Which spokes support the load?

jobst.brandt said:

That may be if you fail to define your terms. Those who have read
"the Bicycle Wheel" instead of taking someone else's word for what it
says know that the terms are defined and the reason for using the
metaphor "stand" explained. How is it that this subject elicits so
much energy from the UK, regularly? I can only conclude that the book
is not readily available there so this is all based on hearsay.

Perhaps if Avocet did a deal with a UK publisher to print it here it might
be more widely read? My copy is definitely an import (through Amazon),
and I don't recollect ever seeing it in the cycling section of any
bookshop.

David Wilson's 3rd edition of Bicycling Science covers some of the ground,
but it's not what I would call popular reading. OTOH MIT Press books
_are_ easily available in the UK, at reasonable prices too, *and* it's
in the bookshops (in Cambridge anyway).

Mike Newmarket, England

Jobst,

I have the book. As I understand it... because the spokes are
pre-tensioned, they can support a load without significantly deforming
until a heavy enough load is applied to cause the spokes to loose all
of their pre-tension. In essance pre-tension is turning the easily
bent wire spokes into a fairly rigid column that can support a load.
This seems to me an important idea because it relates the strength of
the wheel to the tension of the spokes. Am I mis-understanding ?

I notice that alot of the people who buy the 'wheels hang' theory also
don't buy the relationship between wheel tension and strength. After
all, if the wheel was truly hanging what role would pre-tension play ?

[email hidden] wrote in message news:<[email hidden]>...

Quoted message said:

David Damerell said:

Quoted message said:

"Two to four spokes near the ground contact point of the average
wheel support the load at any moment."

Quoted message said:

It is the case that the greatest change in tension is in the bottom
spokes, far greater than the increase in the other spokes.

Quoted message said:

You can verify that with a tensionmeter.

By the way, it's a tensiometer.

http://www.m-w.com/cgi-bin/dictionary?book=Dictionary&va=tensiometer

Quoted message said:

Conversely, the semantic argument is utterly unproductive.

That may be if you fail to define your terms. Those who have read
"the Bicycle Wheel" instead of taking someone else's word for what it
says know that the terms are defined and the reason for using the
metaphor "stand" explained. How is it that this subject elicits so
much energy from the UK, regularly? I can only conclude that the book
is not readily available there so this is all based on hearsay.

Jobst Brandt
[email hidden]

Quoted message said:

Quoted message said:

That may be if you fail to define your terms. Those who have read
"the Bicycle Wheel" instead of taking someone else's word for what it
says know that the terms are defined and the reason for using the
metaphor "stand" explained. How is it that this subject elicits so
much energy from the UK, regularly? I can only conclude that the book

Over time Jobst you have softened you line. It is now just a metaphor, I
see.

From _The Bicycle Wheel_:

,----
| THE WHEEL STANDS ON ITS SPOKES
| Of course the wheel is not supported by the bottom spokes only. Without
| the rest of the spokes, the bottom ones would have no tension. Standing,
| in this case, means that the spokes at the bottom are the ones that change
| stress; they are being shortened and respond structurally as rigid columns.
`----

Seems pretty clear to me -- the word "standing" is explicitly defined.

--
Benjamin Lewis

Politics is the ability to foretell what is going to happen tomorrow, next
week, next month and next year. And to have the ability afterwards to
explain why it didn't happen.
-- Winston Churchill

Thank you to all who have replied on this topic. I feel that I should
apologize for repeating a FAQ.

I read the analysis at:

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

I cannot argue with this analysis as a description of what happens when a
bicycle wheel is loaded in the usual fashiom. As a mathematician, I
certainly believe in the superposition principle--for linear problems.

If I can venture a few comments:

1. The change in tension of each spoke is directly proportional to the
change in strain on the spoke, which in turn is directly proportional to
(the deformation in the rim, plus any displacement of the hub relative to
that point of the rim).

2. Upper spokes show small changes in tension because there is little
deformation in the upper part of the rim, and furthermore there is,
apparently, little displacement of the hub relative to the upper part of the
rim.

I also read the analysis of forces in the rim at

http://www.achrn.demon.co.uk/astounding/ian/wheel/3c_rim.html

This page only analyzes radial (not axial) forces on the rim, and bending
forces on the rim. Tangential compressive stresses in the rim are not
analyzed. Those could be interesting, but of course I don't really know.

The following is a quibble, but I am a bit concerned by the statement in the
above cited page on rims:

" Total peak stress in the rim from applying 1000N to the wheel is therefore
1.5 + 19.2 = 20.7 N/mm2."

It is not right to add stresses in two different directions as scalars. This
should be treated as the norm of a vector.

Most of the argument on this topic has to do with "semantics", or
interpretation. As a non-engineer I am reluctant to stick my neck out (once
more), but I think that the average bicyclist would get the most correct
understanding of this problem if we said that the hub is supported by the
difference in tension between the upper spokes and the lower spokes, and
that this difference results from the large change in tension in the spokes
closest to the point of contactt.

Thanks again for your discussion,

David Wagner

David Damerell <[email hidden]> wrote in message

Quoted message said:

<snip>

[1] Note that I am carefully avoiding expressing an opinion on this
subject myself.

Wow! Are you feeling OK?

David Wagner <[email hidden]> wrote in message news:<[email hidden]>...

Quoted message said:

Jobst Brandt wrote, in FAQ Subject: 8c.4 Ideal Wheel Sizes:

"Two to four spokes near the ground contact point of the average wheel
support the load at any moment."

I would think that the weight load of the bicycle is transferred from the
frame to the hubs, and then through the hub to the *upper spokes* to the top
of the rim via tensile forces, and then from the top of the rim to the
bottom of the rim --- the rim being held in shape by the spokes through
tension---and then to the tires and the ground. Isn't this the correct view?

I expect that the bottom spokes have the lowest tensile force.

David Wagner

OH, GOD!!! HERE WE GO!!!

Tim McNamara said:

PK said:

Tim McNamara said:

>
The short answer is that a wheel is a prestressed or pretensioned
structure, and supports the load through the compression of the
roughly four spokes below the hub. You can test it for yourself by
plucking spokes like a guitar string at various points on a wheel
unloaded and then while a load is applied- the ones where you can
hear the greatest change in pitch are the ones holding up the load.

No matter how often you repeat this, it will STILL be wrong.

In your opinion, PK. In the opinions of multiple mechanical engineers
who have verified the observations, it is correct. I'll take their
opinions over someone whose grasp of physics seems a bit shaky.
Cheers!

An you will still be wrong!

The spokes ahowing the most change in tension is not the same thing as the
spkes holding up the load.

draw a vector diagram of the hub,

which spokes act upwards on the hub?

simple really!

pk

In article <[email hidden]>, spam.trap100
@btinternet.com says...

Quoted message said:

simple really!

Only if you assume the rim is infinitely stiff and does not deform.

Rick

Carl Fogel said:

Quoted message said:

The rim deforms very slightly where it rests on the road. This
"dent" makes the bottom few spokes go slacker, and the tension
rises in the immediately adjacent spokes - where the rim bulges -
which keeps the hub in the same place.

Quoted message said:

Quoted message said:

The tension in all the other spokes barely changes, if at all.

Quoted message said:

Er, not to deny anything, but the tension rises in all the other 31
spokes on a 36-spoke calculated projection where 5 spokes are
centered under a loaded hub--see the second column from the left
here:

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

Quoted message said:

None of the 31 spokes increase as much in tension as is lost by the
least active of the 5 spokes under the hub that lose tension.

You aren't doing anyone any favors by emphasizing the minuscule
increases in tension that are not related to hob support but are
caused by the flattening of the arch of the rim. In doing so, the
flat spot spreads the round hoop of the rim ever so slightly (cosine
error) and a commensurately small increase in tension results in the
remainder of the spoke complement. As has been pointed out often, the
sum of the vertical components of these increases (depending on the
number of spokes) is either zero or close to it, there being
discretization with lower spoke counts.

Quoted message said:

This calculation is consistent with [actual] measured spoke strains
of a loaded wheel while rolling:

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

Measuring this in motion is like determining how long it takes for a
rock to fall to earth by measuring its speed by radar and integrating
instead of timing it. There are no dynamics in wheel loadings, all
parts having a response at least 100 times faster than any changes.
This can and should all be done statically.

Quoted message said:

See figure 11--all the other spokes gain tension.

I suppose that is appropriate considering these folks don't have the
book where this is described in more detail that in those pages.

Jobst Brandt
[email hidden]

Mike Causer said:

Quoted message said:

That may be if you fail to define your terms. Those who have read
"the Bicycle Wheel" instead of taking someone else's word for what
it says know that the terms are defined and the reason for using
the metaphor "stand" explained. How is it that this subject
elicits so much energy from the UK, regularly? I can only conclude
that the book is not readily available there so this is all based
on hearsay.

Quoted message said:

Perhaps if Avocet did a deal with a UK publisher to print it here it
might be more widely read? My copy is definitely an import (through
Amazon), and I don't recollect ever seeing it in the cycling section
of any bookshop.

Quoted message said:

David Wilson's 3rd edition of Bicycling Science covers some of the
ground, but it's not what I would call popular reading. OTOH MIT
Press books _are_ easily available in the UK, at reasonable prices
too, *and* it's in the bookshops (in Cambridge anyway).

http://tinyurl.com/4p9r5
http://sheldonbrown.com/harris/books.html#brandt

Jobst Brandt
[email hidden]

Quoted message said:

Carl Fogel said:

Quoted message said:

The rim deforms very slightly where it rests on the road. This
"dent" makes the bottom few spokes go slacker, and the tension
rises in the immediately adjacent spokes - where the rim bulges -
which keeps the hub in the same place.

Quoted message said:

Quoted message said:

The tension in all the other spokes barely changes, if at all.

Quoted message said:

Er, not to deny anything, but the tension rises in all the other 31
spokes on a 36-spoke calculated projection where 5 spokes are
centered under a loaded hub--see the second column from the left
here:

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

Quoted message said:

None of the 31 spokes increase as much in tension as is lost by the
least active of the 5 spokes under the hub that lose tension.

You aren't doing anyone any favors by emphasizing the minuscule
increases in tension that are not related to hob support but are
caused by the flattening of the arch of the rim.

[snip]

Dear Jobst,

Physics isn't about doing you favors.

All the other spokes show an increase in tension.

Carl Fogel

Matt Cahill said:

Quoted message said:

Quoted message said:

> "Two to four spokes near the ground contact point of the average
> wheel support the load at any moment."

Quoted message said:

Quoted message said:

Quoted message said:

It is the case that the greatest change in tension is in the bottom
spokes, far greater than the increase in the other spokes.

Quoted message said:

Quoted message said:

Quoted message said:

You can verify that with a tensionmeter.

Quoted message said:

Quoted message said:

By the way, it's a tensiometer.

http://www.m-w.com/cgi-bin/dictionary?book=Dictionary&va=tensiometer

Quoted message said:

Quoted message said:

Quoted message said:

Conversely, the semantic argument is utterly unproductive.

Quoted message said:

Quoted message said:

That may be if you fail to define your terms. Those who have read
"the Bicycle Wheel" instead of taking someone else's word for what
it says know that the terms are defined and the reason for using
the metaphor "stand" explained. How is it that this subject
elicits so much energy from the UK, regularly? I can only conclude
that the book is not readily available there so this is all based
on hearsay.

Quoted message said:

I have the book. As I understand it... because the spokes are
pre-tensioned, they can support a load without significantly
deforming until a heavy enough load is applied to cause the spokes
to loose all of their pre-tension. In essence pre-tension is
turning the easily bent wire spokes into a fairly rigid column that
can support a load. This seems to me an important idea because it
relates the strength of the wheel to the tension of the spokes. Am
I mis-understanding ?

Quoted message said:

I notice that alot of the people who buy the 'wheels hang' theory
also don't buy the relationship between wheel tension and strength.
After all, if the wheel was truly hanging what role would
pre-tension play?

The book has raised hackles since its introduction, because nearly all
parts of it step on bicycling myth and lore of the past starting with
low tension to avoid spoke failure to time aging of steel spokes. As
you see the concepts still raise tempers, the most recent counter
attack from a certain Trevor (UK) who was rude with accusations and
insults.

http://www.avocet.com/wheelbook/wheelbook.html

Jobst Brandt
[email hidden]

Java Man said:

In article <[email hidden]>, spam.trap100
@btinternet.com says...

Quoted message said:

simple really!

Only if you assume the rim is infinitely stiff and does not deform.

Rick

not at all. I'm looking at the static position after the load is applied.

Vertical equilibrium.

Vector diagram of the hub.

what forces are acting and in which directions?

the spokes below the hub are not doing anything to support the hub.

As I said, simple really.

pk

Carl Fogel said:

Physics isn't about doing you favors.

Dear Mr Barlett:

I urge you to add the statement above to your very next edition of
"Familiar Quotations".

-------------------------------
John Dacey
Business Cycles, Miami, Florida
http://www.businesscycles.com
Since 1983
Our catalog of track equipment: online since 1996
-------------------------------

Carl Fogel said:

Quoted message said:

Quoted message said:

> The rim deforms very slightly where it rests on the road. This
> "dent" makes the bottom few spokes go slacker, and the tension
> rises in the immediately adjacent spokes - where the rim bulges -
> which keeps the hub in the same place.

Quoted message said:

Quoted message said:

Quoted message said:

> The tension in all the other spokes barely changes, if at all.

Quoted message said:

Quoted message said:

Quoted message said:

Er, not to deny anything, but the tension rises in all the other 31
spokes on a 36-spoke calculated projection where 5 spokes are
centered under a loaded hub--see the second column from the left
here:

Quoted message said:

Quoted message said:

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

Quoted message said:

Quoted message said:

Quoted message said:

None of the 31 spokes increase as much in tension as is lost by
the least active of the 5 spokes under the hub that lose tension.

Quoted message said:

Quoted message said:

You aren't doing anyone any favors by emphasizing the minuscule
increases in tension that are not related to hub support but are
caused by the flattening of the arch of the rim.

Quoted message said:

Physics isn't about doing you favors.

Quoted message said:

All the other spokes show an increase in tension.

Don't lose perspective. I'm sure you can detect my keystrokes at your
keyboard if you had sufficiently sensitive sensors and a suitable
filter, but that's not what earthquakes are about... nor does the
increase in tension of the spokes outside the "load affected zone"
have any significance in supporting radial loads (normal bicycle
loads). In this context, mentioning that the upper spokes increase in
tension has classically been cited as proof that this increase is what
keeps the hub from dropping to the road. It is a secondary effect and
without stating that and how small these changes are and that they sum
to zero around the wheel, is the difference between a red herring and
useful information.

Jobst Brandt
[email hidden]

In article <[email hidden]>,
[email hidden] says...

Quoted message said:

Java Man said:

In article <[email hidden]>, spam.trap100
@btinternet.com says...

Quoted message said:

simple really!

Only if you assume the rim is infinitely stiff and does not deform.

Rick

not at all. I'm looking at the static position after the load is applied.

Vertical equilibrium.

Vector diagram of the hub.

what forces are acting and in which directions?

the spokes below the hub are not doing anything to support the hub.

A semantic argument, just as is the methaphorical phrase "the wheel
stands on its spokes". "Support" or not, they help the hub to remain in
an equilibrium position. Try the wheel without them. ;-)

Quoted message said:

As I said, simple really.

Yes, to some.

Rick

PK said:

An you will still be wrong!

The spokes ahowing the most change in tension is not the same thing
as the spkes holding up the load.

draw a vector diagram of the hub,

which spokes act upwards on the hub?

simple really!

The only thing simple about your posts is your logic, PK. However,
it's been explained to you time and again, and there's no further
point in wasting electrons on your intentional thickness.

Quoted message said:

Carl Fogel said:

Quoted message said:

>> The rim deforms very slightly where it rests on the road. This
>> "dent" makes the bottom few spokes go slacker, and the tension
>> rises in the immediately adjacent spokes - where the rim bulges -
>> which keeps the hub in the same place.

Quoted message said:

Quoted message said:

>> The tension in all the other spokes barely changes, if at all.

Quoted message said:

Quoted message said:

> Er, not to deny anything, but the tension rises in all the other 31
> spokes on a 36-spoke calculated projection where 5 spokes are
> centered under a loaded hub--see the second column from the left
> here:

Quoted message said:

Quoted message said:

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

Quoted message said:

Quoted message said:

> None of the 31 spokes increase as much in tension as is lost by
> the least active of the 5 spokes under the hub that lose tension.

Quoted message said:

Quoted message said:

You aren't doing anyone any favors by emphasizing the minuscule
increases in tension that are not related to hub support but are
caused by the flattening of the arch of the rim.

Quoted message said:

Physics isn't about doing you favors.

Quoted message said:

All the other spokes show an increase in tension.

Don't lose perspective. I'm sure you can detect my keystrokes at your
keyboard if you had sufficiently sensitive sensors and a suitable
filter, but that's not what earthquakes are about... nor does the
increase in tension of the spokes outside the "load affected zone"
have any significance in supporting radial loads (normal bicycle
loads). In this context, mentioning that the upper spokes increase in
tension has classically been cited as proof that this increase is what
keeps the hub from dropping to the road. It is a secondary effect and
without stating that and how small these changes are and that they sum
to zero around the wheel, is the difference between a red herring and
useful information.

Jobst Brandt
[email hidden]

Dear Jobst,

All the other spokes.

Carl Fogel

"David Wagner" <[email hidden]> wrote in message
news:[email hidden]...

Quoted message said:

Thank you to all who have replied on this topic. I feel that I should
apologize for repeating a FAQ.

I read the analysis at:

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

I cannot argue with this analysis as a description of what happens
when a
bicycle wheel is loaded in the usual fashiom. As a mathematician, I
certainly believe in the superposition principle--for linear problems.

If I can venture a few comments:

1. The change in tension of each spoke is directly proportional to
the
change in strain on the spoke, which in turn is directly proportional
to
(the deformation in the rim, plus any displacement of the hub relative
to
that point of the rim).

2. Upper spokes show small changes in tension because there is little
deformation in the upper part of the rim, and furthermore there is,
apparently, little displacement of the hub relative to the upper part
of the
rim.

I also read the analysis of forces in the rim at

http://www.achrn.demon.co.uk/astounding/ian/wheel/3c_rim.html

This page only analyzes radial (not axial) forces on the rim, and
bending
forces on the rim. Tangential compressive stresses in the rim are not
analyzed. Those could be interesting, but of course I don't really
know.

The following is a quibble, but I am a bit concerned by the statement
in the
above cited page on rims:

" Total peak stress in the rim from applying 1000N to the wheel is
therefore
1.5 + 19.2 = 20.7 N/mm2."

It is not right to add stresses in two different directions as
scalars. This
should be treated as the norm of a vector.

Both of these are in the same direction. Max bending stress is at the
extreme fiber (furthest from the neutral axis)and is either compressive
or tensile. Peak stress is therefore the sum of the max compressive
bending (19.2) and the max compressive axial (1.5). However, the writer
did go on to explain that these do not occur at the same time.

PH

in article [email hidden], Philip Holman at
[email hidden] wrote on 11/16/04 9:31 PM:

Quoted message said:

"David Wagner" <[email hidden]> wrote in message
news:[email hidden]...

Quoted message said:

Quoted message said:

I also read the analysis of forces in the rim at

http://www.achrn.demon.co.uk/astounding/ian/wheel/3c_rim.html

The following is a quibble, but I am a bit concerned by the statement
in the
above cited page on rims:

" Total peak stress in the rim from applying 1000N to the wheel is
therefore
1.5 + 19.2 = 20.7 N/mm2."

It is not right to add stresses in two different directions as
scalars. This
should be treated as the norm of a vector.

Both of these are in the same direction. Max bending stress is at the
extreme fiber (furthest from the neutral axis)and is either compressive
or tensile. Peak stress is therefore the sum of the max compressive
bending (19.2) and the max compressive axial (1.5). However, the writer
did go on to explain that these do not occur at the same time.

As you describe it, I would think that the bending stress is mostly
tangential rather than radial (that is, radial with respect to the rim,
axial with respect to the spoke). However, as the rim resists bending by
restoring itself to a circle, there will be a radial component. Perhaps that
is the 19.2 figure mentioned in the article. I just gave the section on
bending stress a quick re-read, and I honestly can't tell.

David Wagner