A physicist's question about tensioning a wheel

Sergio SERVADIO said:

The higher the spokes' tension the stiffer the wheel, of course. Why so?

The data I know of do not support that assumption.

Take a few quick measurements. Here's one way: sheldonbrown.comindex.htmOpen ↗

First, I hope you can suggest a way to get better repeatability in measuring the stiffness of
wheels. On this site sheldonbrown.comindex.htmOpen ↗ there appears to be some
variation, up to about 0.007". Maybe that is part of the roughness of the rim side wall where the
dial indicator takes the reading?

Second, a bit further up the page at sheldonbrown.comindex.htmOpen ↗ the
wheel appears to become slightly stiffer with decreasing spoke tension, the opposite of your
assumption. But I don't believe those measurements reflect any significant trend. Is the variation
in that data supported by the reported variation in the measurements at #3 above? I don't know how
to determine that.

My strategy: I don't consider wheel stiffness while tensioning; I make spoke tension high for good
wheel strength.

Sergio SERVADIO said:

The higher the spokes' tension the stiffer the wheel, of course.

Bracing angle of the spokes. However, bicycle wheels are not very stiff laterally and are very stiff
radially. This is OK because the wheels rarely see a significant lateral load.

Sergio SERVADIO said:

The higher the spokes' tension the stiffer the wheel, of course. Why so?

By turning the nipples a little bit more we effectively shorten the rest length of the spokes, not
changing a bit their elastic constant . Now, a change of anyone of the rest lengths of an elastic
system does not change at all its elastic constant/s, but changes only its rest configuration when
under no load [the elastic quadratic coefficient does not change]. So, by turning nipples a bit
more or a bit less, barring the possibility of having spokes go slack, the wheel should remain
just as stiff.

So, the questions. Am I totally wrong? Or, is it that we are exploiting the non-elasticity [non
linear in fact] of some component of the wheel? Which one: the spokes or the rim?

I don't know, but I'd like to add one completely surprising observation. Among the bikes in this
household is a twenty year old Raleigh Royale with 27" wheels which, until this year, hadn't been
ridden for about six years (it was my sister's; she died). The rear wheel is original. All the
spokes are quite noticably slack - you can take any individual spoke and rattle it. But the wheel is
reasonably true - true enough not to rub on the brakes or interfere with the mudguard. I'm so
surprised at this that I've left it that way to see what will happen, and what has happened is...
precisely nothing. It's been ridden for over 400 miles over the past three months in this state, and
the wheel is still adequately true. Sooner or later of course I'm going to have to take it out and
tension it because apart from anything else it just doesn't look right... but I'm amazed that it has
remained usable.

Twenty years ago it was a reasonable wheel; the Royale was one of the more upmarket Raleighs (531c
tubing, etc). It's an aluminium rim marked 'WEINMANN Made in Belgium'. It's not a specially strong
or stiff rim.

--
[email hidden] (Simon Brooke) jasmine.org.uk~simonOpen ↗

;; Life would be much easier if I had the source code.

dianne_1234 said:

Sergio SERVADIO said:

The higher the spokes' tension the stiffer the wheel, of course. Why so?

The data I know of do not support that assumption.

Well, thank you. You are saying that I had a wrong assumption in the back of my mind. One of those I
must have picked up without thinking too much.

No wonder I could not 'explain' why it should be so. I tell you, I feel elated!

Thanks again

Sergio Pisa

On Sat, 03 Jan 2004 18:05:03 GMT, Simon Brooke <[email hidden]>

Quoted message said:

Sergio SERVADIO said:

The higher the spokes' tension the stiffer the wheel, of course. Why so?

By turning the nipples a little bit more we effectively shorten the rest length of the spokes,
not changing a bit their elastic constant . Now, a change of anyone of the rest lengths of an
elastic system does not change at all its elastic constant/s, but changes only its rest
configuration when under no load [the elastic quadratic coefficient does not change]. So, by
turning nipples a bit more or a bit less, barring the possibility of having spokes go slack, the
wheel should remain just as stiff.

So, the questions. Am I totally wrong? Or, is it that we are exploiting the non-elasticity [non
linear in fact] of some component of the wheel? Which one: the spokes or the rim?

I don't know, but I'd like to add one completely surprising observation. Among the bikes in this
household is a twenty year old Raleigh Royale with 27" wheels which, until this year, hadn't been
ridden for about six years (it was my sister's; she died). The rear wheel is original. All the
spokes are quite noticably slack - you can take any individual spoke and rattle it. But the wheel
is reasonably true - true enough not to rub on the brakes or interfere with the mudguard. I'm so
surprised at this that I've left it that way to see what will happen, and what has happened is...
precisely nothing. It's been ridden for over 400 miles over the past three months in this state,
and the wheel is still adequately true. Sooner or later of course I'm going to have to take it out
and tension it because apart from anything else it just doesn't look right... but I'm amazed that
it has remained usable.

Since you have argued here extensively about how how ridiculous the notion is that the bottom spokes
compress and carry almost all of the load, your loosely spoked wheel must be quite strong by your
reckoning (from the point of view of tensile overload in the upper spokes) and indeed you are here
saying it works fine.

Go with it!

Simon Brooke said:

I'd like to add one completely surprising observation. Among the bikes in this household is a
twenty year old Raleigh Royale with 27" wheels which, until this year, hadn't been ridden for
about six years (it was my sister's; she died). The rear wheel is original. All the spokes are
quite noticably slack - you can take any individual spoke and rattle it. But the wheel is
reasonably true - true enough not to rub on the brakes or interfere with the mudguard. I'm so
surprised at this that I've left it that way to see what will happen, and what has happened is...
precisely nothing. It's been ridden for over 400 miles over the past three months in this state,
and the wheel is still adequately true. Sooner or later of course I'm going to have to take it out
and tension it because apart from anything else it just doesn't look right... but I'm amazed that
it has remained usable.

You're likely to get broken spokes through metal fatigue if you continue with them slack.

~PB

Quoth Simon Brooke:

Quoted message said:

I'd like to add one completely surprising observation. Among the bikes in this household is a
twenty year old Raleigh Royale with 27" wheels which, until this year, hadn't been ridden for
about six years (it was my sister's; she died). The rear wheel is original. All the spokes are
quite noticably slack - you can take any individual spoke and rattle it. But the wheel is
reasonably true - true enough not to rub on the brakes or interfere with the mudguard. I'm so
surprised at this that I've left it that way to see what will happen, and what has happened is...
precisely nothing. It's been ridden for over 400 miles over the past three months in this state,
and the wheel is still adequately true. Sooner or later of course I'm going to have to take it
out and tension it because apart from anything else it just doesn't look right... but I'm amazed
that it has remained usable.

Twenty years ago it was a reasonable wheel; the Royale was one of the more upmarket Raleighs
(531c tubing, etc). It's an aluminium rim marked 'WEINMANN Made in Belgium'. It's not a specially
strong or stiff rim.

It probably has carbon-steel spokes, as did most bikes back then. Although carbon-steel spokes are
not as strong as stainless (and prone to rusting) they are less subject to fatigue than stainless
spokes are.

Loosely spoked wheels were the norm on production bikes back then, and manufacturers relied on using
plenty of spokes and fairly (or very) rigid rims.

Your wheel may give good service for a long time if used with care, but the loose spokes will make
it less resistant to getting dented inward, by potholes, kerbs and the like. If you manage to avoid
such road hazards, it should be OK.

Sheldon "Stainless" Brown +--------------------------------------------+
| Life is what happens to you, | while you're busy making other plans. | --John Lennon |
+--------------------------------------------+ Harris Cyclery, West Newton, Massachusetts Phone 617-244-
9772 FAX 617-244-1041 harriscyclery.comharriscyclery.comOpen ↗ Hard-to-find parts shipped Worldwide
captainbike.comcaptainbike.comOpen ↗ sheldonbrown.comsheldonbrown.comOpen ↗

Pete Biggs said:

Quoted message said:

I'd like to add one completely surprising observation. Among the bikes in this household is a
twenty year old Raleigh Royale with 27" wheels which, until this year, hadn't been ridden for
about six years (it was my sister's; she died). The rear wheel is original. All the spokes are
quite noticeably slack - you can take any individual spoke and rattle it. But the wheel is
reasonably true - true enough not to rub on the brakes or interfere with the mudguard. I'm so
surprised at this that I've left it that way to see what will happen, and what has happened is...
precisely nothing. It's been ridden for over 400 miles over the past three months in this state,
and the wheel is still adequately true. Sooner or later of course I'm going to have to take it
out and tension it because apart from anything else it just doesn't look right... but I'm amazed
that it has remained usable.

Quoted message said:

You're likely to get broken spokes through metal fatigue if you continue with them slack.

I read this admonition now and then and have not heard an explanation of how slack spokes cause
fatigue failures. More likely loose spokes will cause wheel collapse at some inopportune moment
where an awkward side load is encountered. I have ridden with light weight riders whose spokes
rattled for many miles before the noise got to the point that I trued and tensioned his wheel. He
was a good hill climber so I dod not have theoption of riding off ahead where I didn''t need to
listen to it. These wheels dis not suffer form the looseness although other that I observed
collpased.

Jobst Brandt [email hidden]

Simon Brooke said:

All the spokes are quite noticeably slack - you can take any individual spoke and rattle it.

An interesting observation that, Simon. I take it you mean when the bike was unloaded all the
spokes rattled.

Worth repeating.

Quoted message said:

All the spokes are quite noticeably slack - you can take any individual spoke and rattle it.

How do you suppose the load on the hub was supported when the slack spokes were at the bottom?

paul

In article <[email hidden]>, "Paul" <[email hidden]>

Quoted message said:

Quoted message said:

All the spokes are quite noticeably slack - you can take any individual spoke and rattle it.

An interesting observation that, Simon. I take it you mean when the bike was unloaded all the
spokes rattled.

Worth repeating.

Quoted message said:

All the spokes are quite noticeably slack - you can take any individual spoke and rattle it.

How do you suppose the load on the hub was supported when the slack spokes were at the bottom?

<plonk!

Simon Brooke said:

All the spokes are quite noticeably slack - you can take any individual spoke and rattle it.

Next time get on the bicycle and have someone else test which spokes are slack. You'll discover that
most of the spokes are tight when you put a load on the wheel. Only the ones near the bottom will be
slack, which of course means you don't have a laterally stable wheel. It can wiggle from side to
side and, if you give it a side load, will collapse. This is not what is known as a "whole" wheel.
It's on the verge of collapse and, as you say, is not a tensioned spoked wheel. Don't expect it to
respond to loads the way a tensioned wheel does.

Jobst Brandt [email hidden]

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

Quoted message said:

The higher the spokes' tension the stiffer the wheel, of course. Why so?

maybe not. physicist? remember that spring thing?: hang a weight 'W' on a spring, it extends 'x'.
hang a 2nd W on, it extends another 'x'. the 1st W, preload if you will, don't change the response
from the 2nd W.

Paul said:

Simon Brooke said:

All the spokes are quite noticeably slack - you can take any individual spoke and rattle it.

An interesting observation that, Simon. I take it you mean when the bike was unloaded all the
spokes rattled.

Yes.

Quoted message said:

Worth repeating.

Quoted message said:

All the spokes are quite noticeably slack - you can take any individual spoke and rattle it.

How do you suppose the load on the hub was supported when the slack spokes were at the bottom?

Why, it was standing on them of course. The Great Jobst has said so, how can any further comment be
other than superfluous? If there is any difference between reality and the pronouncements of the
Great Jobst, it is always reality which is wrong.

--
[email hidden] (Simon Brooke) jasmine.org.uk~simonOpen ↗ ;; gif ye hes forget our auld
plane Scottis quhilk your mother lerit you, ;; in tymes cuming I sall wryte to you my mind in Latin,
for I am nocht ;; acquyntit with your Southeron ;; Letter frae Ninian Winyet tae John Knox datit 27t
October 1563

Simon Brooke wrote: <snip>

Quoted message said:

I don't know, but I'd like to add one completely surprising observation. Among the bikes in this
household is a twenty year old Raleigh Royale with 27" wheels which, until this year, hadn't been
ridden for about six years (it was my sister's; she died). The rear wheel is original. All the
spokes are quite noticably slack - you can take any individual spoke and rattle it. But the wheel
is reasonably true - true enough not to rub on the brakes or interfere with the mudguard. I'm so
surprised at this that I've left it that way to see what will happen, and what has happened is...
precisely nothing. It's been ridden for over 400 miles over the past three months in this state,
and the wheel is still adequately true. Sooner or later of course I'm going to have to take it out
and tension it because apart from anything else it just doesn't look right... but I'm amazed that
it has remained usable.

my mother used to go shopping on a bike like that and would come home /loaded/ with groceries. dare
i say it, she was no bantam weight either. this bike used to get ridden most days of the week. loose
spokes, just like you say.

then one day, just as she was pulling up in front of our house, the rear wheel started to collapse.
it was a bit like watching a mime comedian walking down an imaginary staircase - she just sunk lower
& lower as she rolled along with more & more spokes giving up the ghost. father got her another
wheel but she never rode it again.

as i recall, the wheel was never superbly true, but was not bad either. the spokes would kind of
rattle. considering the use it had, i think it had lasted quite well. 50's vintage?

jb

Sergio SERVADIO said:

So, the questions. Am I totally wrong? Or, is it that we are exploiting the non-elasticity [non
linear in fact] of some component of the wheel? Which one: the spokes or the rim?

The tensioning creates stiffness side-to-side by preventing even the slackest spoke from going
slack. The spokes work in pairs side to side, the one taking up tension and the other losing it, as
a side-to-side restoring force. Once one stops losing tension because it's finally loose, additional
restoring force is partly missing.
--
Ron Hardin [email hidden]

On the internet, nobody knows you're a jerk.

Sheldon Brown wrote: <snip>

Quoted message said:

It probably has carbon-steel spokes, as did most bikes back then. Although carbon-steel spokes are
not as strong as stainless (and prone to rusting) they are less subject to fatigue than stainless
spokes are.

the carbon alloy steel spokes were galvanized most likely. flashy [literally] ones were
chrome plated.

technically, carbon alloy steel wire is usually stronger than stainless. it's still used in steel
rope where strength [&/or price] outweighs weather considerations.

carbon steel spokes /were/ less prone to fatigue. modern stainless steels are significantly better
than they used to be and now the two are roughly comparable. high strength carbon alloy steels do
not typically have a fatigue endurance limit - it's just that it's been possible to make "cleaner"
carbon alloy steels [cheaper] longer than has been possible for stainless.

if ever you travel to san francisco, there are two pieces of interesting wire that you must see:

one is at the golden gate bridge. there is a section of the main span rope cut open for inspection
at the visitor center. interesting un-twisted strand design. high strength carbon alloy steel.

the other is the crowd barrier rope at the cable car turnaround on powell & market. it's a piece of
actual cable car traction rope. unlike all the [wire] rope you normally see that is twisted to make
the exterior strands run axially, this one is twisted to make the exterior stranding as close to
perpendicular as possible. this is to give maximum possible friction for the cable car's rope
clutching mechanism as it goes up the hills. again, carbon alloy steel.

/utterly/ useless trivia, but thrillingly geeky!

jb

Jim Beam said:

Quoted message said:

I don't know, but I'd like to add one completely surprising observation. Among the bikes in this
household is a twenty year old Raleigh Royale with 27" wheels which, until this year, hadn't been
ridden for about six years (it was my sister's; she died). The rear wheel is original. All the
spokes are quite noticeably slack - you can take any individual spoke and rattle it. But the
wheel is reasonably true - true enough not to rub on the brakes or interfere with the mudguard.
I'm so surprised at this that I've left it that way to see what will happen, and what has
happened is... precisely nothing. It's been ridden for over 400 miles over the past three months
in this state, and the wheel is still adequately true. Sooner or later of course I'm going to
have to take it out and tension it because apart from anything else it just doesn't look right...
but I'm amazed that it has remained usable.

Quoted message said:

My mother used to go shopping on a bike like that and would come home /loaded/ with groceries.
Dare I say it, she was no bantam weight either. This bike used to get ridden most days of the
week. Loose spokes, just like you say.

Quoted message said:

Then one day, just as she was pulling up in front of our house, the rear wheel started to
collapse. It was a bit like watching a mime comedian walking down an imaginary staircase - she
just sunk lower & lower as she rolled along with more & more spokes giving up the ghost. Father
got her another wheel but she never rode it again.

That's a nice story but I think you are reconstructing the event from imagination. Wheels cannot
slowly sink to a lower rolling diameter. The failure mode is lateral collapse and that jams the
wheel in the frame so it won't turn. It makes a nice story but it didn't happen.

Quoted message said:

As I recall, the wheel was never superbly true, but was not bad either. The spokes would kind of
rattle. Considering the use it had, I think it had lasted quite well. 50's vintage?

I suppose the upshot is that "we don't need no steenkin tension in our wheels". I see no other
reason for these testimonials, phony as they sound to wheelbuilders. Loose wheels can be ridden but
it isn't a reasonable thing to do if you know the wheel is rattlingly loose.

That such a wheel is true is an old story, something on which inept wheel builders rely, because
they don't know how to true a wheel once the spokes are tight enough to overcome the original
trueness of a new rim. New rims are true and remain that way in the absence of spoke tension. This
should not be amazing. What is amazing is that some people ride so timidly that their wheels rarely
see much stress for which they would need to demonstrate strength, strength that depends primarily
on spoke tension, if there is any.

Jobst Brandt [email hidden]

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

Quoted message said:

Paul said:

Simon Brooke said:

All the spokes are quite noticeably slack - you can take any individual spoke and rattle it.

An interesting observation that, Simon. I take it you mean when the

bike was

Quoted message said:

Quoted message said:

unloaded all the spokes rattled.

Yes.

Quoted message said:

Worth repeating.

Quoted message said:

All the spokes are quite noticeably slack - you can take any individual spoke and rattle it.

How do you suppose the load on the hub was supported when the slack

spokes

Quoted message said:

Quoted message said:

were at the bottom?

Why, it was standing on them of course. The Great Jobst has said so, how can any further comment
be other than superfluous? If there is any difference between reality and the pronouncements of
the Great Jobst, it is always reality which is wrong.

"The power of accurate observation is called cynicism by those who have not got it." - G. B. Shaw

Phil Holman

Jim Beam said:

Quoted message said:

It probably has carbon-steel spokes, as did most bikes back then. Although carbon-steel spokes
are not as strong as stainless (and prone to rusting) they are less subject to fatigue than
stainless spokes are.

Quoted message said:

The carbon alloy steel spokes were galvanized most likely. Flashy [literally] ones were
chrome plated.

Quoted message said:

Technically, carbon alloy steel wire is usually stronger than stainless. It's still used in steel
rope where strength [&/or price] outweighs weather considerations.

If exposed to weather, such cables are galvanized and often painted to protect them from rusting.
This is mostly a matter of cost, stainless cables being far more expensive than carbon steel.

Quoted message said:

Carbon steel spokes /were/ less prone to fatigue. Modern stainless steels are significantly better
than they used to be and now the two are roughly comparable. High strength carbon alloy steels do
not typically have a fatigue endurance limit - it's just that it's been possible to make "cleaner"
carbon alloy steels [cheaper] longer than has been possible for stainless.

Quoted message said:

If ever you travel to San Francisco, there are two pieces of interesting wire that you must see:

Quoted message said:

One is at the golden gate bridge. There is a section of the main span rope cut open for inspection
at the visitor center. Interesting un-twisted strand design. High strength carbon alloy steel.

You will notice that these "cables" are completely encased in a waterproof steel jacket and are in
real life pumped solidly full of grease like preservative... as they are on most suspension bridges.
The suspenders on the GG Bridge are exposed strands but are helically wound and are galvanized and
painted with the traditional red paint of that bridge. What is less evident to the casual observer
is that because the bridge lives in fog and salt spray, it does not have exposed riveted lattice-
work as other bridges around the bay. It's towers are enclosed so the structural elements within the
towers can be kept dry and clean.

Quoted message said:

The other is the crowd barrier rope at the cable car turnaround on Powell & Market. It's a piece
of actual cable car traction rope. Unlike all the [wire] rope you normally see that is twisted to
make the exterior strands run axially, this one is twisted to make the exterior stranding as close
to perpendicular as possible. This is to give maximum possible friction for the cable car's rope
clutching mechanism as it goes up the hills. Again, carbon alloy steel.

Since these cables bend around pulleys and curves, they must be helically wound or they would break
immediately. They are made this way for the same reason control cables on bicycles are helically
wound... so they will have uniform stress in all strands when bending around curves. Cable car cable
has a special layer of external friction strands that are smooth and rectangular, like the ones for
aerial trams where cables are sued as rails on which the tram rides. This is done to reduce wear
that would occur if the outer strands had a round cross section or even themselves made of strands,
as are old Campagnolo bar-end shift cables.

Quoted message said:

/utterly/ useless trivia, but thrillingly geeky!

cablecarmuseum.comAnat.htmlOpen ↗

Don't pass along myth and lore.

Jobst Brandt [email hidden]