually exists in teh real
world.

> I have in no way assumed the rim to be infinitely rigid, I mentioned that
> all the materials in the uni are elastic, increase tension in any spoke and
> the rim will see a resultant deformation, but in order to deform the rim or
> to change its deformation, some of the spoke tensions have to change!!!

I have never said anything different.

> The concept of rim also having elasticity and deformation seemed too obvious
> to need to mention. It does not change the principles involved at all.

It fundamentally alters the distribution of teh forces. In particular,
with a ‘normally’ stiff rim, the rim deforms more readily than the spokes,
resulting in most of the load being carried in the lower spokes.

> amongst the increased number of spokes. But bear in mind that: if the
> upper spokes are NOT taking part in supporting your weight as you seem to
> be (wrongly) suggesting, then your weight must be being supported by the
> lower spokes. Need I tell you how weak spokes are in compression?

Have you ever heard of prestress?

The lower spokes carry all the imposed load by means of a reduction in
their tension. I was assuming you were familiar with teh principles of
linear superposition.
It’s a fundamental principle of linear elastic analysis.

> I suspect I do… they will bend. EASILY, and again you fall!

No-one has proposed any spokes go into compression. All of this was
covered very early in teh thread, did you read that?

> NS: What a load of ridiculous claptrap.

OK, I’ll be more specific, rather than trying to accomodate your elastic
bands. The elastic bands are a very poor analogy to the true system,
because of the fact that they are orders of magnitude less stiff than the
rim.

Consider your wheel. Suppose you apply a load at the hub, and the hub
moves closer to teh ground. Suppose in doing so it causes a deformation
in the rim which is entirely concentrated in teh vicinity of the contact
between the wheel and the ground. If there is no distortion of teh rim
away from teh ground, and the part of the rim above the hub displaces
by teh same amount as the hub, the spokes around teh upper part of the
wheel will not alter their tension from unloaded state.

OK? Do you agree with all that, IF the if clause is true?

Now - what is it that causes you to say my “if” is invalid?

That is, why do you assume that teh hub moves relative to teh upper part
of the rim? Why not assume that teh upper part of teh rim deflects with
teh hub, resulting in no change in force in teh spokes? Why do you assume
that the hub moving downwards stretches teh spokes, rather than assuming
the hub moving downwards takes the upper part of the rim downwards at teh
same time?

> As above: if the spokes do not change in tension there will be no rim
> distortion. one goes with the other.

As above: no-one (that I have seen) has argued that none of the spokes
change their tension - the discussion was about which.

Onto tyres:

> Agreed with the purpose of the threads, to strengthen the tyre against
> blowouts/stretching caused by the high internal pressure. Watch any
> unicyclist as he bunny hops. Then tell me the tyre is not significantly
> elastic.

It can bulge without any net axial deformation of the side-wall. The
sidewall is designed to flex, but not extend.

> affects its behaviour. In use the lower part of a tyre suffers major
> deformation with every revolution, nothing tiny, tiny about it…

Are you saying that flexure of a component necesarily introduces net
axial extension (or indeed compression)?

I’m still waiting for your explanation of why pressing the tyre with my
thumb doesn’t result in teh deflections you predicted, despite applying
three times teh force you predicted. You seem to have missed responding
to that.

Incidentally, there’s actually a much bigger flaw in my argument regarding
the operation of tyres than anything you’ve latched onto - you could try
attacking this:
My arguments thus far depend upon no change in volume and no change in
axial extension of the tyre material when undergoing deformation.
Clearly, this is somewhat flaky, since if you consider the energy state in
teh tyre system, if teh air hasn’t compressed and the tyre carcase hasn’t
elongated, then it’s difficult to see what drives any restoring of any
deflection. By my argument, if you press the tyre and it deflects, when
you release teh pressure it will stay deflected. Comparison with teh real
world indicates this does not occur. Have you any thoughts on that?

> In conclusion, I sincerely hope you are not using your “engineering degree”
> to design any structures on which life might depend.

You tell me - after all, you’re the expert on my career.

regards, Ian SMith

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Re: wheel puzzle

Muniuni,
Thank you for that. Nice to hear your support.

Ian,
I am not going to reply in detail to all that. You have distorted far too
many of my statements either in print or in your head when trying to
understand them. I did NOT say “I teach: therefore I am right”. I do
teach, and added a jest that maybe I should be paid for this sort of advice
in the newsgroup. That it was just a jest, one you apparently had the
inability to see as such, and which you therefore, in obvious desperation,
tried to use to bolster your argument, or to nullify mine.

You yourself implied your qualifications as being an engineering degree, or
at least similar. You even added several years of engineering experience to
the statement. Surely sufficiently specific for me and others to have taken
that as read? I might have indeed been more accurate to suggest you were a
nursery school dropout, but were I correct in my surmises, and you did have
an authentic engineering degree, then on that basis your engineering
qualifications are still way way lower than my own. I did suggest that your
inability to understand the resolution and balance of forces was
incompatible with an engineering degree. I should perhaps have said your
reluctance to intelligently apply such knowledge…etc etc.

You also started the mud throwing, with the “clever girl” and “baby talk”
jibes, totally unnecessarily, at someone trying to help you, and others,
understand the problem.

The tyre and inner tube are IRRELEVANT to what happens at the spokes in
principle, the overall tension in the spokes is irrelevant, and hence using
PRESTRESSED elastic bands as in my example is a valid analogy. Moving to
actual materials becomes necessary only if you wish to evaluate actual
values for stress etc etc . The fact that an elastic spoked wheel
encompasses lower values of stress in no way invalidates the principles.

Of course the spokes are prestressed, that is what creates the rim
stiffness. Of course it is not infinitely stiff. The core of this is that,
AS I HAVE SAID, spoke tensions change. Distortion of the rim therefore does
occur, to a small degree. What does NOT happen is that the upper rim
distorts to remove any difference in tension in the upper spokes when hub
load is added. A balance is achieved between the distortion and the new
tensions. You however have adopted the attitude “I cannot see this, I
cannot understand this, I cannot envisage this, therefore I will ignore it,
fight against it, introduce all sorts of irrelevancies and complications,
and disbelieve on principle anything else I am told.” Little more thought
than the average ostrich. Your latest idea is to suggest we now also
consider that the pressure in the tyre changes as it is loaded. Another
irrelevance. The next thing you will introduce is that the spokes are not
radial. Again true, and they are so for a very good reason, but this fact is
also irrelevant to the principles involved here. You could remove the tyre
completely and the principles of what happens to spokes will remain, remove
most of the spokes, principle is the same, replace the spokes with elastic
and the principle is the same but the problem then becomes far easier for
most people to visualise .
Stick with the basics, simplify the structures to their base components,
work out what is happening in that and you might stand a chance of
understanding what is going on. You will then probably no longer need my
help. As it is you have complicated the problem way beyond your level of
understanding, and in your head only, made a very simple problem into your
next nightmare.
You have driven your way through this thread, wondering if throwing your
cigarette butt in the ashtray will cause the car to deviate dangerously from
its path.
Get real, and if it really matters to you what happens when you sit on a
wheel, then address the problem sensibly.
Finally, accept offers of help for what they are, do not get annoyed and
interpret them as personal attacks on your intelligence.

Over and very definitely out.

Naomi

Re: wheel puzzle

On 20 May 2002 18:51:11 GMT, Ian Smith <ian@achrn.demon.co.uk> wrote:
> On Sun, 19 May 2002 19:04:25 +0100,
> Naomi Sajeri <Naomi_Sajeri@hotmail.com> wrote:
>
> > NS: What a load of ridiculous claptrap.
>
> That is, why do you assume that teh hub moves relative to teh upper part
> of the rim? Why not assume that teh upper part of teh rim deflects with
> teh hub, resulting in no change in force in teh spokes? Why do you assume
> that the hub moving downwards stretches teh spokes, rather than assuming
> the hub moving downwards takes the upper part of the rim downwards at teh
> same time?

OK, I’ve got a ‘thought experiment’ to help with this.

Suppose you remove the spokes and substitute a solid disk of steel. Make
it thick enough that buckling is not an issue.

Now, if you load the hub, why do you expect the steel above the hub to be
stressed? I’d expect only the steel between the hub and the point of
contact with the ground (plus a little shearing to each side) to carry any
load, but by your argument those parts of teh steel disk above the hub
will be under tension.

Now discretise the solid disk into lots of spokes - why do you maintain
this immediately fundamentally changes the load paths in the structure?

Presumably only because it has changed teh relative stiffness of rim
versus the spokes/disk. But, if the ratios of stiffness has that much
effect, what makes you so sure that a real wheel isn’t closer to the solid
disk situation, with upper spokes that don’t strain, than the rubber band
situation?

To demonstrate this one way or the other you’d need some analysis taking
into account teh stiffnesses. The problem is actually such that you could
formulate and solve it algabreically, but personally I think I’d throw FE
analysis at it (just because it would be quicker, if less tidy) . Have
you done either of them? Do you have references where anyone else has
done that? What did you/they conclude?

Incidentally, I’m still curious to know what you’ve found out about my
qualifications - you were sure yours ‘outranked’ mine, if you recall.

regards, Ian SMith

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Re: wheel puzzle

On Tue, 21 May 2002 16:42:18 +0100,
Naomi Sajeri <Naomi_Sajeri@hotmail.com> wrote:

> nursery school dropout, but were I correct in my surmises, and you did have
> an authentic engineering degree, then on that basis your engineering
> qualifications are still way way lower than my own.

Right, so what have you found out about my qualifications?
What are these qualifications of yours that are so terrific?

> at someone trying to help you, and others, understand the problem.

I do understand the problem. I’m still waiting for you to explain what’s
wrong with my engineering, rather than with my education, my experience,
my previous employment, my attitude, anything I might ever have designed,
etc. etc. etc.

I don’t want to know what’s wrong with me, I want to know what you think
is wrong with my engineering.

> The tyre and inner tube are IRRELEVANT to what happens at the spokes in
> principle,

Absolutely. No-one has claimed otherwise. I have certainly not claimed
they are relevant, so why do you imply that I have?

> the overall tension in the spokes is irrelevant, and hence using
> PRESTRESSED elastic bands as in my example is a valid analogy. Moving to
> actual materials becomes necessary only if you wish to evaluate actual
> values for stress etc etc . The fact that an elastic spoked wheel
> encompasses lower values of stress in no way invalidates the principles.

That’s not what I said. What I said was that the relative stiffness of
rim and spokes is relevant, because it alters the stress DISTRIBUTION.
Note that I am not and have not been talking about stress values, but
about distribution. The relative stiffness of spokes and rim is relevant
here.

You seem to be saying that the distribution of load effects in a
statically indeterminate structure is not affected by teh stiffnesses of
teh component elements. Do you believe that? Do you teach that? Do your
superiors know you teach that? (or are your qualifications such that you
have no superiors, in which case do your peers know you teach that?).

> AS I HAVE SAID, spoke tensions change. Distortion of the rim therefore does
> occur, to a small degree. What does NOT happen is that the upper rim
> distorts to remove any difference in tension in the upper spokes when hub
> load is added.

I have never said it has. In fact, I’ve said the distortion of the rim is
concentrated in teh vicinity of teh contact with teh ground. Most of teh
rim simply deflects with teh hub, resulting in no strain and no change in
tension in teh spokes.

If you agree that distortion does not occur in the upper part of teh rim,
surely you agree that there are no significant loads being induced in teh
spokes? Unless you are assuming the rim does not distort anywhere, but
you maintain you are not assuming an impossibly stiff rim, so that can’t
be.

> You however have adopted the attitude “I cannot see this, I
> cannot understand this, I cannot envisage this, therefore I will ignore it,
> fight against it, introduce all sorts of irrelevancies and complications,
> and disbelieve on principle anything else I am told.”

Would you like to concentarte on my engineering rather than my attitude?

How have you determined that there is strain in the upper spokes?

Why is it impossible that the rim distorts locally to the point of contact
and the only changes in spoke tensions are in teh vicinity of that
distortion? What prevents this?

> than the average ostrich. Your latest idea is to suggest we now also
> consider that the pressure in the tyre changes as it is loaded.

No, that’s a separate question. If you read teh thread you will find
there are two questions, one about spokes and one about tyres. Nowhere
have I said that the tyre behaviour has a significant effect on teh
qualitative behaviour of a wheel. Once again you are misrepresenting what
I have said. Why is that?

> irrelevance. The next thing you will introduce is that the spokes are not
> radial. Again true, and they are so for a very good reason, but this fact is
> also irrelevant to the principles involved here.

Absolutely. Once again, we discussed that early in the thread.
Have you read the thread?

The angle of the spokes is not desperately relevant to radial loads. It
does increase spoke lengths by 5 to 10% (I guess), which has a
corresponding effect on their stiffness, but not enough to affect the
general behaviour of teh wheel.

> You could remove the tyre
> completely and the principles of what happens to spokes will remain,

Absolutely, I have never said differently.
Once again you seem intent on misrepresenting what I said. Why is that?

> remove most of the spokes, principle is the same, replace the spokes
> with elastic and the principle is the same but the problem then becomes
> far easier for most people to visualise .

No, because if teh rim is dramatically stiffer than teh spokes then the
pattern of load distribution changes fundamentally.

Consider a rim that’s a disk of solid steel. If you load this, would you
expect teh steel above the hub to have any stress arising from the
loading, or would you assume the load simply travels down teh disk to teh
contact point with the ground?

Surely the steel that is remote from both the point of application of teh
load, the point of support and teh points between the two would be
substantially unstressed?

If you accept that wheel works in that way, why does discretising the disk
into spokes fundamentally alter the load path?

Still waiting, incidentally, for the basis of your comments about my
qualifications.

regards, Ian SMith

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Re: wheel puzzle

Early on in this thread Ian , you said:
"When you are on the unicycle, your weight is applied to the hub (either
through the cranks or the frame via the bearings, but that’s incidental).
Your weight is a downwards force. Your weight is conducted from teh hub
through the spokes to the rim. The rim therefore resists your weight.
However, the rim is not touching the ground. The rim is held off the
ground, supported by the air in the tyre. Since the air is fluid with
very low viscosity, and there is only a single chamber, the pressure
everywhere within it must be the same. But if the pressure is everywhere
the same, how can it resist the downward force? The air must be pushing
upwards on teh rim to hold it off the ground, but it must have the same
pressure in teh top of the tyre pushing down just as hard. This is his
conundrum…So the question is, where is the force that holds the
rim off the ground? "

Not really a conundrum at all. the air pressure of the tube for all
practical purposes acts equally on the rim, therefore it does not really
play a part in supporting the weight of the rider. what it does is make the
tire more rigid, and introduces cushioning for uneven ground. It allows the
tire to transfer the weight to the ground without becoming completely flat
in the process. The weight is actually tranferred from the rim , directly
through the tire to the ground. This is why the tire can be seen to change
shape at its point of ground contact. Air pressures on the rim remain
uniform. The contact area of tire with the ground is then as Naomi said,
larger , and conforming to an equation of the form weight supported
=pressure * area. Does yout thumb still not believe this? Put it under a
ridden unicycle and it may change its mind. With no air in the tire the
weight is still transferred rim to tire to ground albeit in a more direct
way.

You then said:

“The question (or rather the answer) is similar to one you can introduce
earlier in the load-path - does the hub hang from teh spokes above it, or
does it push on teh spokes below? If it hangs, why can’t you stand on an
unlaced wheel rim without knackering it? If it stands, why can’t you
stand on teh ends of a few spokes without them buckling?”

I don’t see why you called that an answer, you seem to have excluded both
your possibilities in this limited analysis. But there is the third option
you have ignored in the paragraph: that both upper and lower spokes
contribute to taking the weight and to preventing the rim being knackered.
My reading of this thread suggests that this is exactly what Naomi is
saying.

But enough from me:

Looks to me Ian, as if Naomi has bowed out of this. I don’t blame her.
She has clearly demonstrated the points to my satisfaction. Ian, you have
not, to me, given any valid arguments or analysis for your case at all. You
seem to disagree without giving any scientific reason for doing so. There
is little in your posts I can see that really contributes positively to the
question.

But as an aside, I have met Naomi a few times, and she may or may may not
approve of my telling the thread this…but anyway here goes:

Her qualifications are: 2 degrees, one in engineering, the other maths. she
is a chartered engineer. She has a european professional quaification as
well, I can’t remember exactly what this is, sorry. Now teaches at
university. Before coming to this country she worked on a number of major
projects in the far east as a structural design engineer and consultant.
Anybody know Ian?

This thread is getting a bit warm!

I know I said I was going but I just wanted to post some links for people interested in tire and wheel experimental data to have a look at.

First tires:
http://www.bsn.com/cycling/articles/radial-force-deflection.html

Now lateral stiffness in spoked wheels:

And here is a real media clip of Paolo Salvagione demonstrating how cycle “professionals” skirt around the question of wheel structure, best leave it to structural engineers and physicist :slight_smile:
http://cxn.exploratorium.edu/ps_wheel.ram

Gary

RE: wheel puzzle

> of the rim is concentrated in teh vicinity of teh contact
> with teh ground. Most of teh rim simply deflects with teh
> hub, resulting in no strain and no change in
> tension in teh spokes.

Can you say flame war? The argument is getting lost in the personal attacks.
One of you is spitting at the other every time he says “teh.” I would expect
there are Web sites out there that have covered these questions in great
detail. Perhaps you should each find the sites that support your arguments,
and send the URLs back and forth.

As we are probably all figuring out, neither qualifications nor experience
necessarily make one good at arguing via email… :slight_smile:

JF

Re: wheel puzzle

Hey John now, don’t spoil teh fun, don’t come in, have a poke from teh
sidelines and tehn tell everyone else to stand back. This is teh classic
ateheist vs mormon front door step argument, and very good fun it is too.
Especially if teh spectators can throw in teh odd tehorem from teh sidelines
On the doorstep, red corner, we have atehist Naomi, arguing her case
logically and scientifically, and now storming off in a huff because she has
been unable to get Ian to see sense. And out in teh cold, blue corner, we
have Ian teh Mormon, prepared to deny all, blindly discounting evidence
because it is contrary to genesis. Its world title fight stuff, and a
pleasant change from the usual.
So come back into teh fray Naomi, and Ian keep denying that a wheel is not a
wheel unless it has metal spokes and we will all have a great time sat in
teh front row. I bought my ticket John, don’t cancel teh event.
And what makes it more fun still is that none of it really matters at all
!!!

:wink: with apologies to both contestants, as well as referee John Foss.

RE: wheel puzzle

> On the doorstep, red corner, we have atehist Naomi, arguing her case
> logically and scientifically, and now storming off in a huff
> because she has been unable to get Ian to see sense. And out in
> teh cold, blue corner, we have Ian teh Mormon, prepared to deny
> all, blindly discounting evidence because it is contrary to genesis.

Definitely sounds like you’re taking sides… :slight_smile:

I’m still waiting for Naomi’s research findings into Ian’s qualifications.

> Its world title fight stuff, and a
> pleasant change from the usual.

You accidentally spelled “the” right.

> So come back into teh fray Naomi, and Ian keep denying that a
> wheel is not a wheel unless it has metal spokes

My wheels have metal spokes. What are you using?

I wonder if it would make the argument more interesting if I suggested you
think of the spokes as pieces of cable, or string. That’s essentially what
they are, as they do all their work by pulling. They certainly don’t support
any weight as a thicker piece of metal could.

This is not a good example, but check this out:

A ferris wheel that uses only cables to support it. And it’s really old,
too. Of course it doesn’t bear any weight except its own.

So I’ll step back, blow my whistle, and say “Continue.” Have fun,

John Foss, the Uni-Cyclone
jfoss@unicycling.com

“Vehicularly-Injured Sperm-Count seat: better known by it’s abbreviated
name, Viscount.” David Stone, on saddle preference

Re: wheel puzzle

On Wed, 22 May 2002 19:50:32 +0100, muniuni <muniuni@hotmail.com> wrote:

> On the doorstep, red corner, we have atehist Naomi, arguing her case
> logically and scientifically, and now storming off in a huff because she has
> been unable to get Ian to see sense. And out in teh cold, blue corner, we
> have Ian teh Mormon, prepared to deny all, blindly discounting evidence
> because it is contrary to genesis.

It’s curious that you present it like that, because all teh technical
references cited in the thread reach the same conclusion that I do. This
includes a book published 20 years ago and which I have never seen
credibly criticised, and which is invariably hailed as teh definitive work
on the topic. Furthermore, I provided an experminental demonstration
supporting my theory regarding tyres.

Naomi, on the other hand, has simply repeatedly said that she is right,
and I’m wrong. Also that my degree must be mail-order, that I was
probably a nursery school dropout, that my attitude is that of an ostrich,
that my qualifications are less than hers, that my experience is less than
hers and so on.

So why is she logical and scientific, and I am the one relying on blind
faith? Admittedly, all the mormons I get at my door are polite and talk
about issues, rather than going for personal abuse, but I guess there’s
something more to your charactisation than that.

regards, Ian SMith

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Re: wheel puzzle

On Wed, 22 May 2002 03:11:18 +0100, JS <jspilsbury@hotmail.com> wrote:

> Early on in this thread Ian , you said:
> "When you are on the unicycle, your weight is applied to the hub (either
[snip]
> This is his conundrum…

> Not really a conundrum at all.

I know. I was rephrasing something presented by gauss. That’s why I said
“HIS conundrum”. Your explanation matches those of everyone else who
proposed an explanation, including mine (and including gauss’s). Thank
you for your agreement.

> The contact area of tire with the ground is then as Naomi said,
> larger , and conforming to an equation of the form weight supported
> =pressure * area. Does yout thumb still not believe this?

No it doesn’t, and I observe that neither does the technical paper found
by unicus. That says: “Thus, it was originally thought that the
structural component of the tire force would be negligible. If this were
the case, then the force would be a function of the contact patch area
alone for a given pressure.” That is, they say that AT FIRST they thought
that what Naomi proposed would be true. However, they then go on to
explain that this theory turns out not to explain what actually happens,
and give their opinion on what causes the obsderved variation from teh
simple theory.

So, Naomi presented a theory. I said it I didn’t think it was a good one,
and provided a simple experimental justification. My experiment
demonstrated that in reality a greater force than that suggested by Naomi
is required.

I get shouted down and ridiculed, but the only technical paper anyone has
found on teh topic concludes that the theory presented by Naomi does not
accurately predict the behaviour of a tyre. I can’t find any published
peer review of the paper (which I actually found quite interesting) - has
anyone else?

Anyway, on to spokes, which is a separate issue:

> You then said:
>
> “The question (or rather the answer) is similar to one you can introduce
> earlier in the load-path - does the hub hang from teh spokes above it, or
> does it push on teh spokes below? If it hangs, why can’t you stand on an
> unlaced wheel rim without knackering it? If it stands, why can’t you
> stand on teh ends of a few spokes without them buckling?”
>
> I don’t see why you called that an answer

I didn’t. I said that the question is similar to another question. The
answer to gauss’s question is similar to teh answer to another question,
being the one about spokes.

The reason the answers are similar is that in both cases very slender
components are used to resist compressive loads, and teh way they achieve
this is by being prestressed with a tensile load which is higher than the
compressive load to be imposed. Thus, the compressive load can be
transmitted by reducing the tensile load originally introduced.

> But there is the third option
> you have ignored in the paragraph: that both upper and lower spokes
> contribute to taking the weight and to preventing the rim being knackered.
> My reading of this thread suggests that this is exactly what Naomi is
> saying.

Indeed, that is a third option, and there are obviously infinite
variations between the extremes, and maybe I should have highlighted that
in teh original phrasing - I was trying to simplify it too much. However,
the answer remains that the predominant effect is that the lower spokes
carry the load.

> Looks to me Ian, as if Naomi has bowed out of this. I don’t blame her.
> She has clearly demonstrated the points to my satisfaction.

The demonstrations are inadequate because her hypothetical models do not
consider the fact that teh rim is similarly flexible to the spokes. For
example, in teh elastic band explanation, she assumes that the hub moves
nearer to the bottom part of teh rim, and further from the upper part of
the rim. That would indeed happen if you used spokes that were very
flexible compared to teh stiffness of teh rim. In a unicycle wheel,
however, that isn’t true. What happens is that the hub moves nearer to
the bottom part of teh rim, but the top part of the rim moves by the same
amount, the upper spokes don’t extend.

I don’t know if you understand teh concept of statical indeterminancy.
It’s key to most structural analysis, because most structures are
statically indeterminate. It can be a little tricky to get your head
round, but I’ll try and explain it in case anyone has not come across it
before. If a stucture is such that you can release a structural action,
and after releasing that action the structure does not become a mechanism,
then the structure is said to be statically indeterminate. For example, a
unicycle wheel is statically indeterminate, because you could release the
tension from one spoke, and teh wheel wouldn’t become immediately floppy
and collapse. Another structural action could be the ability to resist
bending. For example, a tree (a normally growing one, anyway) is not
statically indeterminate because if you took a branch and somehow took
away it’s ability to resist bending, you would get a mechanism - the
branch would bend and a lump of the tree would pivot down 'till it either
got to teh ground or it was hanging straight down. If you like, I expect
Naomi will be able to confirm that this is true.

Static indeterminancy is relevant because if you have a statically
indeterminate structure you cannot ignore the stiffness of teh components
when determining what load they carry. In a statically indeterminate
structure, if you make one part (or one support) significantly stiffer, it
effectively attracts load to it, and away from teh less stiff parts. If
you like, I expect Naomi will confirm this is broadly true, though talk of
structures “attracting” load is not exactly rigorous.

The reason Naomis explanations don’t tie up with reality is because she
seems to have ignored this effect. I have no idea why - from what you
report her qualifications to be this should be very basic stuff to her,
and I’d certainly be intereted to know why she doesn’t think it is
relevant in this case.

In her elastic-band wheel she’s made the spokes much much less stiff than
they really are, but she doesn’t seem to have made teh rim correspondingly
less stiff. This has the effect of attracting load away from teh spokes
and around the rim. Obviously the load has to get to the hub eventually,
but it would distribute all around the rim, and move approximately equally
down all teh spokes. In real life, however, with real spokes and real
rims, this doesn’t happen. The spokes near the bottom are stiffer in
tension/compression than teh rim is in bending, so those spokes attract
the load, it doesn’t distribute all around the rim, it just goes straight
up teh spokes to teh hub.

This is what I have been saying. It’s what Jobst Brandt demonstrates in
his book, and it’s what I’ll show you finite elenment output for once I’ve
put the page together (I’ve done teh analysis already).

> Ian, you have
> not, to me, given any valid arguments or analysis for your case at all. You
> seem to disagree without giving any scientific reason for doing so.

OK, that’s a fair observation. In general I’ve tried to explain what
happens and why it happens, rather than provide supporting evidence. Of
course, no-one else has provided any cites supporting their point of
view either, but never mind.

The definitive work on bicycle wheels is Jobst Brandt’s book. He has
theory, finite element analysis and experimental results. It’s a good
read (for a structural engineer, anyhow). P19 of my copy (which is a
second edition) contains the statement (talking about a wheel under a
radial load) that the spokes around teh upper part of the wheel have “an
insignificant increase in spoke tension of less than 4% of teh change of
experienced by the spokes in the load-affected zone.” A little later it
observes that the behaviour of the spokes round the majority of the wheel
cause no lift on the hub. Also, figure 8 in the book shows what I have
been asserting - that there is local deformation near the contact patch,
but the spokes round the upper part of teh wheel do not extend, and thus
do not see significant load.

> There is little in your posts I can see that really contributes
> positively to the question.

Well, only the fact that my posts contain teh right answer, I suppose ;-).

Just for entertainment, I’ve run a similar finite element analysis to taht
which Jobst Brandt describes. I’ll write it up in a separate post or on a
web page, but you might have to wait for tomorrow for it - I’m a bit short
of time tonight. In the mean time, anyone that has teh book will be able
to confirm the truth of what I’ve said above.

> But as an aside, I have met Naomi a few times, and she may or may may not
> approve of my telling the thread this…but anyway here goes:
>
> Her qualifications are: 2 degrees, one in engineering, the other maths. she
> is a chartered engineer. She has a european professional quaification as
> well, I can’t remember exactly what this is, sorry.

Interesting. That means her engineering quialifications are substantially
identical to mine, which are: engineering degree (mainly structural),
chartered engineer, and a member of a major European engineering
association. 11 years practical experience, including design of major
projects in teh far east (Hong Kong and Kuala Lumpur mainly), and smaller
projects in the UK (mainly because there are very few projects here as big
as there are over there). My experience is split roughly equally between
structural analysis (FE work, linear and non-linear, impact analysis,
steel, concrete and fibre (and other) composites) and design. Despite
Naomi’s slanderous comments, there are major bridges in existence carrying
motorway (freeway) type roads in which I played a key design role, and I
don’t see the professional indemnity insurers running for cover yet.

So, do you have any idea why she said “I assure you I outrank you
considerably in both engineering qualifications and experience” - was she
maybe just shooting her mouth off from a position of ignorance?

If you meet her again, could you ask her to point out any flaw in my
engineering, rather than flaws in my character, my attitude, my
experience, my education and my qualifications?

regards, Ian SMith

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Re: wheel puzzle

On Wed, 22 May 2002 19:50:32 +0100, muniuni <muniuni@hotmail.com> wrote:

> On the doorstep, red corner, we have atehist Naomi, arguing her case
> logically and scientifically, and now storming off in a huff because she has
> been unable to get Ian to see sense. And out in teh cold, blue corner, we
> have Ian teh Mormon, prepared to deny all, blindly discounting evidence
> because it is contrary to genesis.

It’s curious that you present it like that, because all teh technical
references cited in the thread reach the same conclusion that I do. This
includes a book published 20 years ago and which I have never seen
credibly criticised, and which is invariably hailed as teh definitive work
on the topic. Furthermore, I provided an experminental demonstration
supporting my theory regarding tyres.

Naomi, on the other hand, has simply repeatedly said that she is right,
and I’m wrong. Also that my degree must be mail-order, that I was
probably a nursery school dropout, that my attitude is that of an ostrich,
that my qualifications are less than hers, that my experience is less than
hers and so on.

So why is she logical and scientific, and I am the one relying on blind
faith? Admittedly, all the mormons I get at my door are polite and talk
about issues, rather than going for personal abuse, but I guess there’s
something more to your charactisation than that.

regards, Ian SMith

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Re: wheel puzzle

On Wed, 22 May 2002 03:11:18 +0100, JS <jspilsbury@hotmail.com> wrote:

> Early on in this thread Ian , you said:
> "When you are on the unicycle, your weight is applied to the hub (either
[snip]
> This is his conundrum…

> Not really a conundrum at all.

I know. I was rephrasing something presented by gauss. That’s why I said
“HIS conundrum”. Your explanation matches those of everyone else who
proposed an explanation, including mine (and including gauss’s). Thank
you for your agreement.

> The contact area of tire with the ground is then as Naomi said,
> larger , and conforming to an equation of the form weight supported
> =pressure * area. Does yout thumb still not believe this?

No it doesn’t, and I observe that neither does the technical paper found
by unicus. That says: “Thus, it was originally thought that the
structural component of the tire force would be negligible. If this were
the case, then the force would be a function of the contact patch area
alone for a given pressure.” That is, they say that AT FIRST they thought
that what Naomi proposed would be true. However, they then go on to
explain that this theory turns out not to explain what actually happens,
and give their opinion on what causes the obsderved variation from teh
simple theory.

So, Naomi presented a theory. I said it I didn’t think it was a good one,
and provided a simple experimental justification. My experiment
demonstrated that in reality a greater force than that suggested by Naomi
is required.

I get shouted down and ridiculed, but the only technical paper anyone has
found on teh topic concludes that the theory presented by Naomi does not
accurately predict the behaviour of a tyre. I can’t find any published
peer review of the paper (which I actually found quite interesting) - has
anyone else?

Anyway, on to spokes, which is a separate issue:

> You then said:
>
> “The question (or rather the answer) is similar to one you can introduce
> earlier in the load-path - does the hub hang from teh spokes above it, or
> does it push on teh spokes below? If it hangs, why can’t you stand on an
> unlaced wheel rim without knackering it? If it stands, why can’t you
> stand on teh ends of a few spokes without them buckling?”
>
> I don’t see why you called that an answer

I didn’t. I said that the question is similar to another question. The
answer to gauss’s question is similar to teh answer to another question,
being the one about spokes.

The reason the answers are similar is that in both cases very slender
components are used to resist compressive loads, and teh way they achieve
this is by being prestressed with a tensile load which is higher than the
compressive load to be imposed. Thus, the compressive load can be
transmitted by reducing the tensile load originally introduced.

> But there is the third option
> you have ignored in the paragraph: that both upper and lower spokes
> contribute to taking the weight and to preventing the rim being knackered.
> My reading of this thread suggests that this is exactly what Naomi is
> saying.

Indeed, that is a third option, and there are obviously infinite
variations between the extremes, and maybe I should have highlighted that
in teh original phrasing - I was trying to simplify it too much. However,
the answer remains that the predominant effect is that the lower spokes
carry the load.

> Looks to me Ian, as if Naomi has bowed out of this. I don’t blame her.
> She has clearly demonstrated the points to my satisfaction.

The demonstrations are inadequate because her hypothetical models do not
consider the fact that teh rim is similarly flexible to the spokes. For
example, in teh elastic band explanation, she assumes that the hub moves
nearer to the bottom part of teh rim, and further from the upper part of
the rim. That would indeed happen if you used spokes that were very
flexible compared to teh stiffness of teh rim. In a unicycle wheel,
however, that isn’t true. What happens is that the hub moves nearer to
the bottom part of teh rim, but the top part of the rim moves by the same
amount, the upper spokes don’t extend.

I don’t know if you understand teh concept of statical indeterminancy.
It’s key to most structural analysis, because most structures are
statically indeterminate. It can be a little tricky to get your head
round, but I’ll try and explain it in case anyone has not come across it
before. If a stucture is such that you can release a structural action,
and after releasing that action the structure does not become a mechanism,
then the structure is said to be statically indeterminate. For example, a
unicycle wheel is statically indeterminate, because you could release the
tension from one spoke, and teh wheel wouldn’t become immediately floppy
and collapse. Another structural action could be the ability to resist
bending. For example, a tree (a normally growing one, anyway) is not
statically indeterminate because if you took a branch and somehow took
away it’s ability to resist bending, you would get a mechanism - the
branch would bend and a lump of the tree would pivot down 'till it either
got to teh ground or it was hanging straight down. If you like, I expect
Naomi will be able to confirm that this is true.

Static indeterminancy is relevant because if you have a statically
indeterminate structure you cannot ignore the stiffness of teh components
when determining what load they carry. In a statically indeterminate
structure, if you make one part (or one support) significantly stiffer, it
effectively attracts load to it, and away from teh less stiff parts. If
you like, I expect Naomi will confirm this is broadly true, though talk of
structures “attracting” load is not exactly rigorous.

The reason Naomis explanations don’t tie up with reality is because she
seems to have ignored this effect. I have no idea why - from what you
report her qualifications to be this should be very basic stuff to her,
and I’d certainly be intereted to know why she doesn’t think it is
relevant in this case.

In her elastic-band wheel she’s made the spokes much much less stiff than
they really are, but she doesn’t seem to have made teh rim correspondingly
less stiff. This has the effect of attracting load away from teh spokes
and around the rim. Obviously the load has to get to the hub eventually,
but it would distribute all around the rim, and move approximately equally
down all teh spokes. In real life, however, with real spokes and real
rims, this doesn’t happen. The spokes near the bottom are stiffer in
tension/compression than teh rim is in bending, so those spokes attract
the load, it doesn’t distribute all around the rim, it just goes straight
up teh spokes to teh hub.

This is what I have been saying. It’s what Jobst Brandt demonstrates in
his book, and it’s what I’ll show you finite elenment output for once I’ve
put the page together (I’ve done teh analysis already).

> Ian, you have
> not, to me, given any valid arguments or analysis for your case at all. You
> seem to disagree without giving any scientific reason for doing so.

OK, that’s a fair observation. In general I’ve tried to explain what
happens and why it happens, rather than provide supporting evidence. Of
course, no-one else has provided any cites supporting their point of
view either, but never mind.

The definitive work on bicycle wheels is Jobst Brandt’s book. He has
theory, finite element analysis and experimental results. It’s a good
read (for a structural engineer, anyhow). P19 of my copy (which is a
second edition) contains the statement (talking about a wheel under a
radial load) that the spokes around teh upper part of the wheel have “an
insignificant increase in spoke tension of less than 4% of teh change of
experienced by the spokes in the load-affected zone.” A little later it
observes that the behaviour of the spokes round the majority of the wheel
cause no lift on the hub. Also, figure 8 in the book shows what I have
been asserting - that there is local deformation near the contact patch,
but the spokes round the upper part of teh wheel do not extend, and thus
do not see significant load.

> There is little in your posts I can see that really contributes
> positively to the question.

Well, only the fact that my posts contain teh right answer, I suppose ;-).

Just for entertainment, I’ve run a similar finite element analysis to taht
which Jobst Brandt describes. I’ll write it up in a separate post or on a
web page, but you might have to wait for tomorrow for it - I’m a bit short
of time tonight. In the mean time, anyone that has teh book will be able
to confirm the truth of what I’ve said above.

> But as an aside, I have met Naomi a few times, and she may or may may not
> approve of my telling the thread this…but anyway here goes:
>
> Her qualifications are: 2 degrees, one in engineering, the other maths. she
> is a chartered engineer. She has a european professional quaification as
> well, I can’t remember exactly what this is, sorry.

Interesting. That means her engineering quialifications are substantially
identical to mine, which are: engineering degree (mainly structural),
chartered engineer, and a member of a major European engineering
association. 11 years practical experience, including design of major
projects in teh far east (Hong Kong and Kuala Lumpur mainly), and smaller
projects in the UK (mainly because there are very few projects here as big
as there are over there). My experience is split roughly equally between
structural analysis (FE work, linear and non-linear, impact analysis,
steel, concrete and fibre (and other) composites) and design. Despite
Naomi’s slanderous comments, there are major bridges in existence carrying
motorway (freeway) type roads in which I played a key design role, and I
don’t see the professional indemnity insurers running for cover yet.

So, do you have any idea why she said “I assure you I outrank you
considerably in both engineering qualifications and experience” - was she
maybe just shooting her mouth off from a position of ignorance?

If you meet her again, could you ask her to point out any flaw in my
engineering, rather than flaws in my character, my attitude, my
experience, my education and my qualifications?

regards, Ian SMith

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Re: wheel puzzle

On Thu, 23 May 2002 09:33:47 -0700, John Foss <john_foss@asinet.com> wrote:

> I’m still waiting for Naomi’s research findings into Ian’s qualifications.

Me too, and her justification for all the slander.

> This is not a good example, but check this out:
> http://www.unicycling.com/coastercam/pix/VIENNA.JPG

Better, do a web search for “british airways london eye”. It’s one of the
structures I had some design input into, though nothing you’ll see in
normal photos. The spokes in this are all cables.

> So I’ll step back, blow my whistle, and say “Continue.” Have fun,

Oh, believe me, I am.

regards, Ian SMith

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|o o|
|/ |

I’m not going to repeat myself but muniuni and John Foss seem to be enjoying it so….
Ian Smith writes:

As far as I was aware there are two distinct structural wheel types, either compression or tension. A solid disc would be the compression type and a tensioned spoke wheel is, yes, a tension type. The load path is different in the two. There is a nice animation demonstrating this here (using a solid spoke cart wheel and a tension spoke cycle wheel BTW) TMS Career Center . They also state:

Which is what I said earlier in a less direct way and is possibly why Jobst Brandt only observed a small increase in tension in the spokes above the hub (load distribution). There is also a bit here http://www.personal.psu.edu/users/e/r/erp117/research/bicycle_materials/gfx/spokes.jpg

So that’s what happens to the forces. In a solid wheel the hub stands on the rim and in a tensioned wheel the hub, well the hub doesn’t stand on the rim.

“The Bicycle and the Walkman" by CJ McMahon and CD Graham is an often used text in academic courses on subjects such as this, apparently, if your interested. Also Princeton have some info on propulsion with some references to wheels, tires etc. go here Propulsion

BTW isn’t the London Eye suspended by its hub?

Enough from me, I’ll hand the baton to whoever cares to take it.

Gary

Re: wheel puzzle

I do hope to meet Naomi again, for she is one hell of a lady, and initially
in her defence I shall say that from the wording in your post I also would
have ASSUMED the qualifications you had mentioned in your post, wrong though
I would have been to do so.

Now I do not have any mechanical or structural degrees, my own area of
professionalism being electrical electronics, and computers, but that has
given me a fairly sound scientific basis underlying my specialisation. I
have read the posts from all concerned and some seems to make good sense,
and other parts appear to me to be based on pure supposition. But it is
interesting, so if you don’t mind Ian I’ll try to condense the parts that
seem right and those that seem wrong. If I had the time I would have just
written a computer model of the whole wheel structure, but I don’t really
have THAT much interest.
I look forwards to your explanation of parts I may get wrong in the next
bits, but don’t spare the science, for I 'll probably cope with all but
very specialist terms.

I have not heard the term statically indeterminate, and can only
guess what it means. Does it mean you cannot calculate all the tensions and
forces in a stationary stable structure? Surely not: It must be easy to
computer model a stationary wheel, even a loaded wheel, and then equally
easy to remove a spoke from the model and see what happens? I have
certainly seen computer models of things that are far far more complex.
Instinctively I would have thought a unicycle wheel was statically
determinate, rather than indeterminate, as you could with the predict its
behaviour, eg its new rest state, when you remove a spoke. But again I may
be misunderstanding the term.

A wheel, with spokes, seems to me to be a 360 degree arch, loaded from
the inside. The tension from the spokes, pulling inwards generates a
compression in the rim, making it work very much like an arch as far as its
load carrying is concerned. Yes? You could put cheese shaped lumps of
metal on the end of each spoke instead of the rim, and it would still roll
and be able to take the spoke tensions.

A corollary of that to me is that as you change the loading on one part
of the wheel, the arch effect would make some component of that load
transmit itself around the rim to its other areas. So from that part alone ,
and some long forgotten A level suggestion that forces have to be in
balance, suggests that spoke tensions would change all around the wheel. I
can’t prove that, at least not without getting my brain hot, so it is
supposition on my part, maybe someone more specialist, and with more time
could do it the detailed maths for me.

Now then though, when I look at Naomi’s wheel, with the elastic band
spokes, and even allowing for a rim is not totally rigid…if I apply weight
to the hub the bands will stretch and apply force to the upper rim (and
lessened force to the lower rim) and hence all the spokes will see a change
in tension. I’ll have to use the word tension 'cos I can’t remember exactly
what stress and strain mean. The rim will suffer some change in shape,
flattening a bit, dependent upon its strength relative to the bands.
Agreed? What Naomi seems to be saying is that all you do effectively when
you replace the bands with spokes is to change the elasticity of the spokes,
and as such the principles involved remain: ie that all tensions will
change, not just the lower ones seems a very reasonable conclusion. If not
then what you, Ian, are saying is that at some value of tension this model
is no longer true and it ceases to be the case that the principle still
applies…I cannot see that at all. Its surely just a model, and if you
apply different forces to the same shape structure.then surely only the
values change?
On that basis I like Naomi’s “thought picture” of the elastic wheel.
It is easy to follow and makes sense to me. I can’t really see why you say
she has assumed a totally rigid rim. I mean its an experiment I could do
with a real rim and I think the upper rubber bands would stretch, as the
lower ones are unstretched by applied weight (another technical term) . I
might see some rim distortion as well, but the upper bands are certainly
going to lengthen

Let me now consider your own model: the solid wheel: There is a major
difference between this and a unicycle wheel. there are no spokes
obviously, but there is also no unloaded stress/strain tension whatever.
Its just a slice of tree trunk that rolls. It is not action in an arch like
way. Surely then it is a far less appropriate model that the elastic
banded wheel? Far less representational of a spoked, tensioned wheel?

I looked through your own writings, especially as you asked Naomi to refute
youe engineering rather than anything else, but whenever you get to say the
load is taken wholly in the lower spokes, I cannot find any engineering
evidence other than your assertions,that it is true, so maybe I missed your
engineering analysis part of that?
If I may now cut/paste a little of one of your posts:

…>>>> I maintain that the force is conducted only through spokes local to
the lowest part of the
rim.

Now that “only” seems very black and white, no resultant force in the upper
spokes, yet the book you yourself mention says that some (4%), of tension
was measured in upper spokes (under certain prescribed conditions as used
for his test). I may have missed it but I don’t think Naomi maintained
there was an EQUAL force in upper/lower spokes, just some in each…I mean
weight supporting force of course. I suspect the value 4% or whatever
may well vary with spoke tension, rim rigidity, choice of wheel, but it
doesn’t look as if it ever goes to zero. Of course I haven’t read or seen
the book, nor do I have any means of asserting its veracity. I guess one
end of the extreme might be Naomi’s elastic wheel, where if we add to it, a
totally rigid rim 50% of the weight would be on the upper spokes.
But what would the other extreme be? What would give 0% on the upper
spokes? It would probably be equally idealistic in the other direction…a
wheel with totally rigid spokes, and a totally elastic rim.
Or a bit like your solid wheel maybe? On consideration of the two, I reckon
Naomi’s elastic wheel, with a non totally rigid rim, is the closest of the 2
models to a real wheel.

Finally Considering the technical article mentioned by unicus: er
isn’t it talking about LATERAL stiffness: (Damon Rinard’s Wheel Stiffness
Test)
If so then it surely is irrelevant to the argument here just how good a
wheel is at not being bent sideways?
An extract from article follows:
This test measures lateral stiffness alone. It does not include the radial
load all wheels see in use. It does not measure radial stiffness, nor
strength of any kind.
Now as I said, I am not structurally qualified, but it seems obvious this
article bears no relation to the difference of opinion that you and Naomi
have.

At the moment I tend towards Naomi’s explanations as being clearer, and more
representational of the real world, but I have an open mind Ian, if you
care to convince me, with science, otherwise.

My own thoughts now are that really the two of you are not really that far
apart, Naomi attacked your assertion that NO weight is taken by the upper
spokes, and you suggested that that her wheel assumed total rim rigidity.
get those two bits sorted and I reckon you two would be identical on the
technical aspects. The rest of it is worth forgetting.


PS: Naomi, I am sure you will be reading this: not seen you for a few
months. Care to get in touch again? Same phone number/and address.

Photos, please.

keep it going fella’s

im sure the last number in Pie is just around the corner!

Re: wheel puzzle

On Sat, 25 May 2002 00:54:18 +0100, JS <jspilsbury@hotmail.com> wrote:

> I do hope to meet Naomi again, for she is one hell of a lady, and
> initially in her defence I shall say that from the wording in your post
> I also would have ASSUMED the qualifications you had mentioned in your
> post, wrong though I would have been to do so.

I’m not sure exactly what this means, but I do have the engineering
qualifications I claimed, and they are substantially the same as Naomi’s.
She hasn’t yet explained the basis on which she spent all that effort
asserting I was an uneducated yobbo, but I wait with anticipation.

> interesting, so if you don’t mind Ian I’ll try to condense the parts that
> seem right and those that seem wrong. If I had the time I would have just
> written a computer model of the whole wheel structure, but I don’t really
> have THAT much interest.

Took me about an hour for a 3D wheel (though 3D is irrelevant at this
stage, becaue no-one has got onto lateral loads). That was on an analysis
package designed for exactly this sort of thing, however. Plus, I was
partly using it as revision on teh package, which I don’t use very often.
Plus, the hour in question was my lunch break, so I was simultaneously
working my way through my lunch.

> I have not heard the term statically indeterminate, and can only
> guess what it means. Does it mean you cannot calculate all the tensions and
> forces in a stationary stable structure? Surely not:

What it actually means is that you cannot calculate all teh forces in a
structure, UNLESS you know something about teh relative stiffnesses. It
also means that if you change the stiffness of one part, but leave the
geometry and the loads and everything else the same, the forces in the
various parts will change.

That also means (and this is the important part), that if you dramatically
change the stiffness of one part while trying to visualise what’s
happening, you are likely to visualise something dramatically different
from reality. That is, your conclusion is liable to be very wrong. I’ve
never heard of statical indeterminancy forming part of a school course.
In teh UK it comes in at first year structural engineering degree. I was
very surprised when Naomi said any reasonably bright 15 year old could
work it out.

It’s a fairly specific, technical term. It’s one that can be difficult to
get your head round, but once it becomes clear, it suddenly seems
straightforward. For that reason, it’s easiest to explain by presenting
examples.

Imagine a flag-pole, with a horizontal force applied at the top. This is
a plain ordinary flag-pole with no guy-ropes or anything like this. Just
a pole, sticks straight up. This is statically determinate - can
calculate the effcts at the base without knowing anything about the
stiffness:
Suppose it’s 6m high.
Suppose there’s a horizontal force at the top of 1kN (N is a newton.
It’s the SI unit of force. A newton is teh force which accelerates 1kg at
1m/s2. 1kg weighs 9.81 newtons (roughly, at sea level, etc. etc.))
At the base, the bending moment will be 6kNm.

Now, imagine a second flag-pole alongside teh first and the two are
connected at teh top by a rod. The rod freely pivots at each end. It can
only conduct a pull or push. It is not unlike a bicycle spoke, though we
are initially assuming it won’t buckle (just to simplify matters). We’ve
arranged the poles and rod so that they line up with the load applied.

Now I cannot calculate the bending moments at teh base of either flagpole
UNLESS I know the bending stiffness of both and teh axial stiffness of the
rod.

For example:
If the two poles are as stiff as each other, and the rod is infinitely
stiff (it does not stretch or compress at all), the load will share
equally (because both poles will deflect the same amount), thus the
bending moment at the bottom of each is 3kNm.

If the rod is infinitely flexible (it stretches with no force), it may as
well not be there and when we apply the force to one pole, it will simply
behave as teh original single pole. The bending moment at the bottom of
one pole will be 6kNm and at the bottom of the other 0kNm.

If both poles and the rod are chosen so they are equally stiff. That is,
1kN at teh top of either pole alone deflects it (say) 100mm, and 1kN in
teh rod makes it stretch 100mm, then we’ll have 4kNm at the base of the
loaded pole, 0.3333kN tension in the rod, and 2kNm at teh base of theother
pole.

If the loaded pole is very flexible, the rod is very stiff and the other
pole is very stiff, we’ll get more bending moment in teh unloaded pole
than there will be in the loaded pole!

> It must be easy to
> computer model a stationary wheel, even a loaded wheel, and then equally
> easy to remove a spoke from the model and see what happens? I have
> certainly seen computer models of things that are far far more complex.
> Instinctively I would have thought a unicycle wheel was statically
> determinate, rather than indeterminate, as you could with the predict its
> behaviour, eg its new rest state, when you remove a spoke. But again I may
> be misunderstanding the term.

I think so. Did the above examples clarify? All the two pole cases were
statically indeterminate, even though I can easily solve them in my head.
However, I need to know the relative stiffnesses of the components to find
the solution.

> A corollary of that to me is that as you change the loading on one part
> of the wheel, the arch effect would make some component of that load
> transmit itself around the rim to its other areas.

Only if you assume that the nearby parts are flexible and the other parts
are stiff, so the stiff parts ‘attract’ the load away.

> Now then though, when I look at Naomi’s wheel, with the elastic band
> spokes, and even allowing for a rim is not totally rigid…if I apply weight
> to the hub the bands will stretch and apply force to the upper rim (and
> lessened force to the lower rim) and hence all the spokes will see a change
> in tension.

OK. I’ll assemble an analogy to Naomi’s analogy, which will hopefully
explain what’s wrong with Naomi’s analogy, and why you can’t simply muck
about with the stiffnesses of one part of teh system and then draw
conclusions.

Back to the flagpoles.

Two flagpoles with a tie between them at the top. In this case a 1kN load
at the tip of either flagpole deflects it 200mm. In this case the tie is
very stiff. A 1kN tension in teh tie deflects it only 4mm.

We apply the 1kN (which is 1000N) load

Person A asserts that the load distributes basically equally down the two
poles. They say the tie shares the load out and all the poles deflect.

Person A is basically correct. The sums feature simultaneous equations,
and assuming you’re happy with them the calculation is a doddle.

Pole 1 is the loaded pole - 1000N applied, but the tie has a tension T
taking some of that 1000N, so the pole itself carries 1000-T. Pole 2 has
teh tie attached, so obviously carrues load T. The tie itself sees
tension T by definition.

From our definition of the pole stiffnesses we see that 1000N causes 200mm
deflection. We are assuming linear elastic behaviour (the whole thread
has assumed this so far, and it’s true for real wheels).
Defining w as the load and d as teh deflection, d = 0.2 x w.

From our definition of teh tie stiffness we see that 1000N causes 4mm
deflection.
Defining w as the load and d as the deflection, d = 0.004 x w.

So, putting all that together:
pole 1: d1 = 0.2 x (1000-T)
pole 2: d2 = 0.2 x T
tie: (d1-d2) = 0.004 x T

Substitute for d2 in the tie equation:
d1 - 0.2 T = 0.004 T

Shuffle the pole 1 equation:
d1 = 200 - 0.2 T

Substitute the shuffled pole 1 into the previous equation and shuffle:
200 - 0.2 T - 0.2 T = 0.004 T
200 - 0.4 T = 0.004 T
200 = 0.404 T
T = 495.05

Thus, pole 1 sees 1000 - 495.05 = 504.95N and pole 2 sees 495.05 N.

That is, teh poles are each carrying within 1% of half teh laod each.

OK? I’m sure Naomi will confirm all of this if you like - it’s all true.

Now, along comes person B. They say this is all nonsense. They say all
the load goes down one pole. They support their argument by saying
"suppose the tie were made of an elastic band … " etc.

Quick calibration exercise:
I have an elastic band. Unloaded it measures 75mm.
I have a load, which is 270g, which is 0.27kg, which is 2.7N (near enough)
Apply load and the band stretches to 200mm
So, 2.7N causes 125mm
Adopting symbols as before, d = 46.3 w

So, back to the flagpoles, and doing the same sum with an elastic band in
place of teh real tie.

d1 = 0.2 x (1000 -T)
d2 = 0.2 x T
d1 - d2 = 46.3 T

d1 - 0.2 T = 46.3 T

d1 = 200 - 0.2 T

200 - 0.2 T - 0.2 T = 46.3 T
200 - 0.4 T = 46.3 T
200 = 46.7 T
T = 4.28

Thus, the elastic band case pole 1 sees 1000 - 4.28 = 995.72 N
and teh elastic band case pole 2 sees 4.28 N

So, while person B is right that IF you replace teh tie with an elastic
band pretty much all the load (over 99%) goes down just one pole.
However, this is irrelevant, because in teh real case, with teh real
stiffness of tie, the loads are shared equally (to within 1%).

This demonstrates teh danger of saying "suppose you replace the spokes
with elastic bands… " and assuming it will tell you anything at all.
It does not, because teh relative stiffness of spokes and rim
fundamentally alters teh load paths.

> I’ll have to use the word tension 'cos I can’t remember exactly
> what stress and strain mean.

Stress is the force carried divided by the area carrying it.
Strain is the deflection divided by the original length.

> On that basis I like Naomi’s “thought picture” of the elastic wheel.
> It is easy to follow and makes sense to me. I can’t really see why you say
> she has assumed a totally rigid rim. I mean its an experiment I could do
> with a real rim and I think the upper rubber bands would stretch,

Absolutely. 100% true, and what this tells you about the behaviour of a
real wheel is roughly absolutely bugger all. Zilch. Nada. Nothing.
It’s like my flagpoles analogy - YES it describes what happens IF you have
an elastic band tie, but unfortunately it tells you nothing about what
happens with teh ‘real’; tie.

> might see some rim distortion as well, but the upper bands are certainly
> going to lengthen

Absolutely, IF the spokes are elastic bands. Are your spokes elastic
bands? All of mine are steel. I have never seen a wheel laced with
elastic bands, only steel or kevlar. Let’s not get distracted by the
kevlar spoking - Tioga made a wheel with it, it works a bit differently
because it had a fundamentally different spoke pattern and had more
flexible spokes (kevlar is more elastic than steel). It was very cool,
and disappeared from teh market very quickly.

> I looked through your own writings, especially as you asked Naomi to refute
> youe engineering rather than anything else, but whenever you get to say the
> load is taken wholly in the lower spokes, I cannot find any engineering
> evidence other than your assertions,that it is true, so maybe I missed your
> engineering analysis part of that?

OK, quote from Jobst Brandt. Everyone agrees this is the definitive work
on bicycle wheels - a whole book devoted to teh topic, written by ex
Stanford, ex Porsche engineer: “Because it is pre-stressed the wheel can
stand on the bottom spokes. Al the action is in these spokes, not in the
top ones. … The idea that the hub hangs from teh upper spokes
contradicts the measured and computed behaviour of the spokes and rim.”

> If I may now cut/paste a little of one of your posts:
>
> .>>>> I maintain that the force is conducted only through spokes local to
> the lowest part of the rim.
>
> Now that “only” seems very black and white, no resultant force in the upper
> spokes, yet the book you yourself mention says that some (4%), of tension
> was measured in upper spokes (under certain prescribed conditions as used
> for his test).

The 4% is actually around all teh spokes. The side spokes pointing
somewhat down have the same value, as do the side spokes pointing somewhat
up, so pretty much all of these cancel each other out. The book discusses
this, but I’m not going to type out the whole thing!

There are two issues:
To a structural engineer, effects at low single digit percentages get
regarded as negligible maybe quicker than to most other engineers. This
is because of uncertainty mostly when dealing with real construction
materials in teh real world. That 4% stress for example, could well be
negligible compared with teh variation in spokes. 4% stress difference
would arise from 2% diameter change, which might be 0.035mm or 0.0014". I
don’t know what the tolerances are, but it wouldn’t surprise me to find
they are of that magnitude, or maybe even larger.

The second is one of linear superposition. This is really a judgement
issue, but teh load pattern looks like a uniform 4% increase in tension
everywhere in every spoke (which obviously has no net lift, because teh
lower ones pull down as much as the top pull up) combined with a 104%
reduction in tension in teh bottom spokes, which is what is carrying the
load. As I said, that’s a personal judgement - I don’t propose to explain
how I reach that, but I’d be a little surprised to find a structural
engineer who, upon looking at the stress distribution values, vehemently
disagreed with it.

> Or a bit like your solid wheel maybe? On consideration of the two, I reckon
> Naomi’s elastic wheel, with a non totally rigid rim, is the closest of the 2
> models to a real wheel.

That’s teh peril of drastically shuffling with teh stiffnesses. I’ve done
some analysis, and have some actual figures with actual stiffnesses.
I’ll put a web page up soon (I know, I said I’d do it yesterday, but in
teh end I went riding instead :slight_smile: ).

> Considering the technical article mentioned by unicus: er
> isn’t it talking about LATERAL stiffness

Yes. The tyre paper was good though.

> Now as I said, I am not structurally qualified, but it seems obvious this
> article bears no relation to the difference of opinion that you and Naomi
> have.

Absolutely correct, so I’ve ignored it.

> PS: Naomi, I am sure you will be reading this: not seen you for a few
> months. Care to get in touch again? Same phone number/and address.

Could you remind her I’m still waiting for her rationale and justification
for rubbishing my education? Also for any disagreement with any of the
engineering I have posted.

regards, Ian Smith

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Re: wheel puzzle

On Sat, 25 May 2002 00:54:18 +0100, JS <jspilsbury@hotmail.com> wrote:

> I looked through your own writings, especially as you asked Naomi to refute
> youe engineering rather than anything else, but whenever you get to say the
> load is taken wholly in the lower spokes, I cannot find any engineering
> evidence other than your assertions,that it is true, so maybe I missed your
> engineering analysis part of that?

http://www.achrn.demon.co.uk/ian/wheel/index.html

Colour pictures and charts and quantitative results and all sorts.

I would genuinely welcome any criticism of teh engineering in teh page.
I’ve had enough of “you must be wrong, cos Naomi says so”, but if there
are any mistakes in teh ENGINEERING I’d like to have them pointed out.

I hope this helps the debate.

regards, Ian SMith

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