Oddball wheel question

This may be an old chestnut, but I'm curious what people
have to say.

Briefly, Kraig Willett took a 3-spoke rear wheel, cut a
section out of one spoke, rode it around, and asks whether
the wheel stands or hangs from the two remaining spokes:

http://www.biketechreview.com/misc/hangin_hub.htm

My first thought is that it doesn't really address the
question of how a pre-tensioned wheel works, since the two
remaining spokes aren't likely to have any pre-tension and
must be awfully strong and anchored in ways different from
wire-spoke wheels.

(Maybe "struts" would be a better word than "spokes" here?)

I assume that the hub hangs from a very stiff rim when the
struts or spokes are overhead, produces a downward shearing
force when they're off to either side, and stands on the rim
when they're underneath.

If so, when would this maimed wheel be most likely to fail?
With the strut/spokes at the side? Or overhead?

Carl Fogel

writes:

This may be an old chestnut, but I'm curious what people have to
say.

Briefly, Kraig Willett took a 3-spoke rear wheel, cut a section out
of one spoke, rode it around, and asks whether the wheel stands or
hangs from the two remaining spokes:

This is one of those misleading hypothetical questions that almost
seems like it means something, but really doesn't. In a pretensioned
wheel, of course, the wheel would be instantly unrideable when the
spoke is cut. If a Tri-Spoke type wheel, the rim would have to be
incredibly rigid in order for it to be at all rideable.

If so, when would this maimed wheel be most likely to fail? With
the strut/spokes at the side? Or overhead?

In my opinion, when the gap is between the hub and the ground. Of
course, that gap covers 240 degrees of the wheel... but I would think
it would collapse as soon as the contact point is equidistant between
the remaining spokes, depending on how close the load is to the
stiffness limits of the rim.

On Thu, 21 Oct 2004 21:51:30 -0600, wrote:

This may be an old chestnut, but I'm curious what people
have to say.

Briefly, Kraig Willett took a 3-spoke rear wheel, cut a
section out of one spoke, rode it around, and asks whether
the wheel stands or hangs from the two remaining spokes:

http://www.biketechreview.com/misc/hangin_hub.htm

My first thought is that it doesn't really address the
question of how a pre-tensioned wheel works, since the two
remaining spokes aren't likely to have any pre-tension and
must be awfully strong and anchored in ways different from
wire-spoke wheels.

(Maybe "struts" would be a better word than "spokes" here?)

I assume that the hub hangs from a very stiff rim when the
struts or spokes are overhead, produces a downward shearing
force when they're off to either side, and stands on the rim
when they're underneath.

If so, when would this maimed wheel be most likely to fail?
With the strut/spokes at the side? Or overhead?

Rather than going through this Yet Again, might I suggest a bit of
Googling and a trip to whatever library has a copy of Jobst's book?
For a normal spoked bike wheel, if you look at it from a vector force
change standpoint, the answer is that the largest vector change is in
the spoke which most nearly points down, and by a perfectly valid but
counterintuitive engineering principle, this means that the wheel
"stands" on the spoke(s) at the bottom.

In my opinion, your example wheel does not closely model a normal
bicycle wheel since the "spokes" are a part of the rim. Effectively,
this is a disc wheel with holes in it. When a "spoke" is removed, and
the wheel is in the position where there's no downward radial section,
it *appears* that the wheel is "hanging from the spokes", but is it
really? In my opinion, no.
--
Typoes are a feature, not a bug.
Some gardening required to reply via email.
Words processed in a facility that contains nuts.

wrote:

This may be an old chestnut, but I'm curious what people
have to say.

Briefly, Kraig Willett took a 3-spoke rear wheel, cut a
section out of one spoke, rode it around, and asks whether
the wheel stands or hangs from the two remaining spokes:

http://www.biketechreview.com/misc/hangin_hub.htm

My first thought is that it doesn't really address the
question of how a pre-tensioned wheel works, since the two
remaining spokes aren't likely to have any pre-tension and
must be awfully strong and anchored in ways different from
wire-spoke wheels.

(Maybe "struts" would be a better word than "spokes" here?)

If one were wondering about how wagon wheels work, this would probably
be a good test. If one wonders about how a spoked bicycle wheel
works... try cutting out a 12 adjacent spokes from a 36 spoke wheel
and see how it goes...

Mark Hickey
Habanero Cycles
http://www.habcycles.com
Home of the $695 ti frame

On Thu, 21 Oct 2004 21:45:47 -0700, Mark Hickey
wrote:

wrote:

This may be an old chestnut, but I'm curious what people
have to say.

Briefly, Kraig Willett took a 3-spoke rear wheel, cut a
section out of one spoke, rode it around, and asks whether
the wheel stands or hangs from the two remaining spokes:

http://www.biketechreview.com/misc/hangin_hub.htm

My first thought is that it doesn't really address the
question of how a pre-tensioned wheel works, since the two
remaining spokes aren't likely to have any pre-tension and
must be awfully strong and anchored in ways different from
wire-spoke wheels.

(Maybe "struts" would be a better word than "spokes" here?)

If one were wondering about how wagon wheels work, this would probably
be a good test. If one wonders about how a spoked bicycle wheel
works... try cutting out a 12 adjacent spokes from a 36 spoke wheel
and see how it goes...

Mark Hickey
Habanero Cycles
http://www.habcycles.com
Home of the $695 ti frame

Dear Mark,

I don't think that it's even really like a wagon-wheel.

As I understand oldd wooden wheels, the spokes are roughly
wooden dowels driven into holes in the hub and the middle of
each rim section, with a heated iron band shrunk into place
around the wooden rim to give enough compression to hold
things together.

I think that if there were only three such spokes, such a
dowel-style wheel would fall apart after a turn or two if
one spoke were removed, depending on how tightly the two
remaining spokes were shoved into the holes--assuming that
it would even hold its shape long enough to turn.

The Willett wheel strikes more as being the solid disk with
some holes in it suggested by Werehatrack--big holes,
admittedly, but with still enough rigid material left to
make a disk.

I'm still wondering in what position it would be most likely
to fail with the two remaining struts forming a 120-degree
angle.

Carl Fogel

carlfogel wrote: (clip) I'm still wondering in what position it would be
most likely to fail with the two remaining struts forming a 120-degree
angle.
^^^^^^^^^^^^^^^^
Let's do this thought experiment: Reduce the angle between the remaining
spokes and visualize the behavior of the wheel. In the limit, the angle is
reduced to the point where you have one spoke. So, let's imagine that we
have cut out two spokes, and have one left. Now run the wheel under load,
and increase the load until it starts to fail. Even without a stress
analysis, I think it is obvious that the weakest position is with the spoke
in a horizontal position, so that is where it will fail. I reason that the
two remaining spokes will fail when their axis of symmetry is
horizontal--IOW, when the axis of the missing spoke is horizontal.

As others have pointed out, this bears no relation to wire spokes, which
have no load bearing capacity except in tension.

Carl Fogel writes:

This may be an old chestnut, but I'm curious what people have to
say.

An ancient one.

Briefly, Kraig Willett took a 3-spoke rear wheel, cut a section out
of one spoke, rode it around, and asks whether the wheel stands or
hangs from the two remaining spokes:

http://www.biketechreview.com/misc/hangin_hub.htm

My first thought is that it doesn't really address the question of
how a pre-tensioned wheel works, since the two remaining spokes
aren't likely to have any pre-tension and must be awfully strong and
anchored in ways different from wire-spoke wheels.

(Maybe "struts" would be a better word than "spokes" here?)

I assume that the hub hangs from a very stiff rim when the struts or
spokes are overhead, produces a downward shearing force when they're
off to either side, and stands on the rim when they're underneath.

If so, when would this maimed wheel be most likely to fail? With
the strut/spokes at the side? Or overhead?

That depends on which is stronger, the spokes or the rim. In either
case, you don't have a complete wheel. If the tri-spoke supports a
rider with only two spokes, then it must be overdesigned. However, I
doubt that anyone would consider riding such a wheel at speed over any
real road. There are also wheels with one spoke much like the old
Girling brake logo with an arm reaching out to grasp a ring shaped
disc brake. These are also used as steering wheels on Citro?n DS's.

http://www.id-ds.com/Pages/Citroen/DS.Barthes.html

So what is it that you are pursuing with this subject? Knowing how
well you search the archives, you must have noticed that this has been
beaten to death for many years. In fact it has been an old chestnut
since "the Bicycle Wheel" reached the bookshelves.

Jobst Brandt

On Fri, 22 Oct 2004 06:44:22 GMT, "Leo Lichtman"
wrote:


carlfogel wrote: (clip) I'm still wondering in what position it would be
most likely to fail with the two remaining struts forming a 120-degree
angle.
^^^^^^^^^^^^^^^^
Let's do this thought experiment: Reduce the angle between the remaining
spokes and visualize the behavior of the wheel. In the limit, the angle is
reduced to the point where you have one spoke. So, let's imagine that we
have cut out two spokes, and have one left. Now run the wheel under load,
and increase the load until it starts to fail. Even without a stress
analysis, I think it is obvious that the weakest position is with the spoke
in a horizontal position, so that is where it will fail. I reason that the
two remaining spokes will fail when their axis of symmetry is
horizontal--IOW, when the axis of the missing spoke is horizontal.

As others have pointed out, this bears no relation to wire spokes, which
have no load bearing capacity except in tension.


Dear Leo,


I think that you're right about a single-spoke/strut being
most likely to fail when horizontal--it would bend down.

But I'm wondering about when two spoke/struts 120 degrees
apart will fail.

And with two spoke/struts, both are in kinda-sorta tension
when overhead, each angling down toward the hub at 60
degrees:

\/

When they're on the side, one is in the same kinda-sorta
tension at 60 degrees (I think), but the other has moved to
being in kinda-sorta compression:

\
/

I expect that these spoke-struts are going to be stronger in
compression than in tension, but I'm not sure.

Nor am I all that sure about whether the damned things are
in tension, compression, shear, or what. And how the rim
would distort is another question.

Carl Fogel

On Fri, 22 Oct 2004 07:12:10 GMT,
wrote:

Carl Fogel writes:

This may be an old chestnut, but I'm curious what people have to
say.

An ancient one.

Briefly, Kraig Willett took a 3-spoke rear wheel, cut a section out
of one spoke, rode it around, and asks whether the wheel stands or
hangs from the two remaining spokes:

http://www.biketechreview.com/misc/hangin_hub.htm

My first thought is that it doesn't really address the question of
how a pre-tensioned wheel works, since the two remaining spokes
aren't likely to have any pre-tension and must be awfully strong and
anchored in ways different from wire-spoke wheels.

(Maybe "struts" would be a better word than "spokes" here?)

I assume that the hub hangs from a very stiff rim when the struts or
spokes are overhead, produces a downward shearing force when they're
off to either side, and stands on the rim when they're underneath.

If so, when would this maimed wheel be most likely to fail? With
the strut/spokes at the side? Or overhead?

That depends on which is stronger, the spokes or the rim. In either
case, you don't have a complete wheel. If the tri-spoke supports a
rider with only two spokes, then it must be overdesigned. However, I
doubt that anyone would consider riding such a wheel at speed over any
real road. There are also wheels with one spoke much like the old
Girling brake logo with an arm reaching out to grasp a ring shaped
disc brake. These are also used as steering wheels on Citro?n DS's.

http://www.id-ds.com/Pages/Citroen/DS.Barthes.html

So what is it that you are pursuing with this subject? Knowing how
well you search the archives, you must have noticed that this has been
beaten to death for many years. In fact it has been an old chestnut
since "the Bicycle Wheel" reached the bookshelves.

Jobst Brandt


Dear Jobst,

What I was pursuing was whether I understood things
correctly when I thought that Willett was wrong (that's
often why we post questions here) and how the weird-looking
thing would fail.

The Citroen steering wheel is a nice bonus.

So how would it fail if the spokes were stronger than the
rim? When the two spokes were overhead, or to one side? Or
what? And what part would break?

And how would it fail if the rim were stronger than the
spokes? Would the rim break in the middle between the
spokes? Just on either side of one spoke or the other? Way
out opposite the two spokes? Or what?

Carl Fogel

Werehatrack wrote:

Rather than going through this Yet Again, might I suggest a bit of
Googling and a trip to whatever library has a copy of Jobst's book?
For a normal spoked bike wheel, if you look at it from a vector force
change standpoint, the answer is that the largest vector change is in
the spoke which most nearly points down, and by a perfectly valid but
counterintuitive engineering principle, this means that the wheel
"stands" on the spoke(s) at the bottom.


what force is exerted by the lower spoke(s) at the point where they are
attached to the hub?



The load is supported by the rim.

The load is transferred to the rim by the spokes.

The rim distortion as it supports the load results in reduced tension in
the lower few spokes.

To ask "hang or stand?" is an irrelvant question as the answer is "neither!"
: THAT is the truly counerintuitive point about the pre-tensioned spoked
wheel!

pk